Appendix: a Selection of Documents1

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APPENDIX: A SELECTION OF DOCUMENTS1

1) A letter from Felix Klein to Heinrich von Mühler, the Prussian Minister of Religious, Educational, and Medical Affairs (Minister of Culture).2

Your Excellency, Düsseldorf – December 19, 1870 In a request dated March 7th of this year, I took the liberty of asking for diplomatic recommendations to travel to France and England for the purpose of undertaking a scientific trip. At the same time, I had offered to submit reports on the conditions of mathematics in these countries upon my return. On March 26th, I was fortunate enough to receive a reply from your Excellency (U 7737) to the effect that the diplomatic recommendations in question had been granted to me, and that your Excellency would be pleased to receive reports on the present state of French and English mathematics. Under the prevailing conditions, unfortunately, the trip could not be underta- ken in the way that I intended. My stay in Paris, where I had arrived on April 19th, was suddenly interrupted by the declaration of war on July 16th. I rushed home (Düsseldorf) and, because I was deemed unfit for military service at the moment by the relevant authorities, I joined an association for voluntary medical care, which had meanwhile been established in Bonn. As a member of this association, I spent the period from August 16th to October 2nd, when I was discharged to return home on account of my poor health, in the theater of war. Having only recently recovered, I did not want to make the trip to England because of the time that I had lost. Rather, I have already applied to habilitate in Göttingen and become a Privatdozent of mathematics there, and I intend to move there at the New Year. Given that it is not possible for me to send you reports on French and English mathematics in the way that I intended, I would at least like to enclose a copy of a short report on French mathematics, which I composed together with one of my student friends (Dr. Lie from Christiania), to demonstrate that I had worked along these lines during my stay in Paris. We had prepared this report for the mathematical [student] union at the University of Berlin and had sent it to this organization on July 7th. At the same time, allow me to enclose an article, “Sur une certaine famille de courbes et de surfaces,” which my friend Lie and I coauthored. We presented this work to the Académie des Sciences in two sessions, on the 6th and 13th of June, and the Académie published it in its Comptes Rendus. By choosing this publica-

1 The original German documents are published in TOBIES 2019, pp. 495–524. 2 [Stabi] Sammlung Darmstaedter. See also Section 2.6.3.

594 Appendix: A Selection of Documents tion venue, we hoped to gain deeper insight into the conditions there and to become personally acquainted with a large number of French mathematicians, and we succeeded in doing so. Finally, allow me to add that we obtained further results – “Ueber die Haupt- tangenten-Curven der Kummer’schen Fläche vierten Grades mit 16 Knotenpunk- ten” [On the Main Tangent Curves of the Fourth-Degree Kummer Surface with 16 Nodal Points] – and we recently informed Professor Kummer privately about them. At his request, we submitted this work to the Academy of Sciences in Ber- lin, which will publish it in its monthly reports with the date of December 15th. By expressing my deepest thanks to your Excellency for your friendly approval of my initial request and by asking for more of your kindness in the future, I remain your Excellency’s most respectfully devoted Dr. Felix Klein.

2) An application submitted by Felix Klein to the Academic Senate of the Univer- sity of Erlangen for funding to improve the collection of the University Library’s mathematical section (November 15, 1872).3

Royal Academic Senate! For the purposes of a mathematician, a small library may be sufficient, but it must be entirely at his disposal, for he must constantly refer to it in the interests of his research and teaching. The mathematical section of the University Library here, however, is unfortunately not in a state that meets even the most modest re- quirements. Allow me to begin by briefly explaining its main lacunae to the Royal Senate. The so-called mathematical section of the University Library consists of ap- proximately 1,200 volumes. A great majority of these, however, is utterly worthless for today’s university purposes because they pertain to engineering, architecture, etc. The smaller minority of genuinely mathematical and related works was not collected according to a uniform principle; rather, chance has played an ever-shifting role in these acquisitions, so that, besides the several works that are worthy of attention, there are also almost unbelievable gaps. Of the works by older authors, for example, the writings of Galileo and New- ton are available almost in their entirety, but the library has only the last three volumes of the new complete edition of Kepler’s works, and it lacks the most important items in its collection of works by Huygens, Euler, and Lagrange. Regarding the collection of mathematical journals, the German ones (to the extent that they should be considered) are all available, but the foreign journals are entirely lacking. This is all the more regrettable because mathematics is a tho- roughly international science, and the progress of a productive mathematician is considerably hindered without him having a universal overview of the findings of others at the same time. In light of the burden that the ongoing acquisition of an

3 [UA Erlangen] Ph. Th. I Pos. 20 V, No. 8. On the context of this application, see Section 3.3. Appendix: A Selection of Documents 595 additional journal represents for the library’s budget, however, I believe that I should limit my requests. My only proposal is that it should subscribe to a French journal which contains up-to-date reports on recent publications: the Bulletin des sciences mathématiques et astronomiques, edited by Darboux. Some time ago, a number of astronomical journals had also been acquired. With the sole exception of the Annalen published by the observatory in Munich, all of them break off at different times without any apparent reason. For example, complete holdings of the Berliner [Astronomisches] Jahrbuch exist from its beginning in 1776 to 1861. I suggest that the missing volumes should be purchased and that the subscription to this Jahrbuch should be renewed. As far as recent books are concerned, geometry is relatively the best-represented of the mathematical disciplines, given that a preference for geometry has always been cultivated in Erlangen. Yet it is far from the level of completeness that I would hope for it to achieve over time; in particular, the collection lacks certain handbooks that seem to be suited for providing an introduction to the special study of geometry. Other branches of mathematics are in part almost entirely unrepresented, and these are hardly unimportant. On mechanics, for example, there is nothing aside from Poisson’s excellent book; likewise, the most important new works on differential and integral calculus are also lacking; there is nothing to be found on mathematical physics, unless there happens to be something useful in the physics section. In these disciplines, it is necessary to create adequate conditions by filling in the discernible gaps, so that the most necessary items are available – failing which constructive instruction is not conceivable at all. I therefore take the liberty of requesting the Royal Academic Senate to apply to the highest authority [the Bavarian Ministry of Culture] for a sum of 350 Gul- den to be allotted from the University’s surplus funds for the purpose of completing the mathematical section of the University Library on the basis of an enclosed cost estimate, the individual items of which are justified in the explanations above. Respectfully and with devotion to the Royal Academic Senate, Felix Klein Professor of Mathematics4

4 Dean Eugen Lommel, a professor of physics known today for the Lommel function and the Lommel differential equation, forwarded Klein’s application with an expert opinion to the Bavarian Ministry of Culture, which granted his request for 350 Gulden ([UA Erlangen] Ph. Th, I. Pos. 20 V. No. 8). – Klein’s abbreviated book titles list (see below) is translated into English; “G” designates a book by a German author or a translation into German; for example: L. Cremona, Einleitung in eine geometrische Theorie der ebenen Curven (Greifswald: Koch, 1865); Poinsot’s Elemente der Statik, als Lehrbuch für den öffentlichen Unterricht und zum Selbststudium (Berlin: Rücker, 1835); Duhamel, Lehrbuch der reinen Mechanik (Braun- schweig: Vieweg, 1853). 596 Appendix: A Selection of Documents

Cost Estimate for Completing the Mathematical Section of the University Library

Older Works Kepler’s Collected Works. Vols.1–5 ...... 25.- Euler. Introductio in analysin ...... 5.- Calculus differentialis ...... 7.20 Mechanica ...... 6.- Methodus inveniendi lineas curvas ...... 4.- Lagrange. Mécanique analytique ...... 15.- Huygens. Horologium oscillatorium ...... 3.- Updating the Journal Collection. Darboux. Bulletin. Two volumes ...... 11.- Astronomical Yearbook. Ten volumes G ...... 20.- Geometry. Grassmann. Extension Theory 1, 2 G ...... 3.15 Plücker. Analyt. geometr. Developments G ...... 1.10 Algebraic Curves G ...... 1.25 Hesse. Lectures. Space, Planes G ...... 4.20 Salmon. Geometry of Planes, of Space G ...... 9.14 Reye. Geometry of Position G ...... 3.- Cremona. Plane Curves G ...... 2.20 Durège. Curves of the Third Order G ...... 2.80 Sturm. Surfaces of the Third Order G ...... 2.20 Lamé. Coordonnées curvilignes ...... 2.- Mechanics. Jacobi. Lectures on Dynamics G ...... 6.- Schell. Theory of Motion G ...... 4.20 Poinsot. Statics G ...... 2.10 Jullien. Mécanique rationnelle ...... 4.20 Duhamel. Mechanics G ...... 2.20 Differential and Integral Calculus. Function Theory. Serret.* Differential-Integral Calculus ...... 7.- Bertrand. ** Differential Calculus ...... 12.20 Integral Calculus ...... 9.- Casorati. *** Function Theory ...... 3.15 Durège. Elliptic Functions G ...... 3.- Function Theory G ...... 1.18 Koenigsberger. Elliptic Functions G ...... 1.10 Heine. Spherical Functions G ...... 2.- Lommel. Bessel Functions G ...... 1.- Neumann. Bessel Functions G ...... -.20 Baltzer. Elements G ...... 3.15 Mathematical Physics. Beer. Optics G ...... 2.- Elasticity, Capillarity G ...... 1.10 Clebsch. Elasticity G ...... 2.20 Lamé. **** Heat ...... 2.- Elasticity ...... 2.- Total 205.20

205 Taler, 20 Silbergroschen = 359 Gulden, 55 Kreuzer Klein

* J.-A. Serret, Cours de calcul différentiel et intégral, 2 vols. (Paris: Gauthier-Villars, 1868); revised German ed. by Axel Harnack, vol. 1 (Leipzig: B.G. Teubner, 11884). ** J. Bertrand, Traité de calcul différentiel et de calcul intégral (Paris: G.-Villars, 1864–70). Appendix: A Selection of Documents 597

*** F. Casorati, Teorica delle funzioni di variabili complesse, vol. 1 (Pavia: Fratelli Fusi, 1868). **** G. Lamé, Leçons sur la théorie analytique de la chaleur (Paris: Mallet-Bachelier, 1861); Leçons sur la théorie mathematique et l’elasticité des corps solides (Paris: Bachelier, 1852).

3) Nomination of Dr. Felix Klein, full professor of mathematics at the Technische Hochschule in Munich, to be made an extraordinary member of the mathematical- physical class of the Royal Bavarian Academy of Sciences, June 7, 1879.5

Since the death of our full member Dr. Otto Hesse, Dr. Felix Klein has been employed as a full professor of mathematics at the Technische Hochschule here (after previously holding the corresponding professorship at the University of Er- langen for a few years). A student of Plücker in Bonn and of Clebsch in Göttin- gen, he can be described as one of the most productive and ingenious representatives of that younger mathematical school in Germany which has received its direction especially from Clebsch and, like him, has chosen a certain border area between geometry and algebra as its main area of activity. – The enclosed list of publications to date, which is unusually long for such a young author, admittedly contains a few repetitions (in that the author has had some of his articles reprinted essentially unchanged in different places) and several variations on the same theme (first, for instance, a provisional announcement of an idea, which is then presented in more detail and later provided with further explanations). Moreover, some of the more significant works owe their origin to impulses provided by the publications of others (e.g., by Schwarz in Göttingen concerning the connection of the so-called hypergeometric series with the icosahedron equation and, in general, with a new way to solve equations of the fifth degree), but even so there is enough left over to cast the author’s mathematical talent, ingenuity, and astuteness in a favorable light, to secure lasting recognition for his work, and to justify further expectations for the future. Furthermore, he has rendered valuable services as one of the editors of Mathematische Annalen, the primary publication venue of the younger school mentioned above, which counts Klein as one of its most outstanding representatives. In his editorial role, he has also performed a valuable service by occasioning the publication of instructive [mathematical] models, especially pertaining to Plücker’s works. Because a vacancy has arisen on account of our associate member Dr. J. Vol- hard’s departure to Erlangen, we believe that no scholar here other than Klein who does not already belong to the Academy and whose work is as relevant to our

5 [AdW München] 18791 (minutes of the election sessions). The Royal Bavarian Academy of Sciences had existed since 1759, and Klein was made a member of it on June 25, 1879. The election process involved two stages, one in the mathematical-physical class (in which Klein received 15 of 15 votes), and the other in a general meeting (where 29 of 34 votes were cast in Klein’s favor). When Klein moved to Leipzig, his extraordinary membership was conver- ted into a corresponding membership. Regarding Klein’s election, see also Paul Gordan’s as- sessment, which is quoted in Section 4.4. 598 Appendix: A Selection of Documents

[mathematical-physical] class could justifiably be given the seat that has become vacant. We therefore propose to the class and eventually the entire academy that Professor Dr. Felix Klein be elected as an extraordinary member of the mathematical-physical class of the Royal Bavarian Academy of Sciences. (We have also sought and received the consent of our absent colleague Dr. C. von Bauernfeind.) Munich – June 7, 1879 Dr. Ludwig Seidel Dr. Gustav Bauer

4) A report by the Philosophical Faculty at the University of Göttingen concerning its decision to propose Felix Klein as the successor to Moritz Abraham Stern, along with separate opinions by the professors Ernst Schering and Hermann Amandus Schwarz (January 1885).

4.1) A report on the Faculty’s hiring proposals for the (third) full professorship for mathematics, to be sent to the Royal Prussian Minister of Culture (Dr. Gustav von Gossler).6

Your Excellency, Göttingen – January 18, 1885 We are honored to submit our most respectful request for the appointment of a full professor of mathematics to fill the chair that has been vacated by the retirement of Professor Stern. The departure of this man, who devoted a long and successful career to our university and whose thorough lectures contributed in no small mea- sure to the flourishing study of mathematics here, has left a conspicuous gap in our teaching staff, and it seems urgently necessary to fill this gap as soon as possible. Out of the glorious past of our university, which counts a number of Ger- many’s most prominent mathematicians as its own, arises our duty to maintain and promote, with all the means at our disposal, the flourishing of mathematical studies at the university and its importance to the progress of mathematical research. The large range of mathematical disciplines, however, has long made it impossible for any one individual to master and till the field as a whole, and thus the subject of mathematics is represented at all of our universities by multiple teaching positions, and at the larger universities by several full professorships. If our university has been the seedbed in which a relatively large number of today’s representatives of mathematics received their education, it has achieved this success in large part because its larger number of full professorships in mathematics has made it possible to represent the various branches of this highly ramified science and thus to offer students a wide-ranging education. In this regard, we would like to stress that, up until the death of Hofrath [Privy Councilor] Ulrich, there were

6 [UAG] Phil. Fak. 170a, No. 41ss–41tt. Regarding the context of this report, see Section 5.8.2. Appendix: A Selection of Documents 599 four full professorships for the subject of mathematics here, whereas presently, after the departure of Professor Stern, there are only two scholars working as full professors of mathematics in our midst. In their teaching and research, the remaining two professors have preferred to focus on the theory of analytic functions, mechanics, number theory, curved surfaces, and curves of double curvature. It is therefore our conviction that the most effective way to complement their activities would be to appoint a representative of the geometric-algebraic approach to work alongside them. As such, our first recommendation is Dr. Felix Klein, a full professor of geometry in Leipzig who was born in 1849. Klein began his mathematical studies in Bonn and, having obtained his doctorate there, spent several semesters in Göttin- gen and Berlin completing them. He finished his Habilitation in Göttingen in 1871, and just a year later he was appointed a full professor in Erlangen. In 1875, he accepted a professorship at the Technische Hochschule in Munich, and he moved to Leipzig in 1880. Even in his earliest works, which proceeded in the direction initiated by Plücker and Cayley, it was possible to recognize the outstanding talent of their author. They were characterized as much by the wealth of their geometric intuition as they were by the breadth of their geometric perspective, and they created the expectation that their author would not limit himself in the further development of his scientific career to the narrow field of purely geometric investigations but would rather also, with the support of the tools of geometry, turn to other problems of mathematics. In fact, his more general examination of the various methods of geometric research led him at first to the theory of transformation groups. This formed the center of his further scientific activity, and since then he has earned a generally respected name in the scientific world through his numerous and extensive studies, which bear witness to the versatility of his intellect. Klein is an excellent teacher whose personality fills his students with sincere admiration and who knows how to inspire his students to conduct mathematical research and to encourage them to carry out independent scientific investigations. He is also very productive as an editor of the Leipzig-based journal Mathemati- sche Annalen, and he is known to be a tireless worker in all the endeavors that he has touched. We would therefore be especially pleased if we were to succeed in bringing this excellent scholar to our university, and we have good reason to believe that he himself is likely inclined to exchange Leipzig for Göttingen for personal reasons. Should we not succeed, however, in gaining Mr. Klein for our university, we are honored to dutifully suggest to your Excellency the following gentlemen se- cundo loco et pari passu [on equal footing in second place]: Dr. Aurel Voß, born in 1845, currently a professor in Dresden, who was appointed to the Technische Hochschule in Munich at Easter this year; and Dr. Alfred Enneper, born 1830, an associate professor at our university. In this respect, we are aware that the direction of Professor Enneper’s scientific activity is less in line with the focal points mentioned at the beginning of this report. Only if we fail to fill the vacant professorship with a geometrician of Pro- 600 Appendix: A Selection of Documents fessor Klein’s caliber do we believe that it might be appropriate to take into account the years of loyal service that Professor Enneper has rendered to science and to our university. […] Should unforeseen obstacles stand in the way of appointing Mr. Klein, Mr. Voß, or Mr. Enneper, we obediently ask your Excellency to grant the faculty the opportunity to offer new proposals. The Philosophical Faculty. The Dean. W.[ilhelm] Müller (signed)

4.2) A separate opinion (Separatvotum) on the Faculty’s report, by Ernst Scher- ing, a full professor of mathematics at the University of Göttingen.7

Your Excellency, Göttingen – January 22, 1885 The humble signee is taking the liberty of submitting, in the most respectful manner, his opinion, in so far as it deviates in essential points from the proposal made by the majority of the members of the Philosophical Faculty. The content of the latter hiring recommendation is based on an overestimation of projective geometry, which, in my opinion and in the opinion of other compe- tent experts, leads to a false impression of the benefits that appointing Professor Felix Klein to Göttingen might bring to our university. In contrast to this proposed appointment, the appointment of our Associate Professor Alfred Enneper or Professor Georg Hettner in Berlin as a full professor in Göttingen would be of considerably greater benefit to the study and further training of the strict methods that were introduced by the great Göttingen mathematicians Gauss and Dirichlet and were also used with brilliant success by Rie- mann. Furthermore, such an appointment would also be of greater benefit to the education of the mathematics teachers to be employed at secondary schools, for whom certainty and clarity of thought are the most important matters. The promotion of […] Associate Professor Enneper would give well-deserved recognition to the merits of his now twenty-six successful years of academic teaching and to his valuable scholarly achievements, and it would ensure that a greater number of scholarly disciplines formerly taught by Professor Stern would still be well-represented by a full professor. In addition, this would create the possibility of appointing a new scholar to the vacant associate professorship [i.e., Enneper’s], who could also […] provide a necessary supplement to the courses offered here for the education of secondary school teachers. As a Privatdozent in Göttingen and as an associate professor in Berlin, Mr. Hettner has developed his academic activity with unusual success, not only in terms of the number of students who attend his courses but also in his ability to teach them with strictly correct and clear thinking. Regarding his research, he has

7 [UAG] Kur. 5956, fols. 9–10v. Appendix: A Selection of Documents 601 made significant contributions with his investigations of determinants composed of hyperelliptic integrals. That Mr. Hettner has not published anything during his appointment at the University of Berlin is essentially due to the fact that the conditions imposed upon him there require him to take on […] a heavy teaching load. His intimate familiarity with the highest branches of various mathematical fields guarantees, however, that he will go on to produce extremely valuable scholarly achievements. His research areas overlap perfectly with the disciplines represented by Professor Stern. Schering (signed)

4.3) A separate opinion (Separatvotum) on the Faculty’s report, by H.A. Schwarz, a full professor of mathematics at the University of Göttingen.8

Your Excellency, Göttingen – January 25, 1885 Please allow me to present my views, which differ in some points from the report submitted by the majority of my colleagues and which agree in essential respects with the opinion of my immediate colleague, Prof. Schering, regarding the candidates to be considered for the appointment of a third full professor of mathematics to our faculty. One of the merits of Prof. Stern, who has now retired, was his ability to meet, with tireless dedication and lasting success as long as his energies allowed, the needs not only of advanced students of mathematics but also of beginners. It is to his great credit that the students of mathematics at our university have always had the opportunity in recent decades to become acquainted with the un- avoidable foundations of almost all higher mathematical disciplines (algebra, differential and integral calculus, and elementary mechanics) through the lectures of an excellent teacher and through the seminar exercises that he conducted. It is in great part due to this merit of Prof. Stern, which cannot be appreciated highly enough by his immediate colleagues, that the study of mathematics at our university could so greatly flourish. If other scholars were able to devote their mathematical lectures to the culti- vation of special disciplines and were able to find a larger number of well-prepared students to attend them, this was undoubtedly only made possible by the fact that the most urgent needs of mathematical instruction were already taken care of in the best possible way by Prof. Stern. This aspect of providing sufficient care for the most urgent needs of mathematical education will also remain, in the future, of the utmost importance for the training of capable secondary school teachers. I am convinced that it will only be possible to maintain the flourishing of mathematical studies at our university if, in selecting the scientist to succeed Prof. Stern, we insist on the requirement that he must not only possess indisputably

8 [UAG] Kur. 5956, fols. 11–14. 602 Appendix: A Selection of Documents outstanding teaching abilities but must also offer the guarantee that, together with the other representatives of mathematics on our faculty, he will adequately tend to the needs of beginners. The subject of algebra is represented by neither of the two current full professors of mathematics here [Schwarz, Schering]; this subject, which is extremely important for the training of future secondary school teacher, is likewise not one of the disciplines represented by the current associate professor of mathematics [Enneper]. Professor Schering and I agree that, in the interest of the fullest possible representation of mathematical disciplines at our university, it is highly desirable that Professor Stern’s successor should be able to take over the representation of algebra in its entirety – without, of course, having his teaching activity restricted in any other way. Likewise in agreement with Prof. Schering, I humbly believe that Dr. Georg Hettner, born in 1854 and currently an associate professor at the University of Berlin, can be described to your Excellency as just such a scholar. Prof. Hettner conducted his algebraic studies under the direction of the most prominent researcher in the field of algebra among all living mathematicians, Mr. Kronecker in Berlin. Moreover, Prof. Hettner is also one of the most talented students of Mr. Kummer and Mr. Weierstrass in Berlin. Regarding the praise that Prof. Hettner has earned, I agree with all of the points made by Prof. Schering in his separate opinion, both with respect to the value of his scientific work and in terms of his eminent talent as a teacher. With respect to the proposals that the majority of the Faculty submitted to your Excellency concerning the appointment of Prof. Stern’s successor, I cannot oppose the proposals in favor of Professors Felix Klein and Aurel Voß. If the appointment of Prof. Klein is successful, an outstanding teacher and an important scholar will be gained for our university and for our Prussian fatherland. The same applies to Prof. Voß. In light of the criteria presented above, however, I regret very much that I cannot accept the suggestion to promote Prof. Enneper to full professor as Prof. Stern’s successor. Your Excellency’s most obedient H.A. Schwarz (signed)

Appendix: A Selection of Documents 603

5) On the scientific polemic between Felix Klein and Lazarus Fuchs. An excerpt of a letter (in draft form) from Felix Klein to Wilhelm Förster (a professor of astronomy at the University of Berlin), January 15, 1892.9

[…] Here are just a few more remarks about my relations with Fuchs. The enclosed package contains, above all, the autograph edition of a lecture that I gave in the summer of 1891.10 There, on pp. 66–89, you will find a presentation on the historical development of the study that, ten years ago, brought about the polemic between Fuchs and myself. Although this presentation was of course originally meant for my students’ ears, it will hopefully be intelligible to someone reading it at some remove. My intention in this presentation, in which I provide a precise account of my earlier ideas, is to leave an impression of utmost candor. You will also gather from the booklet that I am once again working energetically on these very issues and that I am in the process of preparing a final presentation on the entire area of research. [[From the same text, incidentally, you will also learn how I consider the task of the geometrician, which is to understand the whole field of mathematics – and, I might add, its applications – from the perspective of geometric intuition.]]11 I should further point out that there have also been two indirect conflicts between Fuchs and myself in recent years […]: 1) Fuchs publishes a theory that turns out to be just plain wrong. 2) A younger mathematician [Hurwitz] notices this, addresses Fuchs himself about it, and discovers that the latter is not as understanding as he had hoped. 3) He [Hurwitz] sends me his view on the matter12 for publication in the Göttinger Nachrichten or Mathematische Annalen, which I, finding them correct, in turn published after smoothing out the manner of his expression when necessary. As it was with Hurwitz in 1887,13 so it is now with the Russian mathematicians Nekrasov and Anisimov. To speak only of the latter: The false developments that Fuchs had originally published in Crelle’s Journal 75 were replaced by him by other erroneous state- ments, after Anisimov had pointed out his errors, in Crelle’s Journal 106, though now in a form with which A. felt personally dissatisfied. Nekrasov provided the

9 [UBG] Cod. MS. F. Klein 1C: 2. On the context of this letter, see Section 6.5.1.1; regarding this polemic, see also Sections 5.5.5 and 5.8.2. 10 The lecture in question was on the theory of linear differential equations. 11 Klein later deleted the sentence printed here in double brackets. 12 In response to Lazarus Fuchs’s article “Über diejenigen algebraischen Gebilde, welche eine Involution zulassen” (published in the Sitzungsberichte of the Berlin Academy, July 1886), Hurwitz had written to Klein: “I recently found that all of these curves can be represented by equations f(s2, z) = 0, from which it immediately follows that they are by no means exhausted by the hyperelliptic curves, as has recently been claimed […].” ([UBG] Cod. MS. F. Klein 9: 1034, letter, Dec. 28, 1886). 13 For further details, see TOBIES 2019, pp. 505–506. 604 Appendix: A Selection of Documents correct theory in Annalen 38,14 but he made a mistake in one of his secondary points, namely when he wanted to uncover the inner reason for the mistake made by Fuchs in vol. 106. Fuchs noticed this and reacted in vol. 108 with an abrasive reply and held firm, without any reservation, about the theory that he had presented in vol. 106! This was followed by passionate letters from Nekrasov and Anisimov to myself, which I just now, during the Christmas holiday, put into a subdued form and will soon publish in Mathematische Annalen.15 Of course, every incident of this sort only serves to renew and increase the blind hatred16 that Fuchs has directed toward me. He has gone so far as to disre- gard the basic laws of decency. My student, Dr. Fricke, who has been living in Berlin in recent years (and whom I hold in exceptionally high esteem both personally and as a mathematician), has told me a few stories about this. A year ago, he sent Fuchs the first volume of my book on elliptic modular functions, which Fricke edited (and which contains no polemics whatsoever), with a request for a personal letter of reference: he received no reply at all. It was precisely at that time when Fricke approached Kronecker (whose research was closely aligned with his own) with the question of how Kr[onecker] would assess his application to the Berlin faculty for approval to submit his Habilitation. Kr[onecker] flatly replied that he was in no position to support an application about which the faculty would yet have to make a decision. If you take all of this together, then the question of how the relationship between F[uchs] and myself would develop if we were to work together at the same university is self-evident. I would certainly not behave provocatively but would rather avoid all external conflicts as much as possible. However, I would not abandon my research plan any more than I would cease publishing what I think is right. No one can demand that I should deny my entire past for the sake of recei- ving a professorship in Berlin. (And even the mere fact that I might be summoned to Berlin would be a grave insult to Fuchs.) Personally, this perspective doesn’t really frighten me very much – my concerns, which I expressed in a letter to A[lthoff], are of a completely different nature – but I do not know how the matter looks from a more general point of view and whether you would want to take responsibility for having helped to bring about such unpleasant conditions. […]

14 See P.A. Nekrassoff [Nekrasov], “Ueber den Fuchs’schen Grenzkreis,” Math. Ann. 38 (1891), pp. 82–90. This article concludes with the following words: “Thus, the cases in which Fuchs’s theorems do not apply should by no means be called exceptional cases.” Hurwitz informed Klein: “Fuchs, [Meyer] Hamburger, and their colleagues are reportedly extremely agitated about Nekrasov’s publication in the Annalen […].” ([UBG] Cod. MS. F. Klein 9: 1090, a letter dated May 1891). 15 See W.A. Anissimoff [V.A. Anisimov], “Ueber den Fuchs’schen Grenzkreis,” Math. Ann. 40 (1892), pp. 145–48. – Anisimov had graduated in Moscow and completed his doctoral thesis, The Fuchsian Boundary Circle and its Applications, at the University of Warsaw in 1892. 16 Later, in this drafted letter, Klein replaced the term “blind hatred” with “feeling of antipathy.” Appendix: A Selection of Documents 605

6) Letters concerning the potential successor to H.A. Schwarz’s full professorship at the University of Göttingen.17

6.1) An excerpt of a letter from Klein to Adolf Hurwitz, February 28, 1892.18

[…] Althoff spent three days here and brought the new appointments in Berlin to a conclusion. Besides Frobenius, Schwarz will be appointed full professor [in Berlin] on April 1st. – I myself, if I may say so here, am quite pleased with the way things have turned out. For I feel as though I was treated rather honorably, and I have also gained some freedom of movement. But to remain on point: now it will be necessary to fill Schwarz’s position here in Göttingen, and this should happen in the near future. I also know exactly what suggestions I would like to make to the Faculty (although you must keep in mind, of course, that I am not the Faculty; I even ex- pressly want to reserve the freedom to modify my current ideas over the course of the forthcoming negotiations): You will roughly guess that I intend to propose you and Hilbert as the only two people who would be able to help me safeguard the status of our scientific reputation in relation to Berlin […]. And now the great difficulty, which required a great deal of deliberation before I decided to write to you about it myself. It goes without saying that I will name you first and Hilbert second. There are, however, a number of concerns about appointing you, and the question is to what extent I should express these concerns and perhaps even admit outright that Hilbert’s presence here might ultimately meet our needs to a greater extent than yours. The first matter is that of your unstable health, the importance of which I do not want to overstate, but I cannot ignore it entirely. Second, there is the far more subtle reason that you are much closer to me than Hilbert, not only personally but also in the way that you think mathematically, so that your activity here would perhaps lend Göttingen mathematics an excessively one-sided character. The third issue – I have to bring it up, as repugnant as the matter is to me and as much as I know how justifiably sensitive you are about it – is the Jewish question. It is not that your appointment would pose any difficulties; these I could overcome. However, we already have Schoenflies, to whom I am always interested in offering a permanent position here (a salaried associate professorship). And I will never be able to accomplish this with the faculty or with the minister if you and Schoenflies are employed side by side! But I must come to an end. For me, the decision between you and Hilbert would be difficult enough if I merely had to weigh the reasons for or against either of you objectively. Now, however, there is also the subjective difficulty, which is that I would like least of all to offend you in the present situation; rather, I would like to do everything I can to be helpful to you. Please write me a line of

17 For the context of these developments, see Section 6.5.1.2. 18 [UBG] Math. Arch. 77: 228. 606 Appendix: A Selection of Documents reassurance immediately, if possible; but in any case, please speak your mind against me just as unreservedly as I have done here. The faculty meeting is sche- duled to take place on Thursday, and I will certainly have your answer by then!19 Whatever the outcome, promise me that our personal relationship will not suffer from it. With best wishes I remain Yours, Felix Klein

6.2) An excerpt of a letter (draft) from Felix Klein to Friedrich Althoff, March 7, 1892.20

Esteemed Senior Privy Councilor! Please allow me to submit a report to you today, even before the faculty’s new hiring proposals are ready, concerning Dr. Schoenflies [a Privatdozent at the Uni- versity of Göttingen]. You touched upon the question of anti-Semitism. The impression I have from all sides is that no one would take any offence at all with one Jew, but that the appointment of two Jews simultaneously would be considered inadmissible.21 So if Hurwitz were to come here (as I still advocate), then I would have to sacrifice Schoenflies. I would deeply regret that, because I have come to appreciate Schoenflies’s unique talent more and more, not only from a personal perspective but also in the interest of our university. In essence, Schoenflies is a highly gifted man; he has a penetrating mind and, what is more, outstanding teaching abilities in the popular sense. I have repeatedly praised his geometric talent. If he lacks anything, it is consistent energy: he must be forced to do things from the outside, but then he works just as quickly as he does surely. (I have no doubt that you will receive different opinions about Sch[oenflies] from other sources. Yet in contrast to what you may hear, I would like to refer to the fact that, from Christmas onwards, I attended the two-hour seminar conducted by Schoenflies and Burkhardt no less than eight times; they were truly scientifically lively, and any doubt about the qualifications of the seminar leader, who repeatedly gave lectures himself, is out of the question for me.) As I have already noted, however, the decisive factor for me is the consideration of the intended appointment [i.e. Schwarz’s successor]. […]

19 Klein was unable at the time to implement Hilbert’s appointment (Hilbert was still a Privat- dozent then), and so he fought on behalf of appointing Hurwitz. 20 [UBG] Cod. MS. F. Klein 1C: 2, fol. 22. See Section 6.5.1.2. 21 Klein was aware of the widespread anti-Semitism at the time, but he made his own judge- ments on professional grounds. On December 13, 1887, for example, Moritz Pasch, who came from a Jewish family, had written to Klein about Klein’s recommendation that Max Noether and Adolf Hurwitz would be fitting candidates for a professorship at the University of Gießen: “Of course, I was not allowed to include any Jewish colleagues on the list, other- wise scholars such as [Max] Noether and Hurwitz would not have been left out of it” (quoted from SCHLIMM 2013, p. 198). Appendix: A Selection of Documents 607

In this respect, I have no doubt that our main goal in the present situation should be to appoint someone who complements my interests and can thus lead to the creation of a more rigorous school. Prof. Schwarz was excellent in this respect; Prof. Lindemann will not be equally so. […]22 After he had enjoyed the encouragement of a particularly gifted teacher of synthetic geometry at school, Prof. Hurwitz originally studied with me, then also in Berlin with Kronecker and especially with Weierstrass. Prepared in this way, he brings together all the premises for the epitome of modern research, which aims to combine function theory (as a central discipline) with number theory and geometry. And to these premises, Hurwitz also adds a brilliant level of productivity, which never falters despite the obstacles that his somewhat delicate health puts in his way. The number of his publications, and the number of different subjects that Hurwitz has written about, is very high: In my ranking (from my subjective point of view), his best works are those in which he tackles the problems of geometric function theory which I originally raised, and takes them much further than I ever could have done. This work represents the complement that I have been looking for, and it does so in tangible reality and the most satisfying completeness. […]

7) Felix Klein on the draft of Ludwig Bieberbach’s dissertation, which was super- vised by the Privatdozent Paul Koebe at the University of Göttingen.23

Dear Mr. Bieberbach! Göttingen – May 15, 1909 I have just read through your dissertation, and I have great reservations about Part I. What is right is not new, and what is new is wrong. The proof: Ad. 1. That the canonical cut systems are by no means determined by the pe- riods of Abelian integrals is not only pointed out but also explained in Math. Ann. XXI, pp. 184–85.24 – Fricke refers to this in Vol. 1 of the Automorphen [Funktio- nen], p. 324, where he proves that two operations are sufficient to produce all canonical cuts.25 Ad. 2. The theorem on the generation of all binary period transformations in the hyperelliptic case by the monodromy of branching points is only correct for p = 2; for p = 3, there are already 36 separate families [Scharen]. I had H.D. Thompson treat this matter in his dissertation (American Journal XV, available in the reading room […]).26

22 What follows here are some laudatory words about Lindemann, because Lindemann had complained about Klein’s preference to appoint the younger Hurwitz and Hilbert. 23 [Deutsches Museum] Nachlass Ludwig Bieberbach. I am indebted to Reinhard Siegmund- Schultze for bringing this letter to my attention. – Regarding the context, see Section 8.5.3. 24 Klein’s reference here is to his own article: “Neue Beiträge zur Riemann’schen Functionen- theorie,” Math. Ann. 21 (1883), pp. 141–218. 25 See, for the English translation, FRICKE/KLEIN 2017 [1897], pp. 263–64. 26 See H.D. Thompson, “Hyperelliptische Schnittsysteme und Zusammenordnung der algebraischen und transcendenten Thetacharacteristiken,” Amer. J. of Math. 15 (1893), pp. 91–123. 608 Appendix: A Selection of Documents

But it is also false to reduce the question of any given Riemann surface to two-sheeted surfaces. The source of the error is the fact that Clebsch-Lüroth did not understand the “sheet” of a R[iemann] surface as a piece of the surface that covers the […] plane exactly once, but rather only as any simply connected piece. Now, what should happen in this situation? I am unfortunately extremely busy these days in light of the negotiations that are about to begin again in the Upper House [of Parliament]. Nevertheless, let me ask you to come to the mathematical collection room on Monday at noon. By the way, would you also please show this letter to Dr. Koebe?27 Yours sincerely, F. Klein

8) Dr. Klaus, a neurologist at the Sanatorium for Neurology and Internal Medicine in Hahnenklee: two reports on the state of Felix Klein’s health.28

Report from March 9, 1912 The full professor of mathematics, Privy Councilor Klein from Göttingen, has been in my sanatorium since December of last year. Owing to years of overexer- tion in his profession, and due to the fact that he has never allowed himself a necessary period of rest and relaxation, he suffers from a state of extreme exhaustion and irritability of his nervous system. There is no trace of an organic disease. This is a matter of genuine neurasthenia, i.e., a temporary and curable weakness of a healthy nervous system. The duration of the healing process will of course be quite long, given the extent and intensity of the damage that has been done. Even though the patient set aside his courses for the winter semester of 1911/12 and came here for a cure, and even though there has been a slight but unmistakable improvement in the state of his nervous exhaustion, it is nevertheless from a medical point of view entirely impossible that Mr. Privy Councilor Klein should be allowed to lecture again in the summer semester of 1912. If he were to return to work prematurely, he would undoubtedly, as a consequence, relapse to his previous state of weakness and thereby prolong the difficult healing of his suf- fering. I therefore humbly request, for the urgent reasons mentioned above, that my patient be granted further leave until the winter semester of 1912/13. He will continue to remain up here in my sanatorium. Dr. Klaus – Neurologist (signed)

27 Bieberbach had attended Klein’s seminar from 1906/07 to 1908 (which Klein directed together with Hilbert and Minkowski) and he transcribed (with Max Caspar) the lectures that Klein gave on automorphic functions from May 1 to July 31, 1907 (see [Protocols] vol. 26). As a full professor, Klein had to evaluate Bieberbach’s dissertation – “Zur Theorie der automorphen Funktionen” [On the Theory of Automorphic Functions] – which had been super- vised by the Privatdozent Paul Koebe. For a brief biography of Bieberbach, including his grades and the subjects of his doctoral examination, see TOBIES 2006, pp. 58. – For Bieber- bach’s support of Nazism, see in particular MEHRTENS 1987; 1990; 2004. 28 [UBG] Cod. MS. F. Klein 2D, fols. 65, 66. See Section 8.5.1. Appendix: A Selection of Documents 609

Report from October 10, 1912 At the end of September of this year, Privy Councilor Professor Dr. Klein, Göttin- gen, left my sanatorium, where he had been staying since the beginning of the year, and returned to his university town. In the peace and quiet that prevails up here, he ultimately felt so rejuvenated that he regained the hope of teaching his lecture course in the winter semester of 1912/13. I have now examined Mr. Klein in detail since his departure from the sanatorium, and I unfortunately found that his nervous system is still very easily exhausted and that he had suffered from especially severe bouts of intestinal neurosis. As a result, the patient became very ill again, though only temporarily. Given the rapid change of environment and the cessation of his cure, such relapses are not alarming and are not a sign of a worse- ning prognosis. However, it is necessary to take them into serious consideration. In order to prevent Privy Councilor Klein from falling victim to greater exhaustion again, I have to prohibit him, from a medical point of view and in the interest of his health and full recovery, from giving lectures in the winter semester of 1912/13. Dr. Klaus

9) Nomination of Felix Klein to be made a corresponding member of the Royal Prussian Academy of Sciences in Berlin, February 27, 1913.29

The undersigned have the honor of proposing to the Academy the election of Pro- fessor Felix Klein as a corresponding member in the field of mathematics. Klein was born on April 25, 1849 in Düsseldorf. He studied in Bonn, Göttingen, and Berlin; received his doctorate in Bonn in 1868; became a Privatdozent in Göttin- gen in 1871, a full professor in Erlangen in 1872, and from there he went to the Technische Hochschule in Munich in 1875. In 1880, he accepted an appointment at the University of Leipzig, and he has been teaching at the University of Göttin- gen since 1887.30 Klein, one of the few mathematicians still able to survey the whole of mathematics, was originally a geometrician. Familiar with the ideas of the ingenious Plücker, he began his career with work pertaining to the theory of line complexes. He set up a simple form for the equation of a second-degree surface in line coor- dinates; determined, together with Sophus Lie, the main tangent curves of Kum- mer’s surface; and provided, for the line complexes, an analogue of Dupin’s theorem of curvature. His own investigations and his knowledge of the ideas of Plü- cker, Staudt, and Sophus Lie led him to consider the questions treated by his pre- decessors from a common point of view, and in his inaugural address in Erlangen he united all the geometric ideas that were new at the time into a whole by pre-

29 [BBAW] Bestand PAW (1812–1945), II-III-135, fols. 70r–71v (Friedrich Schottky’s hand- writing). 30 The year 1887 is incorrect; Klein began working in Göttingen in April of 1886. 610 Appendix: A Selection of Documents senting thoughts rather than formulas.31 For a geometrician who thought in such general terms, Riemann’s theory of Abelian functions must have had a strong attraction. The interest that Klein always showed for Riemann is particularly evident in his book on elliptic modular functions. This book – two imposing volu- mes32 – contains lectures given by Klein and includes many of his previously published articles. One fine chapter in it contains Klein’s presentation of Riemann’s theory. Essentially, the book is concerned with a single, but highly important, function: the modular function. Its function-theoretical character had first been recognized by Gauss, who never published anything about it himself; however, a page from his estate with a few characteristic drawings by Gauss was discovered and published in time to establish Gauss’s priority on this point. Modular functions were already associated with highly interesting algebraic research by Gauss and Jacobi, and Klein treated these ideas with new means and in a new form. Klein, however, regarded this entire work as just a preliminary stage for conduc- ting a comprehensive investigation of those functions which were discovered around that time (in some cases much earlier); Poincaré called these Fuchsian functions and Kleinian functions, while Klein referred to them as automorphic functions. If, as Klein did, we take the Gauss-Jacobi modular functions as our starting point, we have the first example of an automorphic function, and this immediately reveals some of the depth and difficulties of the theory that Klein for- mulated in competition with Poincaré. If the issue at hand were to define, in a direct way, the simplest and essentially most important functions newly developed by German mathematicians at the time, then one would have to proceed differ- ently. Besides Poincaré, however, it was Felix Klein who did the most work on automorphic functions. These investigations also fill two imposing volumes.33 Klein also made his other Göttingen lectures, which contain the most important results of his work, accessible to wider circles by having them reproduced in autograph copies. The latter include lectures on the icosahedron, on non-Eucli- dean geometry, on the application of differential and integral calculus to geometry (a revision of principles), on the hypergeometric function, and on Riemann surfaces. It is to be hoped that all of these will be printed as books.34 Then there will exist a large multivolume textbook on analysis, full of unique geometric methods and with a geometric inclination, for Germany – and this is very desirable. Felix Klein’s tireless activity has not been restricted to his own scientific research. It is to his credit that the difficult task of publishing Gauss’s Nachlass has now been achieved almost completely and in an exemplary manner, and that the

31 What is meant here is not Klein’s inaugural address [Antrittsrede] in Erlangen (see Section 3.2) but rather his booklet Erlangen Program (KLEIN 1872). 32 See KLEIN/FRICKE 2017 (1890/92). 33 See FRICKE/KLEIN 2017 (1897/1912). 34 Klein’s lectures on the icosahedron – Vorlesungen über das Ikosaeder (Leipzig: B.G. Teub- ner, 1884) – already appeared as a book in its first edition (English trans., 1888; repr. 2019). The other lectures mentioned here were first reproduced in handwritten (autograph) copies. Later, Klein himself prepared some of them to be published as books; see Section 9.2.3. Appendix: A Selection of Documents 611 great work of the mathematical ENCYKLOPÄDIE was begun and vigorously conti- nues. He was indefatigably active at congresses to promote the union of mathematicians and to identify important goals. Almost all academies and mathematical societies count him among their members, and several universities have awarded him an honorary doctorate. In recent years, his zeal has mainly been devoted to elevating the level of mathematical education at universities and secondary schools, and he has been just as tireless in these efforts as he was as a mathematician in the decades before. H.A. Schwarz, [Georg] Frobenius, [Friedrich] Schottky, [Max] Planck35

10) Speeches given on May 25, 1913 upon the presentation of Max Liebermann’s portrait to Felix Klein.36

10.1) A welcome speech by the physicist Eduard Riecke.

Dear friend! Old age is generally a somewhat dubious asset; today, however, I am grateful for it, for it gives me the beautiful duty and heartfelt pleasure of address- ing a few words to you on behalf of our colleagues. I still vividly remember Clebsch’s course that we attended, where I saw you for the first time and where I, without having exchanged a word with you, told myself that there was something special behind those eyes and that forehead. When I got closer to you over the course of the semester, I recognized that my eyes had not deceived me. During the following semesters, the events of the war took you away from Göttingen, and it was not until the summer of 1871 that we reunited as Privatdozenten in Göttingen. In addition to the geometric problems that occupied you at that time, you had a lively interest in physics; you also gave a lecture course on the theory of light, accompanied by experiments. The Fresnel mirror that was constructed at the time is still in the Institute of Physics today, though not entirely in its original state.37 When Stern resigned from his professorship in 1885,38 the distant hope of winning you back to Göttingen appeared. The endeavor was successful, despite

35 Klein’s election as a corresponding member of the Berlin Academy took place at the same sessions as Hilbert’s. In the mathematical-physical class, both were elected unanimously on May 29, 1913. In the election that took place during the Academy’s general assembly on June 10, 1913, Klein received 40 out of 44 votes, while Hilbert was elected unanimously. 36 [UBG] Cod. MS. F. Klein 107. Regarding the context, see Section 8.5.2. 37 In 1816, the French physicist Augustin-Jean Fresnel had first described his double-mirror experiment, which was used to demonstrate interference phenomena. 38 Moritz Stern had already applied to be released from his duties on April 19, 1884, and his request was approved on October 1, 1884 (see Section 5.8.2). 612 Appendix: A Selection of Documents the great difficulties involved. Althoff, who was sympathetic to the plan itself, feared that it would be rejected. I accompanied him on the way back from the observatory into town [Göttingen], and it was then that his resolution was made. At the corner where the Schildweg branches off from the yard of the barracks, he asked me: “Can you promise that Klein will accept?” “Yes,” I replied, and there- upon he agreed to initiate your appointment. I was well aware that you, as our new colleague, would not be guided by the saying “quieta non movere,”39 but that is precisely why I considered your appointment so important and why it seemed to me to be a matter of life and death for our university. At that time, there was a danger that it would sink to the level of a purely provincial university, so a new impulse from the outside was urgently needed. That we were not mistaken in this assumption is clear from the history of the last decades: the reorganization of mathematical instruction, the reorganization of the Society of Sciences [i.e., the Academy], the Göttingen Association – to name only those things that pertain especially to Göttingen. In all of this organizational work, we have always admired three things above all: the high standpoint and the broad perspective with which you embraced all the issues under consideration; the way in which you knew how to recognize the relationship between the most varied things in order to direct all of them toward one and the same goal; finally, your perfect sense of justice toward all matters and people, and the idealism and selflessness with which you put your work at the service of the general public. In the end, everything depends on the point of view from which one looks at things; the higher this is, the more personal opinions disappear, and the more clearly objective interests appear. Thus, the way that you have been working for the good of our university, for the good of science, and for the good of our whole culture has unintentionally had another effect. Surely the highest values of man do not lie in the intellectual but in the ethical sphere. Many of your friends and colleagues may have experienced that after chatting with you, they felt like a hiker in the pure mountain air high above the daily hustle and bustle of people, which disappears in an unsubstantial glimmer far below. Everything petty and limited has vanished and fallen away, and the soul is filled with great and pure feeling. For some of your students, this effect may have even been of deeper significance than the immediate effects of your teaching, and so an especially warm thanks for this as well. I am not merely standing here, however, as a representative of your Göttingen colleagues but rather on behalf of a large number of friends, admirers, and students from all parts of the world, and on their behalf I would now like to read what they have to say to you today, what they would like to thank you for, and what their wishes are for you.40

39 Quieta non movere = “Do not move settled things,” i.e., “Don’t rock the boat.” 40 The message that Riecke then read out contains nothing new. What is interesting, however, are the seventy-one names of the people who signed an appeal for donations for the portrait at the beginning of 1912: A. Ackermann-Teubner, L. Bianchi, O. Blumenthal, M. Bôcher, H. v.

Appendix: A Selection of Documents 613

10.2) Felix Klein’s acceptance speech.

My dear colleagues and friends! For the extraordinary honor that you have bestowed on me with your words and with this painting, I would like to express my deepest thanks to you and to those who commissioned it. I regard this picture as a symbol for the hope that the construction of the independent Mathematical Institute, as we have planned to build it in the immediate vicinity of the Institute of Physics, will in fact come about.41 May it there find its place as a symbol of my efforts to bring the mathematical sciences into a lively relationship with their neighboring disciplines to form a large and versatile whole, which goes beyond the achievements of any individual and certainly beyond my own modest contributions. Your address, however, is a dear reminder to me of the many friends and colleagues with whom I have been able to establish a relationship along my way. Cooperation with like-minded people has always been my real element of life. I also hope, on this basis, to be able to encourage the continuation of the summarizing works that I have been managing for years despite the inhibitions that the state of my health imposes on me. In the meantime, new life is blossoming around me, enriching me and pushing me ever onward and upward, and I accompany its increasing importance with ever more participation. I could wish for nothing better than to have the time in which I worked appear later, in retrospective contemplation, as a time that prepared the way for a new ascent. I thank you again and ask you to convey these thanks in a suitable form to everyone involved.

Böttinger, A. v. Brill, H. Burkhardt, C. Carathéodory, G. Darboux, R. Dedekind, W. v. Dyck, E. Ehlers, F. Enriques, H. Fehr, L. Fejér, R. Fricke, R. Fueter, P. Gordan, G. Greenhill, G.B. Guccia, A. Gutzmer, J. Hadamard, O. Henrici, D. Hilbert, E.W. Hobson, A. Höfler, O. Höl- der, A. Hurwitz, G. Kerschensteiner, P. Koebe, J. König, A. Krazer, E. Landau, E. Lange, W. Lietzmann, C. v. Linde, F. Lindemann, F. Mertens, F. Meyer, O. v. Miller, G. Mittag-Leffler, J. Molk, E.H. Moore, C.H. Müller, M. Noether, W. Osgood, E. Picard, H. Poincaré, E. Riecke, K. Rohn, C. Runge, R. Schimmack, H. Schotten, F. Schur, A. Sommerfeld, P. Stä- ckel, V.A. Steklov [W. Steckloff], O. Taaks, A. Thaer, P. Treutlein, A.V. Vasilev [A. Wassi- liew ], G. Veronese, W. Voigt, V. Volterra, K. Von der Mühll, A. Voss [Voß], E. Waelsch, H. Weber, A. Wiman, W. Wirtinger, H.G. Zeuthen. (Not all of those who signed this appeal were themselves among the donors, see Figure 43). The appeal attracted 331 donors. They came from Austria-Hungary (J. König, G. Rados, G. Zemplén ...), Australia, Belgium, Canada (J.C. Fields), Denmark (P. Heegaard...), France (P. Appell, E. Borel, B. Boutroux ...), Germany, Great Britain (A. Berry, G. Darwin, A.E.H. Love), Greece (C. Stephanos), India, Italy (G. Castelnuovo, G. Loria, E. d’Ovidio, E. Pascal, C. Segre, ...), Japan (R. Fujisawa, T. Yoshiye), the Netherlands (L.E.J. Brouwer, ...), Portugal (F.G. Teixeira). They were Polish mathematicians (S. Dickstein, K. Zorawski), came from Russia (including Nadezhda N. Gernet, A.N. Krylov [Kriloff], A.A. Markov [Markoff], D.M. Sintsov [Sinzov], ... ), from Sweden, Switzerland (including E. Fiedler, C. Jaccottet, F. Rudio, A. Weiler), the USA (F.N. Cole, F. Franklin, M.W. Haskell, D.E. Smith, V. Snyder, H.W. Tyler, E.B. Van Vleck, F.S. Woods, ...). 41 As mentioned, the institute (Bunsenstraße 3–5) was not completed until 1929; see 9.4.2. 614 Appendix: A Selection of Documents

Figure 43: A list of donors who sponsored Max Liebermann’s painting of Klein’s portrait in 1912 [Hillebrand]. Appendix: A Selection of Documents 615

Figure 43: A list of donors who sponsored Max Liebermann’s painting of Klein’s portrait in 1912 [Hillebrand].

616 Appendix: A Selection of Documents

Figure 43: A list of donors who sponsored Max Liebermann’s painting of Klein’s portrait in 1912 [Hillebrand]. Appendix: A Selection of Documents 617

Figure 43: A list of donors who sponsored Max Liebermann’s painting of Klein’s portrait in 1912 [Hillebrand]. 618 Appendix: A Selection of Documents

11) Virgil Snyder from Ithaca (New York) to Felix Klein, a letter, dated July 4, 1924, concerning the International Congress of Mathematicians in Toronto, Canada from 11 August to 16 August 1924.42

Dear Mr. Privy Councilor, My sincerest thanks for your kind letter, which arrived here just as I had to go to the hospital for an operation. I would now like to return your greetings and, at the same time, explain my position regarding the upcoming Congress in Canada. It was during my stay in Rome two years ago that I first learned that the next Congress would be held in the United States, but I heard nothing then about the participation or non-participation of various nations. As far as I know, the matter was never discussed by the American Mathematical Society; it certainly, in any case, never came to a vote. Professor R.C. Archibald,43 who was in Rome at the same time, and I made plans to invite at least some of the mathematicians who would participate in the Congress to give lectures, after its conclusion, at our universities, perhaps in the form of shorter courses that could be taught in a few weeks. In this way, we hoped that the students and faculty at our universities could get to know these men and that we could ease the financial burden of the long journey for the mathematicians themselves. It will interest you to hear that Castelnuovo, Enriques, Levi-Civita, Segre, and Severi,44 to whom I communicated this plan, found it extremely acceptable, and each of them wished that such invitations would also be sent to representatives from Central Europe. I never learned why the financial support that was initially promised to us was then withdrawn, but this made it necessary to cancel the American invitations. As soon as the invitation from Canada arrived and was accepted, I presented our plan (Archibald’s and mine) to the chairman of the Committee of the Cana-

42 [UBG] Cod. MS. F. Klein 11: 1040A (the original letter, written in German, is published in TOBIES 2019, pp. 521–23). Snyder had spent four semesters (1892/93 to 1894) attending Klein’s lecture courses, and he twice lectured in Klein’s seminar. On the basis of Snyder’s presentation on sphere geometry ([Protocols] vol. 11, pp. 265–73), Klein steered him toward his dissertation: “Ueber die linearen Komplexe der Lie’schen Kugelgeometrie” [On the Li- near Complexes of Lie’s Sphere Geometry] (1895). As of 1910, Snyder was a full professor at Cornell University (Ithaca, New York). Following in Klein’s footsteps, he concentrated his research primarily on the field of algebraic geometry. See also PARSHALL/ROWE 1994. 43 The Canadian-born Raymond Clare Archibald (as of 1908 at Brown University, Rhode Is- land, USA) had completed his doctorate in 1900 with Theodor Reye in Straßburg. 44 About these Italian mathematicians, Klein wrote: “The general algebraic problem of biratio- nal transformation of surfaces was then developed further [after Clebsch and M. Noether], especially by the young Italian school, to which belonged Segre, Veronese, Enriques, Castel- nuovo, and Severi” (KLEIN 1979 [1926], p. 295). Appendix: A Selection of Documents 619 dian Congress, Professor J.C. Fields45. He approved it and asked me to develop it further, etc. There was no talk about restricting the invitations. I then sent inquiries to the universities of Chicago, Harvard, and Cornell. From Chicago I received the news that participation in the Congress would be restricted. I was asked to abandon my plan because it would only serve to embar- rass the Canadian committee. When I asked for further clarification, I received a long letter from Professor Dickson.46 He wrote that the whole world was aware of the situation – why rustle everything up again? But at the meeting of the Mathematical Society in New York soon thereafter, nobody knew anything about it. I spoke with about forty partici- pants. After a long discussion with Mr. Fields, however, I realized that I could not carry out my plan and I gave it up. Yet now I have an opportunity to implement something that is very dear to my heart. Various American organizations (the Mathematical Society, the Physi- cal Society, the National Academy, etc.) were asked to appoint representatives to form the American group of the International Mathematical Union. Of these representatives – seventeen in all – three have now been elected as delegates to To- ronto. The elected delegates are Coble, Richardson,47 and Snyder. We were asked to submit the following proposal: “Resolved that the Interna- tional Mathematical Union request the International Research Council to consider whether the time is ripe for removing the restrictions on membership in the Inter- national Union, now imposed by the rules of that Council.”48 Should this matter not be considered, we have decided to withdraw completely from the [Mathematical] Union.49 In the hope that you are back in good health, and with best regards to you, I am Your devoted Virgil Snyder

45 The aforementioned Fields Medal donor, see Section 8.2.2. In the winter semester 1894/95, John Charles Fields had attended Felix Klein’s lectures on number theory ([UBG] Cod. MS. F. Klein 7E, p.175v) and participated in his seminar without giving a lecture. 46 Primarily an expert in algebra and number theory, Leonard Eugene Dickson had studied at the University of Chicago under H. Maschke, O. Bolza, and E.H. Moore. Dickson had also spent time studying under Sophus Lie in Leipzig and C. Jordan in Paris. He was aware of the anti- German attitude that then prevailed among French mathematicians. See also Section 9.1.1. 47 Regarding A.B. Coble, see also Section 6.3.1. R.G.D. Richardson had studied in Göttingen, before earning his doctorate from Yale (1906). He became a professor at Brown University. 48 This quotation appears in English in the letter. 49 The proposal made by the American delegates in Toronto in 1924 was supported by partici- pants from Denmark, Great Britain, Italy, the Netherlands, Norway, and Sweden. Snyder, the president of the American Mathematical Society in 1927/28, also served as a delegate at the 1928 Congress in Bologna, where German mathematicians were once again allowed to participate, though not without heavy resistance from nationalistically minded mathematicians (see SIEGMUND-SCHULTZE 2016a). 620 Appendix: A Selection of Documents

Figure 44: The certification of Felix Klein’s election as a foreign associate of the National Academy of Sciences of the United States of America, April 21, 1898 ([UBG] Cod. MS. F. Klein 114: 22).

Appendix: A Selection of Documents 621

12) David Hilbert’s eulogy for Felix Klein, delivered at the session of the Göttin- gen Mathematical Society held on June 23, 1925, one day after Klein’s death.50

Ladies and Gentlemen. Allow me to say a few words before today’s agenda begins. Our dear teacher, colleague, and friend Felix Klein passed away gently in his sleep last night. His end was peaceful and painless; it did not come as a surprise but was long foreseen. Now that it is here, however, the event has touched us all deeply and has shocked us all in the most painful way. For until that moment, Felix Klein was still with us; we could visit him, listen to his advice, and see how vivaciously he participated in matters of all sorts. Now this is over. A great spirit, a strong will, and a noble character has been taken from us. – This is not the place to pay tribute to Klein; no such tribute could be made in just a few words. For his activity and work were so varied and so enormous that it is impossible to focus on any single aspect. It is even impossible to decide whether he was most effective as a teacher, as a researcher, or as a personality. As a teacher, we commemorate here above all his brilliant presentations and lectures. But if we want to identify his great feature, we would have to describe how, in contrast to the prevailing trend toward abstraction and formal aspects, he always emphasized what was intuitive [das Anschauliche] and applicable, thus expressing and underscoring the multifaceted nature of mathematics. And with this tendency he was successful, despite strong countercurrents. And the scientific sign in which he conquered was the name Riemann,51 which he wrote onto his banner. As far as Klein the researcher is concerned, there is hardly a single mathematical field that has not been cultivated by him. Especially geometry and, in particular, geometric function theory. It was precisely the most profound theorems about uniformization that he first foresaw; he also provided the bases for the proofs, and today the whole structure stands strong, elaborated by his students.52 He used the remaining energy of his final years to give us an especially precious gift: the three volumes of his collected works, a prime example of how to edit the works of a scholar.53 Yet even if Klein’s activities for the world and for science may be the main issue, for us there is still the essential question of what he created for Göttingen: a new golden era [Blütezeit], and for this he not only laid the foundations but also issued the guidelines for how to perpetuate it into the future. Everything that you see here is the product of his personality: the reading room, the model collection, the […] institutes, the appointments, the goodwill of the ministry, the important figures from industry whom he won over [as Göttingen’s patrons]. We owe this to

50 [UBG] Cod MS. Hilbert 575: No. 3. 51 An allusion to the Latin expression “In hoc signo vinces” [In this sign thou shalt conquer]. 52 See Section 5.5.4. 53 KLEIN 1921/1922/1923. 622 Appendix: A Selection of Documents his personality, through which he always and everywhere had success on his side. But what was it about his personality that led to such success? The secret to his success lay in his incorruptible objectivity. Grand goals, never petty or personal ancillary goals. Thus did Klein also bequeath his spirit to us, so that we might continue to work in his spirit. Let us continue as long as this spirit does not fade away.

Figure 45: Felix and Anna Klein’s gravestone in Göttingen’s old city cemetery (photograph courtesy of Dr. W. Mahler).

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Figure 46: Felix Klein’s diploma for his honory doctorate (doctoris rerum politicarum dignitatem et ornamenta) from the University of Berlin, April 25, 1924. ([UBG] Cod. MS. F. Klein 113: 10)

INDEX OF NAMES

In the index, “DMV” denotes a member of the German Mathematical Society, “Enc” denotes a contributor to the ENCYKLOPÄDIE, and “Enc(f)” indicates a contributor to the French edition of the ENCYKLOPÄDIE (Encyclopédie des sciences mathématiques pures et appliquées). Names appearing in figures are included in the index only if they appear elsewhere in the book or if they belong to particularly important mathematicians.

Abbe, Ernst 1840–1905, physicist, math., Anisimov, Vasily A. 1860–1907, Russian entrepreneur, DMV: 35, 438, 565, 590. math.: 603, 604 Abel, Niels Henrik 1802–1929, Norweg. Appell, Paul 1855–1930, French math., math.: vii, 25, 47, 63, 67-69, 80, 98, Enc(f): 268, 352, 495, 579, 613-14 108, 153, 178, 180, 216, 228, 261, 264, Archenhold, Friedrich Simon 1861–1939, 272, 292, 298, 309, 322, 339, 344, 366, astr., DMV: 369 392, 405, 457, 580, 607, 610 Archibald, Raymond Clare 1875–1955, Abraham, Max 1875–1922, theor. physicist, Canadian-American math., hist., DMV: DMV, Enc: 44, 394, 465, 542 347, 618 Ackermann-Teubner, Alfred Gustav Bene- Argelander, Friedrich Wilhelm 1799–1875, dictus 1857–1941, publisher, DMV: astronom: 30, 31 215, 300, 301, 303, 304, 305, 306, 307, Aronhold, Siegfried 1819–1884, math.: 48, 429, 612, 614, 624 53, 119 Afanasyeva (md. Ehrenfest), Tatyana A. Artin, Emil 1898–1962, Austrian math., 1876–1964, Russian math., Enc: 433 DMV: 536 Ahrens, Wilhelm 1872–1927, math., DMV, Ascoli, Giulio 1843–1896, Ital. math.: 153 Enc: 428 Assmann, Richard 1845–1918, meteorolo- Airy, George Biddell 1801–1892, British gist: 451-52 math., astronom: 470 Asthöwer, Fritz 1835–1913, eng.: 422 Aleksandrov, Pavel S. 1896–1982, Russian Augustus, né Gaius Octavius 63 BC–14 AD, math., DMV: 533, 538, 649 Roman emperor: 396 Alekseyevsky, Vladimir P. 1858–1916, Baade, Walter 1893–1960, astronom, DMV: Ukrainian math.: 393 535, 536 Althoff, Friedrich 1839–1907, Prussian Bach, Carl von 1847–1931, eng.: 304, 614 official: 7, 83, 86, 233-34, 242, 318- Bacharach, Isaak 1854–1942, math., DMV: 19, 331-32, 335-36, 354-55, 359-60, 204 363-64, 366, 373-75, 377-81, 384, 387, Bäcklund, Albert Victor 1845–1922, Swe- 401, 407-08, 410-14, 419, 421-23, 434, dish math., DMV: 136 438, 440-46, 451, 488, 491, 500-01, Baeyer, Adolf (as of 1885 Ritter von) 1835– 510-12, 519, 546, 581, 605-06, 612, 1917, chem.: 379, 560 626, 633, 642, 649 Ball, Robert Stawell 1840–1913, Irish math., Amelung, Julius *1864, stud., teacher: 201 astromomer: 150, 330, 353 Ameseder, Adolf 1858–1891, Austrian Baltzer, Richard 1818–1887, math.: 102, math.: 231, 248 311-12, 596 Amsler-Laffon, Jakob 1823–1912, Swiss Barkhausen, Heinrich 1881–1956, physicist: math., eng.: 146 466, 614

656 Index of Names

Barnum, Charlotte Cynthia 1860–1934, Berry, Arthur 1862–1929, British math., American math.: 413 DMV: 334, 613-14 Bartling, Friedrich Gottlieb 1798–1875, Bertheau, Ernst 1812–1888, orient.: 90 botanist: 89 Bertini, Eugenio 1846–1933, Italian math.: Battaglini, Giuseppe 1826–1894, Italian 153, 157 math.: 40, 41, 44, 76, 87, 153-56 Bertrand, Joseph 1822–1900, French math.: Bauer, Gustav 1820–1906, math., DMV: 84, 312, 351, 572, 596 124, 172-73, 193-94, 209, 241, 598 Berzolari, Luigi 1863–1949, Italian math., Bauer, Max 1844–1917, mineral.: 115 Enc: 431 Bauernfeind, Karl Maximilian (Max) von Bessel-Hagen, Erich 1898–1946, math., 1818–1894, geodesist: 171, 173, 206, DMV: 281, 536-37 598 Betti, Enrico 1823–1892, Ital. math.: 154, Baumgart, Oswald, math.: 230 156-157, 199, 623 Bauschinger, Johann 1834–1893, math., Beumer, Wilhelm 1848–1929, teacher, construction eng.: 172-73, 201 politician: 422 Bauschinger, Julius 1860–1934, astronom, Bezold, Wilhelm von 1837–1907, physicist, DMV, Enc: 201, 557, 559-60 meteorol.: 202-03 Bayer, Friedrich 1851–1920, entrepreneur: Bianchi, Luigi 1856–1928, Italian math.: 561 195, 198, 200-01, 210, 214, 359, 576, Bechmann (as of 1891 Ritter von), August 585, 612, 614 1834–1907, legal scholar: 144 Bieberbach, Ludwig 1886–1982, math., Becker, Carl Heinrich 1876–1933, oriental., DMV, Enc: 428, 457, 491, 505, 522, politician: 531-34 550, 555, 560, 607-08, 614, 639 Beer, August 1825–1863, math., physicist, Biedermann, Paul *1862, math., PhD with chemist: 596 Klein: 67, 226, 230, 293, 311, 614 Beetz (as of 1876 von), Wilhelm 1822– Biot, Jean-Baptiste 1774–1862, French 1886, physicist: 172, 173 math.: 37 Behnke, Heinrich 1898–1979, math., DMV: Bischof, Johann N. 1827–1893, math.: 172- 64, 546, 564, 625, 631 73, 175, 212 Behrendsen, Otto 1850–1921, Gymn.-Prof.: Bischof, Karl Gustav 1792–1870, geo- 392-93, 398, 614, 636 chemist: 32 Behrens, Wilhelm 1885–1917, math., PhD Bismarck, Otto von 1815–1898, politician: with Klein, DMV: 491, 517, 614 28, 84, 329, 499, 511 Beke, Emanuel (Manó) 1862–1946, Hunga- Blake, Edwin Mortimer 1868–1955, Ame- rian math., DMV: 393, 493, 527 rican math.: 404 Beltrami, Eugenio 1835–1900, Italian math.: Blaschke, Wilhelm 1885–1962, Austrian 54, 87, 102-03, 154-56, 247, 256, 348, math., DMV: 131, 387, 433, 523, 547- 382, 634 48, 623, 636 Beman, Wooster Woodruff 1850–1922, Blumenbach, Johann Friedrich 1752–1840, American math., DMV: 399, 635 zoologist, anthropol.: 45 Beneke, Carl Gustav 1800–1864, pastor: Blumenthal, Otto 1876–1944, math., DMV: 481 v, 57-58, 394, 436, 453-54, 461, 543- Beneke, Friedrich Eduard 1798–1854, phi- 44, 559, 565, 612, 614, 626, 644 losopher: 481-82, 485-86 Bobek, Karl 1855–1899, Austrian math., Benfey, Bruno 1891–1962, pastor: 170 DMV: 230, 248 Benfey, Theodor 1809–1881, orient.: 362 Bôcher, Maxime 1867–1918, American Bernays, Paul 1888–1977, math., DMV: math., PhD with Klein, DMV, Enc: 536 100, 302, 334, 344, 345-46, 372, 393, Berneker, Erich 1874–1937, Slavicist: 532 405, 455, 612, 614, 625 Bernstein, Felix 1878–1956, math., DMV: Bödiker, Tonio 1843–1907, Prussian 168, 302, 394, 420, 480, 487, 490-92, official: 439 516, 534, 614, 649 Index of Names 657

Boehm, Karl 1873–1958, math., DMV: 237, Brater (md. Sapper), Agnes 1852–1929, 426 writer: 163 Boelitz, Otto 1876–1951, pedag., politician: Brater, Karl Ludwig Theodor 1819–1869, 555 publicist: 163 Börnstein, Richard 1852–1913, physicist: Brater (neé Pfaff), Pauline 1827–1907: 163 97 Brauer, Richard 1901–1977, math., DMV: Böttger, Adolf, math., teacher: 230, 232 289 Böttinger (as of 1907 von), Henry Theodore Braun, Wilhelm *1852, Math., PhD with 1848–1920, industrialist: 422-24, 439- Klein: 133, 136 41, 443-44, 449, 451-53, 500, 502, 512, Braune, Christian 1831–1892, anatomist: 561, 582, 613-14, 637 310, 313 Bohlmann, Georg 1869–1928, math., actua- Bravais, Auguste 1811–1863, French phy- ry, DMV, Enc: 393, 419-20, 447, 614, sicist, crystallographer: 356 636 Brendel, Martin 1862–1939, astronom, Bokowski, Adalbert 1899–1948, math., DMV: 420, 447, 465, 478, 614 DMV: 536 Bretschneider, Wilhelm 1847–1931, math., Boltzmann, Ludwig 1844–1906, Austrian teacher, prof., PhD with Klein, DMV: physicist, DMV, Enc: vii, 119, 306, 108, 133-35, 614 364-65, 379, 426, 450, 482, 489, 512, Brill (as of 1897 von), Alexander 1842– 591, 632, 637 1935, math., DMV: 47-50, 53, 87, 119- Bolyai, János (Johann) 1802–1860, Hunga- 20, 161, 173-77, 191, 193, 195, 202-04, rian math.: 70, 72-73, 101-02, 126, 206-07, 209-10, 212, 221, 227, 249, 250, 579-80, 642 264, 270, 372, 386, 451, 555, 613-14 Bolza, Oskar 1857–1942, math., DMV: Brill, Ludwig, publisher: 108, 175, 206 168, 337, 365, 402, 404, 415, 614 Brioschi, Francesco 1824–1897, Italian Bolzano, Bernhard 1781–1848, Bohemian math.: 153-54, 157, 180-84, 186, 189, math., philosopher, theologian: 139 209, 288, 575 Boole, George 1815–1864, Engl. math.: 56 Brouwer, Luitzen 1881–1966, Dutch math., Borchardt, Carl Wilhelm 1817–1880, math.: DMV: 57- 58, 279-80, 457, 522-23, 63-64, 247, 267, 282, 284, 337-38, 365, 572, 613-14, 652 411 Bruhns, Karl Christian 1830–1881, astrono- Borel, Émile 1871–1956, French math., Enc, mer: 222 Enc(f): 302, 430, 452, 613-14 Brunel, Georges 1856–1900, French math., Born, Max 1882–1970, physicist, DMV, Enc: 10, 230, 244-45, 268, 270 Enc: viii, 301, 357, 394, 439, 473, 544, Bruns, Heinrich 1848–1919, math., astr., 562, 577, 582, 614, 626 DMV: 67, 114, 222, 229-30, 308, 371, Bortkiewicz, Ladislaus von 1868–1931, 614, 648 Polish-Russ. statistician, Enc: 419 Bryan, George Hartley 1864–1928 British Bosse, Robert 1832–1901, lawyer, poli- applied math., Enc: 432 tician: 400, 438 Buchheim, Arthur 1859–1888, British math.: Bosworth (md. Focke), Anne Lucy 1868– 150, 230, 244 1907, American math.: 393 Budde, Emil A. 1842–1921, physicist: 42, Boulanger, Auguste 1866–1923, French 614 math., Enc(f): 333 Büttner, Friedrich 1859–1915, math., Boussinesq, Valentin Joseph 1842–1929, teacher 230, 268 French math., physicist: 430, 467 Burkhardt, Heinrich 1861–1914, math., Boutroux, Pierre 1880–1922, French math., DMV, Enc: 172, 263, 331-32, 338-41, Enc(f): 613-14 360, 366, 369-70, 384, 392, 394, 402- Boyd, James H. 1862–1946, American 03, 417, 429-30, 463, 606, 613-14, 638 math.: 334 Burnside, William 1852–1927, Engl. math.: Branford, Benchara 1867–1944, Scottish 283, 624 math., : 302, 584 658 Index of Names

Busch, Wilhelm 1832–1908, poet, illus- 124-26, 128-29, 132-34, 136-37, 139- trator: 163 40, 153, 155-56, 158-60, 162, 173, 185, Campbell, George Ashley 1870–1954, Ame- 191-92, 198, 209, 212, 216-17, 221, rican math.: 345, 399, 466 223, 249, 260, 264-65, 299, 330, 334, Cantor, Georg 1845–1918, math., DMV: 338, 358, 361, 379, 404, 477-79, 482, 54, 64, 130, 192, 239, 361, 367-72, 510, 526, 546, 569-70, 574-76, 578, 374, 454, 483, 491, 511, 525, 538, 569, 589, 596-97, 608, 611, 618, 627, 638, 627, 631, 642 642, 647, 650, 652 Cantor, Moritz 1829–1920, math. historian, Clifford, William Kingdon 1845–1879, DMV: 208, 303-04, 306, 479, 495 Engl. math.: 4, 48, 103, 148-49, 152, Capelli, Alfredo 1855–1910, Italian math.: 192 402 Coble, Arthur Byron 1878–1966, American Carathéodory, Constantin 1873–1950, Greek math.: 339, 619 math., DMV: 1, 4, 57, 123, 327, 390, Cohn-Vossen, Stephan 1902–1936, math., 465, 480, 522, 523, 524, 528, 532, 536, DMV: 237, 257, 539, 632 537, 568, 613-14, 626 Cole, Frank Nelson 1861–1926, American Cartan, Élie Joseph 1869–1951, French math., PhD with Klein: 231, 246, 290, math., Enc(f): 131, 352, 646-47 337, 613-14 Casorati, Felice 1835–1890, Italian math.: Collatz, Lothar 1910–1990, math., DMV: 154, 596 448-50, 627 Cassirer, Ernst 1874–1945, philosopher: Columbus, Christopher ca. 1451–1506, Ita- 131, 244, 625 lian explorer: 401 Castelnuovo, Guido 1865–1952, Italian Comba, Paul G. 1926–2017, Italian-Ameri- math., Enc: 431, 585, 613-14, 618, 623 can amateur astronomer: 27 Cauchy, Augustin-Louis 1789–1857, French Copley, Godfrey Sir 1653–1709, English math.: 44, 217, 223, 295, 410, 412, landowner: 38, 151, 354, 518 569, 579 Cornelius, Hans 1863–1947, philos.: 231 Cauer (née Schelle), Wilhelmine (Minna) Courant, Richard 1888–1972, math., DMV: 1841–1922, educator: 506 vii, 117, 421, 480, 523-25, 536-37, 539, Cayley, Arthur 1821–1895, British math.: 4, 547, 555, 559, 563, 566-67, 585-86, 37, 47-48, 52, 54, 66, 70-73, 87, 90, 614, 627, 643 101-03, 147-52, 190, 192, 199, 204, Cram (md. Klein), Myrthel, American 211, 214, 242, 290, 314-15, 334, 348, daughter-in-law of F. Klein: x, 166 353, 416, 473, 570, 575, 585, 599 Crelle, August Leopold 1780–1855, math.: Chasles, Michel 1793–1880, French math.: 63, 628 50, 68, 74-75, 79, 84, 105, 108, 130, Cremona, Luigi 1830–1903, Italian math., 192, 197, 241 DMV: 7, 38, 52, 87, 108, 154-58, 190, Chebyshev, Pafnuty L. 1821–1894, Russian 206, 216, 246, 339, 348, 382, 408, 468, math.: 177, 250, 355, 436, 485-87 495, 569, 595-96, 623, 627, 633, 639 Chisholm (md. Young), Grace 1868–1944, Culmann, Karl 1821–1881, German-Swiss Engl. math., PhD with Klein: xix, 302, eng.: 73, 468 354, 393-94, 399, 413-16, 429, 522, Czapski, Siegfried 1861–1907, physicist: 529-30, 538, 547, 576, 631, 640, 653 114 Christoffel, Elwin Bruno 1829–1900, math.: Czermak, Johann Nepomuk 1828–1873, 120, 264, 434, 494 physiologist: 219 Cicero, Marcus Tullius 106–43 BC, Roman Czuber, Emmanuel, 1851–1925, Austrian statesman, philos.: 23 math., DMV, Enc: 495 Clausius, Rudolf 1822–1888, physicist: 147 Dalwigk, Friedrich von 1864–1943, math., Clebsch, Alfred 1833–1872, math.: 2-3, 6, DMV: 393 9, 10, 12, 17, 32, 37, 39-40, 45-55, 57- Darboux, Gaston 1842–1917, French math.: 59, 61-65, 67-69, 74-75, 77, 88-93, 95- 6, 14, 44, 74-76, 80, 83-85, 87, 96, 99, 98, 100-02, 106-11, 113, 116, 118-20, 100, 102, 107-08, 120, 123, 126-27, Index of Names 659

132, 138, 161, 181, 192, 195-96, 209, Dove, Richard Wilhelm 1833–1907, Canon 213, 244-45, 250, 254, 268, 270, 292, Law scholar: 88, 499 311-12, 322, 333, 397, 411, 428, 503, Drenckhahn, Friedrich 1894–1977, math., 512, 525, 529, 573, 575, 579-80, 583- pedag., DMV: 505, 536 84, 595-96, 613-14, 623, 627, 630, 643 Dressler, Heinrich, math. teacher, author: Darwin, Charles Robert 1809–1882, British 230, 232, 262, 614 biologist: 36, 205, 591, 633 Du Bois-Reymond, Emil Heinrich 1818– Darwin, George Howard 1845–1912, British 1896, physiologist: 62, 65, 496, 628 astronomer, Enc: 353, 613-14 Du Bois-Reymond, Paul 1831–1889, math.: Debye, Peter 1884–1966, Dutch physicist, 65, 220, 237, 322, 330, 489 DMV, Enc: 327, 480, 562, 623, 645 Duhamel, Jean-Marie Constant 1797–1872, Decoster, Paul 1886–1939, Belgian philoso- French math., physicist: 595-96 pher: 491 Dühring, Eugen 1833–1921, philos.: 116 Dedekind, Richard 1831–1916, math., Duisberg, Carl 1861–1935, chemist, indus- DMV: 51, 94, 108, 184-85, 232, 249, trialist: 498, 561-63, 614, 637 264, 282, 284, 341-42, 344, 359, 366, Dupin, Charles 1784–1873, French math., 405, 613-14, 643, 645 eng.: 80, 99, 609 Dehn, Max 1878–1952, math., DMV, Enc: Durège, Heinrich 1821–1893, math.: 296, 95, 338, 395, 614, 627, 640 596 Des Coudres, Theodor 1862–1926, physi- Dyck (as of 1901 Ritter von), Walther 1856– cist: 229, 424, 439, 449, 636 1934, math., PhD with Klein, DMV, Despeyroux, Théodore 1815–1883, French Enc: 7, 56-57, 87, 151, 177, 193-95, math., physicist: 397 200, 204, 208, 210-11, 219, 223, 225- Deussen, Gustav Adolf Hugo *15.10.1837, 27, 230, 233-34, 260-61, 266, 270, 285, religion teacher: 23 296, 299, 303-05, 308, 311, 339-40, Dickson, Leonard Eugene 1874–1954, 367, 369-72, 375, 381, 393, 401-02, American math.: 619 410, 426, 429, 430, 433, 447-48, 475, Dickstein, Samuel 1851–1939, Polish math., 493, 503, 512-13, 516, 519-21, 543, math.hist., DMV: 130, 613-14 557, 566-67, 578, 613-14, 628, 632 Diekmann, Joseph 1848–1905, math., PhD Ebert, Hermann 1861–1913, physicist: 169, with Klein: 107, 113 614 Diels, Hermann 1848–1922, classical scho- Ehlers, Ernst 1835–1925, zoologist: 135, lar: 444, 513 150, 613 Diestel, Friedrich 1863–1925, math., libra- Ehlers, J., student: 399 rian, DMV: 392, 394, 614 Ehrenfest, Paul 1880–1933, Austrian physi- Diesterweg, Adolph 1790–1866, educator: cist, Enc: 426, 433 531 Ehrenfeuchter, Friedrich 1814–1878, theolo- Dingeldey, Friedrich 1859–1939, math., gian, University prof.: 90 PhD with Klein, DMV, Enc: 230, 232, Ehrensberger, Emil 1858–1940, chemist, 262, 309, 614 industry manager: 440, 561, 614 Dini, Ulisse 1845–1918, Italian math.: 157, Einstein, Albert 1879–1955, physicist, 199 DMV: ix, 44, 57, 168, 235, 394, 396, Dirichlet [Lejeune Dirichlet], Peter Gustav 472, 490, 513, 525, 535, 538-544, 549, 1805–1859, math.: vii, 9, 32, 45, 62, 560, 569, 578, 591, 628, 632, 643, 650 69, 92, 254, 258, 261-63, 271, 276, Eisenstein, Gottlob 1823–1852, math.: 199 288, 328, 359-60, 399, 479, 491, 523, Elster, Ludwig 1856–1935, economist, 545, 600, 640 senior officer: 518 Domsch, Paul 1860–1918, math., PhD with Eneström, Gustaf 1852–1923, Swedish Klein, DMV: 100, 230-31, 264-65, 310 math., hist., DMV: 232, 304-05, 474, Donadt, Alfred *1857, math., teacher: 219 479 Dove, Heinrich Wilhelm 1803–1879, physi- Engel, Friedrich 1861–1941, math., DMV: cist, meteorologist: 69, 88 68, 77, 81, 104, 128, 231, 233, 239, 660 Index of Names

240, 287, 303, 313, 320, 349, 478, 578, Finsterwalder, Sebastian 1862–1951, math, 614, 623, 638 DMV, Enc: 49, 174, 176, 368, 451, Engels, Hubert 1854–1945, hydraulic eng.: 629 467 Fischer, Emil 1852–1919, chemist: 560 Enneper, Alfred 1830–1885, math.: 18, 93, Fischer, Gottlob, math., Klein’s first assis- 95, 120, 238, 317-18, 331, 599-600, tent: 177 602 Fischer, Otto 1861–1916, math., physiolo- Enriques, Federigo 1871–1946, Italian gist, PhD with Klein, DMV, Enc: 226, math., math.hist., Enc: 103, 302, 352, 289, 311, 313, 614 399, 431, 492, 613, 618 Fleck, Ludwik 1896–1961, Polish and Israeli Epsteen, Saul *10.8.1878, American math., physician, biologist: 8 DMV: 394 Fleischer, Hermann, math., PhD Göttingen, Epstein, Paul 1871–1939, math., DMV: DMV: 394 222, 614 Flender (née Klein), Aline Leonore 1847– Errera, Alfred 1886–1960, Belg. math.: 491 1914, F. Klein’s sister: x, 21 Escherich, Gustav von 1849–1935, Austrian Flender, Hermann August 1839–1882, ma- math., DMV: 426-27 nufact., F. Klein’s broth.-in-law: x, 21 Euclid, ca. 300 BC, Greek math.: 44, 70-72, Föppl, August 1854–1924, mech., DMV, 101, 103, 105, 116, 126, 143, 149, 183, Enc: 222-23, 368, 390, 449, 468, 614 351, 479, 485, 491, 496, 629 Föppl, Ludwig 1887–1976, math., mech., Euler, Leonhard 1707–1783, Swiss math.: DMV: 223, 390, 614 9, 114, 160, 240, 471, 479, 594, 596, Förster, Wilhelm 1832–1921, astronomer: 626 369, 376, 528, 603 Faltings, Gerd *28.7.1954, math., DMV: Ford, Lester Randolph 1886–1967, Ameri- 460 can math.: 255, 629 Fano, Gino 1871–1952, Italian math., DMV, Forsyth, Andrew Russell 1858–1942, British Enc: 10, 41, 130-31, 154, 393, 399, math.: 103, 258, 353-54, 413, 575 447, 648 Fourier, Jean Baptiste Joseph 1768–1830, Fanta (Fanla), Ernst 1878–1936, Austrian French math.: 48, 94, 146, 195, 237, math., DMV: 394 241, 293, 407 Faraday, Michael 1791–1867, British physi- Fraenkel, Abraham A. 1891–1965, German- cist: 410 born Israeli math., DMV: 12, 478, 525, Fedorov, Evgraf S. 1853–1919, Russian 581, 591, 629 math., mineralogist: 6, 356 Frahm, Wilhelm 1849–1875, math.: 191 Fehr, Henri 1870–1954, Swiss math., DMV: Franck, James 1882–1964, phycisist: 562 493-94, 507, 517, 549-50, 613-14, 629 Franklin, Fabian 1853–1939, American Fellmann, Emil 1927–2012, Swiss science math., DMV: 290, 334, 360, 404, 412- historian: 13 13, 613-14 Fermat Pierre de 1607–1665, French poly- Frege, Gottlob 1848–1925, logician, DMV: math., lawyer: 381 56 Fick, Richard 1867–1944, librarian: 380 Fresnel, Augustin Jean 1788–1827, French Fiedler, Ernst 1861–1954, Swiss math., PhD physicist, eng.: 206, 611 with Klein, DMV: 231, 248, 293, 614 Freundlich (Finley-Freundlich), Erwin Fiedler, Wilhelm 1832–1912, German-Swiss 1885–1964, math. astron., DMV: 491 math., DMV: 41, 71, 102, 248, 349, Freytag (md. Loeschcke), Thekla 1887– 652 1932, teacher: 418, 506, 650 Fields, John Charles 1863–1932, Canadian Fricke (née Flender), Leonore 1873–1912, math., DMV: 460, 613-14, 619 Klein’s niece: x, 21 Fine, Henry Buchard 1858–1928, Americ. Fricke, Robert 1861–1930, math., PhD with math., PhD with Klein: 231, 246, 407 Klein, DMV, Enc: ix, x, 4, 11, 13, 21, 169, 184, 189, 196, 200, 226, 231-32, 258, 272-73, 279-81, 290-91, 293-95, Index of Names 661

297-98, 341-44, 367, 375-77, 384, 388, Geibel, Emanuel 1815–1884, poet: 362 392, 394, 397, 402, 417, 426, 437, 454- Geiringer (md. Pollazcek, md. von Mises), 57, 465, 544-46, 565, 572, 579, 581, Hilda 1893–1973, Austrian-American 604, 607, 610, 613-14, 624, 630, 636 math., DMV: 417 Friedrich, Georg *1860, math. PhD with Geiser, Carl Friedrich 1843–1934, Swiss Klein: 231, 293 math.: 87 Friedrich Wilhelm III 1770–1840, King of Geißler, Heinrich 1814–1879, glass blower, Prussia: 28 mechanic: 34, 36, 628 Friedrichs, Kurt Otto 1901–1983, math., Gentry, Ruth 1862–1917, American math.: DMV: 584 412 Friesendorff, Theophil 1871–1913, Russian Gerbaldi, Francesco 1858–1934, Italian math., eng., DMV: 301 math., DMV: 154, 231, 247, 285 Frobenius, Georg 1849–1917, math., DMV: Gerber, Carl von 1823–1891, Saxon Minis- 66, 108, 357, 372, 374-378, 427-28, ter of Culture: 211, 216, 218, 315, 319 457, 461, 523, 587, 605, 611, 632 Gerber, Heinrich 1832–1912, eng.: 471 Fröbel, Friedrich 1782–1852, pedag.: 531 Gernet, Nadezhda N. 1877–1943, Russ. Fuchs, Lazarus 1833–1902, math., DMV: 4, math., DMV: 372, 396, 613, 615 6, 64, 97, 181, 247, 253, 267, 274, 282, Gibbs, Josiah Willard 1839–1903, American 284-85, 318, 342-44, 355, 365, 373-76, physicist: 406-07, 637 436, 454-57, 603 Gibbs, Oliver Wolcott 1822–1908, Ameri- Fueter, Rudolf 1880–1950, Swiss math., can chemist: 408, 620 DMV: 580, 613, 615 Gierster, Josef 1854–1893, math., PhD with Fujisawa, Rikitarō 1861–1933, Japanese Klein, DMV: 177, 188, 195-96, 204, math.: 494, 613, 615, 630 228, 270, 285, 295, 311 Fujiwara, Matsusaburō 1881–1946, Japanese Gilman, Daniel Coit 1831–1908, American math., historian, DMV: 399-400 educator, academic: 315, 407 Furtwängler, Philipp 1869–1940, math., Goeb, Margarethe 1892–1962, teacher: 522 PhD with Klein, DMV, Enc: 389, 417, Göpel, Adolph 1812–1847, math.: 265 458-60, 615 Görres, Joseph 1776–1848, philosopher, Galilei, Galileo 1564–1642, polymath., publisher: 22 astronomer, physicist: 594, 648 Goethe, Johann Wolfgang von 1749–1832, Gallenkamp, Wilhelm 1820–1890, teacher, poet: 23, 30-31, 135, 220 author: 496 Götting, Eduard 1860–1926, teacher, DMV: Galois, Évariste 1811–1832, French math.: 392-93, 398, 615, 636 6, 25, 60, 74, 77, 79, 100, 181, 186, Gontschareff, A., Russian fellow student of 188, 196, 238, 395, 427, 626, 631 Klein: 29 Gauss [Gauß], Carl Friedrich 1777–1855, Gordan, Paul 1837–1912, math., DMV: 47, math., astr.: 1, 9, 30, 45, 72-73, 90, 92, 48, 53-55, 57, 120, 127, 133-34, 137, 94-95, 101, 114, 126, 129, 151, 156-57, 144, 158-60, 178, 182-83, 187-89, 191- 183-85, 263, 288, 295, 301, 366-67, 92, 195, 198, 208-12, 214, 223, 234, 372, 402, 437, 439, 449, 458, 478-79, 242, 248-49, 264-65, 267, 278, 288, 485-86, 491, 525, 559-60, 562, 569, 299, 315, 334, 357-58, 369-72, 377, 571, 600, 610, 642 379, 381, 398, 404, 574, 576, 578, 597, Gauthier-Villars, Albert 1861–1918, French 613, 615, 641 publisher, DMV: 76-77, 192, 409, 429, Goßler, Gustav von 1838–1902, Prussian 464, 596, 627, 634, 643 Minister of Culture: 236, 598 Gay-Lussac, Joseph Louis 1778–1850, Graefe, Walther *26.8.1892, teacher: 390, French chemist, physicist: 203 535 Gegenbauer, Leopold 1849–1903, Austrian Graf, Ulrich 1908–1954, math., DMV: 505 math., DMV: 295-96, 419 Grassmann, Hermann Günther 1809–1877, Gehlhoff, Georg 1882–1931, physicist: 561 math.: 2, 37, 90, 104-05, 107, 120, Gehring, Franz 1838–1884, math.: 30-31 126, 129, 217, 240-42, 301, 303, 312- 662 Index of Names

13, 407, 478, 483, 596, 631, 642, 644, Hankel, Hermann 1839–1873, math.: 124 646, 650 Hankel, Wilhelm Gottlieb 1814–1899, phy- Green, George 1793–1841, British math., sicist: 321 physicist: 343, 479, 494, 517 Hanstein, Johannes von 1822–1880, bota- Greenhill, Alfred George Sir 1847–1927, nist: 31-32 British math., DMV: 343, 354, 430, Hardcastle, Frances 1866–1941, Engl. 479, 493-95, 549-50, 575, 613, 631 math.: 257-59, 354, 417, 634 Griess, Jean French math.: 399 Harkness, James 1864–1923, Engl., Amer., Groth, Paul von 1843–1927, mineralogist: Canad. math., Enc: 184, 258, 417, 630 vii, 379 Harnack (as of 1914 von), Adolf 1851– Grüning, Martin 1869–1932, eng.: 470 1930, theol.: 163, 444, 501, 507, 557 Gruson, Johann Philipp 1768–1857, teacher, Harnack, Axel 1851–1888, math., PhD with math.: 164 Klein: 135-36, 163, 179, 191-92, 212, Guccia, Giovanni Battista 1855–1914, 216, 232, 237, 311, 321, 501, 596 Italian math., DMV: 613, 615 Hartnack, Eduard 1826–1891, optometrist: Günther, Siegmund 1848–1923, math., geo- 36 grapher, math. historian, DMV: 132- Haskell, Mellen Woodman 1863–1948, 34, 172, 577 American math., PhD with Klein, Guilleaume (Freiherr von), Theodor 1861– DMV: 127, 130, 285, 334, 339-41, 1933, entrepreneur: 440 372, 613, 615, 634 Gundelfinger, Sigmund 1846–1910, math., Hauck, Guido 1845–1905, math., DMV: DMV: 191, 208 304, 500, 502 Gutzmer, August 1860–1924, math., DMV: Haussner, Robert 1863–1948, math., DMV: 6, 120, 304, 306, 447, 453, 493-94, 479, 615 498-99, 506, 532, 584, 613, 615, 631, Hayashi, Tsuruichi 1873–1935, Japanese 649 math., hist., DMV: 399, 573 Haber, Fritz 1868–1934, chemist: 557-58 Hecke, Erich 1887–1947, math., DMV, Enc: Hadamard, Jacques 1865–1963, French 184, 508, 515, 523, 537, 544, 615, 623 math.: 613, 615 Hedrick, E. Raymond 1876–1943, American Haeckel, Ernst 1834–1919, zool.: 36, 205, math., DMV: 399 240, 528, 591, 629, 643, 653 Heegaard, Poul 1871–1948, Danish math., Haenisch, Konrad 1876–1925, journalist, DMV, Enc: 81, 95, 338, 393, 395, 399, politician: 526, 552 494, 575, 613, 615, 627-28, 638 Haeseler, Gottlieb Graf v. 1836–1919, Heffter, Lothar 1862–1962, math., DMV: officer: 500, 507 229, 369-70, 402, 473 Hagemann, Eberhard 1880–1958, lawyer, F. Hegel, Friedrich Wilhelm Karl (Ritter von) Klein’s son-in-law: x, 166, 170 1813–1901, hist., Klein’s fath.-in-law: Hahn, Hans 1879–1934, Austrian math., x, 35, 116, 161, 163-65, 167, 637 DMV: 467, 615, 646 Hegel, Georg Wilhelm Friedrich 1770– Hall, G. Stanley 1846–1924, psychol.: 354 1831, philosopher: x, 164, 481 Halphen, Georges Henri 1844–1889, French Hegel, Georg, 1856–1933, Bavarian colonel, math.: 79, 241-42, 249, 267, 269 Klein’s broth.-in-law: x, 166 Hamburger, Meyer 1838–1903, math., Hegel (md. Lommel), Louise Friederike DMV: 604 Caroline 1853–1924, Klein’s sist.-in- Hamel, Georg 1877–1854, math., DMV: law: x, 166 394, 471, 487, 550, 553, 555, 615 Hegel, Maria 1855–1929, Klein’s sist.-in- Hamilton, William Rowan 1805–1865, Irish law: x, 166-67 math.: 104-05, 114, 168, 198, 243, Hegel (née Tucher von Simmelsdorf), Maria 371, 407 Helene Susanne 1791–1855: x, 164 Hammerschmidt (md. Klein), Maria Cathari- Hegel, Sophie Louise 1861–1940, Klein’s na 1787–1871, paternal grandmother of sist.-in-law: x, 166-67, 286, 354, 567 F. Klein: x, 17 Index of Names 663

Hegel (née Tucher von Simmelsdorf), Hilbert, David 1862–1943, math., DMV, Susanne 1826–1878, F. Klein’s mother- Enc: viii, ix, 1, 6, 8-11, 39, 48, 50, 57, in-law: x, 165 65, 87-88, 104, 159, 168, 184, 192, Hegel, Wilhelm Sigmund 1863–1945, gov. 197, 199, 223, 228-29, 231, 235-37, councilor, F. Klein’s broth.-in-law: x, 241-43, 246, 250, 257-58, 263, 269, 166-67 279-81, 286, 303-04, 307, 311, 321, Heimsoeth, Friedrich 1818–1877, class. 324, 327, 331, 333, 346, 349-53, 357- philologist: 35 60, 366, 368-73, 375, 377-78, 383, 385, Heine, Eduard 1821–1881, math.: 119, 596 390-96, 399, 402, 404-05, 417, 421, Heine, Heinrich 1797–1856, poet, writer: 425, 434-36, 439, 441-42, 447, 454-61, ix, 22, 210, 517 465-67, 473, 481, 483-85, 488-90, 497, Heinemann, Käthe *8.5.1889, math., botan., 504, 510-11, 518-19, 522-23, 528-29, pedag.: 535, 537 533, 535, 537-41, 543-47, 549, 553, Hellinger, Ernst 1883–1950, math., DMV, 556, 566, 571-72, 577-84, 586, 587, Enc: 346, 390-91, 615 590, 605-08, 611, 613, 615, 621, 624, Helmert, Robert 1843–1917, geodesist, 629-30, 632, 640-45, 647, 650 DMV, Enc: 304, 615, 648 Hildebrand, Rudolf, math.: 231, 615 Helmholtz, Hermann von 1821–1894, Hillebrand, Meinolf Rudolf *3.3.1937, F. physicist, physician: 64, 94, 96, 112, Klein’s great-grandson: v, x, 13, 17-21, 119, 157, 323, 347, 348, 350-52, 374, 166-67, 414, 520, 568, 614-17, 623 376, 387, 401, 405, 410, 421, 440, 466, Hillebrandt, Alfred 1853–1927, philologist: 468, 484, 525, 560-63, 582, 625, 637 444, 499-500, 531-32 Henneberg, Lebrecht 1850–1933, math., Hinneberg, Paul 1862–1934, hist.: 475, 513 DMV, Enc: 207, 468, 469-70, 615 Hirst, Thomas Archer 1830–1892, British Henrici, Olaus 1840–1918, math., DMV 48, math.: 48 146, 185, 192, 613, 615 Hirzebruch, Friedrich 1927–2012, math., Hensel, Kurt 1861–1941, math., DMV, Enc: DMV: 222, 629 288-89, 615, 637 Hjelmslev (Petersen), Johannes 1873–1950, Herglotz, Gustav 1881–1953, math., DMV, Danish math.: 433 Enc: 346, 466-67, 523, 615 Hobson, Ernest William 1856–1933, British Hermite, Charles 1822–1901, French math.: math., Enc: 613, 615 viii, 6, 56, 131, 180, 183-84, 186, 192, Hoeck, Karl Friedrich Christian 1794–1877, 265, 267-68, 270, 282, 288, 292, 342, hist., philol., librarian: 89-90 346, 352, 358-59, 392, 402, 408, 409- Höckner, Georg 1860–1938, math., actuary: 10, 416, 455, 458-59, 461-64, 509, 569, 230 586, 631, 643 Höfler, Alois 1853–1922, Austrian math.- Herrmann, Oskar *1859, teacher, PhD with didact., philos., DMV: 306, 482, 503, Klein: 228, 230 613, 615, 632 Herrmann, Theodor, math.: 230 Hölder, Otto 1859–1937, math., DMV, Enc: Herschel, John 1792–1871, Engl. astr.: 258 57, 60, 71, 220-21, 231-34, 238, 246, Hertz, Heinrich 1857–1894, physicist: 371 266-67, 301, 328-36, 361-62, 375, 427, Herz, Norbert 1858–1927, Austrian astrono- 535, 577, 590, 613, 615, 632 mer, DMV: 402 Höpfner, Ernst 1836–1915, pedag., Prussian Heß, Wilhelm 1858–1937, math.: 195, 615 official, curator: 389, 414, 419, 439 Hesse, Otto 1811–1874, math.: 47-49, 139, Hoetzsch, Otto 1876–1946, historian: 533 172, 176, 178, 596-97, 634 Hofmann, August Wilhelm 1818–1893, Hettner, Georg 1854–1914, math., DMV: chemist: 36 256, 317-18, 600-02 Holst, Elling Bolt 1849–1915, Norwegian Heun, Karl 1859–1929, math., DMV, Enc: math.: 70, 137, 191, 324, 633 473, 486, 615 Holzmüller, Gustav 1844–1914, math., Hilb, Emil 1882–1929, math., DMV, Enc: DMV: 462, 497 278, 346, 381, 457, 615 664 Index of Names

Hoppe, Heinrich 1857–1899, math., teacher, Jürgens, Enno 1849–1907, math., DMV: DMV: 230-31, 262 369-70 Hoppe, Reinhold 1816–1900, math., DMV: Jullien, Michel Marie 1827–1911, French 120, 208, 369-70 Jesuit, scholar: 596 Hoüel, Jules 1823–1886, French math.: 75- Jung, Giuseppe 1845–1924, Italian math., 76, 102, 630, 632 Enc: 157, 190, 208 Humboldt, Alexander von 1769–1859, Kamerlingh Onnes, Heike 1853–1926, natural scientist: 569 Dutch physicist, Enc: 431 Humboldt, Wilhelm von 1767–1835, Kant, Immanuel 1724–1804, philosopher: academic: 22 116, 489 Hurwitz, Adolf 1859–1919, math., DMV: Kantor, Seligmann 1857–1903, Austrian 10, 13, 51, 56, 117, 177-78, 183, 192, math.: 230, 248 195-99, 210-11, 214, 223, 225, 227-30, Karagiannides [Carajianides], Athanasios 233-36, 238, 240, 242, 248, 252, 255, 1868–?, Greek math., DMV: 335 260-62, 268, 270-72, 274-75, 284-86, Kármán, Theodore von 1881–1963, Hunga- 291-99, 308-09, 311-12, 314, 316, 320- rian-American math., eng., DMV, Enc: 21, 323, 326-28, 332-33, 339-41, 346, 449, 468, 544, 565, 633 348-49, 353, 355, 357, 359-62, 365, Kasner, Edward 1878–1955, American 369, 371, 373, 375-79, 381, 384-85, math.: 131, 246 398, 402, 408, 412, 417, 429-30, 434- Kasten, H. math. teacher in Bremen, DMV: 35, 457, 459, 461, 484, 511, 564, 571, 369-70 576, 578-79, 603-07, 613, 615, 624, Katz, David 1884–1953, psychol.: 492, 615 632, 641, 644, 652 Kayser (née Schleicher), Eleonore 1793– Hurwitz, Julius 1857–1919, math., DMV: 1875, F. Klein’s mat. grandmother: 20 641 Kayser, Christian Gottfried 1791–1849, Husserl, Edmund 1859–1938, philos.: 489 wool merchant, F. Klein’s mat. grand- Huygens, Christiaan 1629–1695, Dutch father: 20 math., physic., astr.: 594, 596 Keesom, Willem Hendrik 1876–1956, Dutch Ihlenburg, Wilhelm *1884, math., PhD with physicist, Enc: 431 Klein: 456 Kekulé, August 1829–1896, chemist: 36 Intze, Otto 1843–1904, eng.: 422 Kępiński, Stanisław 1867–1908, Polish Jaccottet, Charles 1872–1938, Swiss math., math., DMV: 283, 335 PhD with Klein, DMV: 333, 346, 393, Kepler, Johannes 1571–1630, math., astro- 399, 613, 615 nomer: 14, 594, 596 Jacobi, Carl Gustav Jacob 1804–1851, Kerry, Benno 1858–1889, Austrian philoso- math.: vii, 9, 37, 47-48, 63, 69, 180, pher: 489 183, 235, 264-65, 272, 288, 294-95, Kerschensteiner, Georg 1854–1932, math., 299, 341, 569, 596, 610 DMV: 555, 613, 615 Jacobs, Konrad 1928–2015, math., DMV: 6 Ketteler, Eduard 1836–1900, physicist: 31, Jaensch, Erich R. 1883–1940, psychol.: 491 35 Jahnke, Eugen 1861–1921, math.: 305, 615 Kiepert, Ludwig 1846–1934, math., DMV: Jerrard, George 1804–1863, British math.: 16, 61, 66-68, 116, 119, 161, 184, 186, 180 199-200, 208, 212, 224, 233, 236, 369, Johnson Ada M. *1870, British math.: 354 419, 615, 633 Jordan, Camille 1838–1922, French math.: Kiesel, Karl 1812–1903, school director: 22 4, 6, 52, 54, 60, 74, 77-79, 85, 87-88, Kirchberger, Paul 1878–1945, math., 90, 100, 104, 130, 140, 153, 180-81, teacher, author: 21, 436, 634 189, 192, 198, 240, 245, 267, 288, 338, Kirchhoff, Arthur 1871–1921, writer: 415 526, 583, 619, 626 Kirchhoff, Gustav Robert 1824–1887, phy- Joubert, Charles 1825–1906, French math.: sicist: 374, 466, 489 180 Kirdorf, Adolph 1845–1923, mining industrialist: 27, 422 Index of Names 665

Klaus, Dr., neurologist: 515, 517, 608-09 Koebe, Paul 1882–1945, math., DMV: 6, Klein, Alfred 1854–1929, lawyer, F. Klein’s 269, 273, 279-81, 307, 456-57, 514-15, brother: x, 17-22, 166-67, 422 522-23, 525, 546, 565-67, 572, 607-08, Klein (md. Flender), Aline 1847–1914, F. 613, 615, 651 Klein’s sister: x, 21 König, Julius 1849–1914, Hungarian math., Klein (née Hegel), Anna Maria Caroline DMV: 102-03, 120, 249-50, 615 1851–1927, F. Klein’s wife: viii, x, Koenigsberger, Leo 1837–1921, math., 161-63, 166-70, 176, 214, 286, 324, DMV: 9, 47, 48, 53, 64, 260, 275, 295, 326, 330, 435-36, 449, 501, 517, 519- 351, 367, 369, 379, 410, 412, 426, 489, 21, 567, 577, 583, 622 596, 637 Klein, Carl 1842–1907, mineralogist: 317 Kötter, Fritz 1857–1912, math., mech., Klein (md. Staiger), Elisabeth Marie Aline DMV: 463 1888–1968, teacher, F. Klein’s daugh- Kohlrausch, Wilhelm 1855–1936, physicist: ter: viii, x, 166-68, 213, 326, 418, 535, 168 537, 541, 567, 585, 649-50 Kollert, Julius 1856–1937, physicist, DMV: Klein, Eugenie 1861–1910, F. Klein’s sister: 230, 262 x, 22, 167 Kopp, Lajos 1860–1928, Hungarian math.: Klein, Johann Peter Friedrich, 1777–1858, 130 smith, F. Klein’s grandfather: x, 17 Koppel, Leopold 1854–1933, banker: 513 Klein (md. Süchting), Luise (Louise) 1879– Korkin, Aleksandr N. 1837–1908, Russian 1961, F. Klein’s daughter: x, xix, 166- math.: 250 67, 169, 414 Korteweg, Diederik J. 1848–1941, Dutch Klein, Otto Karl 1876–1963, eng., F. Klein’s math.: 432 son: x, 166-69, 567 Kortum, Carl Arnold 1745–1824, physician, Klein, Peter Caspar 1809–1889, Prussian poet: 163 official, F. Klein’s father: x, 18 Kottler, Friedrich 1886–1965, Austrian- Klein, Sophie Elise (née Kayser) 1819– American physicist: 541 1890, F. Klein’s mother: x, 19-20 Kovalevskaya (née Korvin-Krukovskaya), Klein (md. Hagemann), Sophie Eugenie Sofya V. 1850–1891, Russian math.: 1885–1965, F. Klein’s daughter: x, 21, 56, 97-98, 411-12, 463 166, 167, 169 Kowalewski, Gerhard 1875–1950, math., Kleine, Friedrich Peter *1731, farmer, F. DMV: 243, 433, 637 Klein’s great-grandfather: 17 Kraepelin, Karl 1848–1915, biologist: 46, Kleine (née Schürfeld), Catharina Marga- 498, 648 rethe, F.Klein’s great-grandmother: 17 Krause, Martin 1851–1920, math., DMV: Klemm, F. math. teacher in Bremen, DMV: 402 369-70 Krauß (as of 1905 Ritter von), Georg 1826– Klingenfeld, Friedrich August 1817–1880, 1906, entrepreneur: 203, 424 math.: 172, 211 Krazer, Adolf 1858–1926, math., DMV, Klinkerfues, Ernst Friedrich Wilhelm 1827– Enc: 231, 233-34, 237-38, 264-65, 1884, astronomer: 92-93, 95, 120 396, 426, 457, 536, 553-54, 557-60, Klitzkowski, Felix, b. in Danzig [Gdansk], 613, 615 (here Krager=Krazer) math.: 333 Kregel von Sternbach, Karl Friedrich 1717– Kluckhohn, August von 1832–1893, 1789, philanthropist: 239 historian: 212 Krell, Otto 1866–1938, eng., industr.: 451 Kneser, Helmuth 1898–1973, math., DMV: Krieg v. Hochfelden, Franz 1857–1919 stud. 536 math.: 231 Kneser, Martin 1928–2004, math., DMV: Kronecker, Leopold 1823–1891, math., 533 DMV: 3, 35, 54, 56, 63-64, 68, 180, Knoblauch, Johannes 1855–1915, math., 182, 184, 188, 196-97, 229, 235, 237- DMV: 89, 229 38, 240, 249-50, 260-61, 264, 266, 288- 89, 292-93, 296, 322, 328, 342, 359, 666 Index of Names

368, 371, 373-74, 376-77, 405, 454, Larmor, Joseph 1857–1942, Irish physicist, 457, 483, 571, 575-76, 580, 591, 602, math.: 431-32, 549 604, 607, 626, 637, 642, 645 Laski, Gerda 1893–1928, Austrian physicist: Krüger, Louis 1857–1923, math., surveyor, 536 DMV: 557, 560, 615 Laue, Max von 1879–1960, theor. physicist, Krull, Wolfgang 1899–1971, math., DMV, DMV, Enc: 357, 541, 615, 624 Enc: 240, 536, 637 Laugel, Léonce 1859–1936, French math., Krupp von Bohlen und Hallbach, Gustav trans., DMV: 350, 409, 458-59, 462, 1870–1950, entrepreneur: 170, 422, 464, 634-35, 643 440, 442, 444, 561, 615 Launhardt, Wilhelm 1832–1918, eng.: 362- Krylov [Kriloff], Alexej, N. 1863–1945, 63, 366 Russ. naval eng., math., Enc: 480, 613, Lederer, Hugo 1871–1940, sculptor: 569 615 Legendre, Adrien-Marie 1752–1833, French Kuhn, Thomas S. 1922–1996, American math.: 30, 252, 272 physicist, philosopher: 8, 629 Leibniz, Gottfried Wilhelm 1646–1716, Kummer, Ernst Eduard 1810–1893, math.: polymath.: 310, 530-31 1, 35, 59-63, 65-67, 71, 77-81, 84-88, Lemoine, Émile 1840–1912, French math.: 98-100, 150, 194, 206-07, 221, 227, 402 229, 233, 250, 298, 309, 340, 366, 374, Lenard, Philipp 1862–1947, physicist: 542, 405, 594, 602, 609 544 Kundt, August 1839–1894, physicist: 376 Lerch, Matyás 1860–1922, Czech math., Kutta, Wilhelm 1867–1944, math., DMV: DMV: 402 448, 450, 453 Levi-Civita, Tullio 1873–1941, Italian Ladd-Franklin, Christine 1847–1930, Ame- math., DMV: 200, 463, 618 rican math., psychologist: 412-13 Lexis, Wilhelm 1837–1914, statistician, Lagarde, Paul Anton de 1827–1891, economist: 401, 414, 419-20, 439, 454, orientalist: 318, 365-66, 638 500, 502, 615, 634, 635 Lagrange, Joseph-Louis 1736–1813, French Lichtenberg, Georg Christoph 1742–1799, math.: 9, 114, 160, 179, 457, 480, 594, physicist, satirist: 45 596 Lichtenstein, Leon 1878–1933, Polish- Laisant, Charles-Ange 1841–1920, French German math., DMV, Enc: 57, 254, math.: 76, 305 263, 281, 560 Lamb, Horace 1849–1934, British math., Lichtwark, Alfred 1852–1914, art historian: physicist, Enc: 302, 432 519, 642 Lamé, Gabriel 1875-1870, French math., Lie, Sophus 1842–1899, Norwegian math., physicist: 253-54, 344, 346, 416, 462, DMV: viii, 1, 5-6, 14, 16, 19, 26, 41, 463, 596 56-57, 59, 61, 65-71, 73-86, 88-91, 95- Lampe, Emil 1840–1918, math., DMV: 76, 96, 98-102, 105, 107-08, 110, 117, 120, 119-20, 305, 369-71, 500, 513 123, 125-31, 133, 136-38, 143, 147-50, Lanchester, Frederick W. 1868–1946, Bri- 153, 156, 158-61, 181, 183, 206-09, tish polymath., eng.: 452 223, 225, 239-40, 243, 253, 267-68, Landau, Edmund 1877–1938, math., DMV: 277, 285, 287, 303, 312, 314-15, 320- viii, 327, 441-42, 456, 460-61, 518, 24, 328, 333, 335, 347, 349, 350-52, 522-23, 526, 532, 545, 572-73, 613, 374, 389, 393, 404, 411, 427, 435, 447, 615, 647 463, 484, 491, 517, 519, 570, 575-76, Landolt, Hans Heinrich 1831–1910, Swiss 578, 583, 586, 609, 619, 623, 627-28, chem.: 31-32, 97 630, 633, 638, 641, 643, 644, 648, 653 Lange, Ernst *1858, math., Saxon official, Liebermann, Max 1847–1935, painter: ix, PhD with Klein: 222, 228, 230, 232, 243, 494, 519-21, 528, 531, 569, 575, 308, 615 577, 611, 614-17, 642 Lange, Helene 1848–1930, pedag.: 506 Liebig (as of 1845 Freiherr von), Justus 1803–1873, chemist: 561 Index of Names 667

Liebisch, Theodor 1852–1922, mineral., Loria, Gino 1862–1954, Italian math., hist., Enc: 317, 356, 366, 385, 388 DMV, Enc: 42, 135, 399, 431, 613, Liebmann, Heinrich 1874–1935, math., 616, 635 DMV, Enc: 302, 339, 463, 615, 638 Lotze, Rudolf Hermann 1817–1881, philo- Lietzmann, Walther 1880–1959, math., sopher: 89, 116 didactics, DMV: 396, 487, 494, 503, Love, Edward Hough 1863–1940, British 505, 515-517, 550-55, 566, 582, 587, math., Enc: 302, 429, 432, 469, 470, 613, 615, 624, 629, 632, 638 616 Linde (as of 1897 Ritter von), Carl 1842– Ludwig, Carl 1816–1895, physiologist: 2, 1934, eng., inventor, entrepreneur: 310, 312-13 172, 201-03, 423-24, 443, 516, 613, Ludwig II, Otto Friedrich Wilhelm von 615 Wittelsbach 1845–1886, King of Lindemann, Ferdinand 1852–1939, math., Bavaria: 124, 171-72 PhD with F. Klein, DMV: 5, 13, 20, Lüders, Otto 1844–1912, class. philol.: 35 40, 48, 63, 87-88, 94-97, 113, 115, 117, Lüroth, Jacob 1844–1910, math., DMV: 40, 120, 133-35, 137, 150, 159, 162-63, 47-48, 50, 53, 87, 100, 120, 173, 208, 171, 191-92, 198, 208-09, 216, 229, 212, 313, 369, 375, 608 236, 264-65, 311, 321-23, 333, 348-49, Luther, Robert Karl Theodor 1822–1900, 357-58, 369, 373-74, 376, 381, 388, astronomer: 27 393, 398, 401, 430, 434, 571-72, 607, Luzin, Nikolai N. 1883–1950, Russ./Soviet 613, 616, 623, 627, 653 math.: 533 Liouville, Joseph 1809–1882, French math.: Mach, Ernst 1838–1916, Austrian physicist, 74, 85, 102, 639 philosopher: 296, 490 Lipschitz, Rudolf 1832–1903, math., DMV: MacKinnon (md Fitch), Annie Louise 1868– 30-33, 41-42, 63-64, 113, 120, 217, 1940, Canadian-American math.: 406 351, 371, 645 Maddison, Ada Isabel, 1869–1950, British Lissajous, Jules Antoine 1822–1880, French math.: 417, 483-84, 635 physicist.: 136 Madelung, Erwin 1881–1972, physicist: Listing, Johann Benedikt 1808–1882, math., 466 physicist: 92-95, 120, 235 Magnus, Gustav 1802–1870, physicist: 62 Lobachevsky, Nikolai I. 1792–1856, Maltby, Margaret Eliza 1860–1944, Ameri- Russian math: 70-73, 101, 126, 251, can physicist: 413 324, 350, 408 Mangoldt, Hans von 1854–1925, math., Loewy, Alfred 1873–1935, math., DMV: DMV: 311 393, 616 Mansion, Paul 1844–1919, Belgian math., Lommel (as of 1892 von), Eugen 1837– DMV: 127-28, 495, 634 1899, physicist, DMV: x, 124, 160, Mariotte, Edme ca. 1620–1684, French 166, 533, 589, 595-96 physicist: 203 Lommel, Herman 1885–1968, philologist, Markov [Markoff], Andrey A. 1856–1922, Indo-Europeanist: 532 Russian math.: 6, 250-51, 301, 345-46, Lorentz, Hendrik Antoon 1853–1928, Dutch 355, 487, 587, 613, 616, 623, 651 physicist, Enc: 150, 304, 395, 431, Marotte, Francisque 1873–1945, French 472-73, 509, 549, 582 math., teacher: 502 Lorenz, Hans 1865–1940, techn. physicist, Maschke, Heinrich 1853–1908, math., DMV: 439, 447, 449, 513, 577, 590 DMV: 337-38, 365-66, 402, 404, 412- Lorey, Wilhelm 1873–1955, math., DMV: 13, 619, 640 30, 48, 51, 66, 89, 94, 96, 107, 114, Massenbach, Leo Freiherr von 1797–1880, 133, 145, 176-77, 219, 232, 275, 313, lawyer, Prussian official: 19 399, 418, 420, 481, 505, 510, 527-28, Maxwell, James Clerk 1831–1879, Scottish 616, 624, 639, 646 physicist: 150, 169, 364, 395, 410, 463, 468-69 668 Index of Names

Mayer, Adolph 1839–1908, math., DMV: 6, 402, 434, 436, 441, 454, 456, 458-60, 47, 53-57, 75, 91, 100, 118, 120-21, 466, 472-73, 511, 572, 580, 590, 640 123, 157, 161, 181-83, 193-95, 208-09, Minkowski, Rudolph 1895–1976, German- 211, 213-15, 219, 222, 225-27, 239-40, American astronomer: 536 250, 267, 303, 308, 311-12, 321-22, Minnigerode, Bernhard 1837–1896, math., 324, 333, 335, 349, 355, 369-70, 427, mineralogist: 52, 93, 95, 120 479, 483, 538, 578, 651 Mises, Richard von 1883–1953, math., Mazurkiewicz, Stefan 1888–1945, Polish DMV, Enc: 7, 266, 304, 428, 449, 471, math.: 421 524, 534, 558, 565-66, 640, 647, 654 McClintock, Emory 1840–1916, American Mittag-Leffler, Gösta 1846–1927, Swedish actuary: 407, 418 math., DMV: viii, 56, 130, 212, 250, Mehmke, Rudolf 1857–1944, math., DMV, 272, 277, 295, 305, 315, 328, 342, 495, Enc: 146, 302-04, 616 519, 613, 616, 640, 643, 648 Meier, Ernst von 1832–1911, lawyer, Młodziejewski, Bolesław 1858–1928, curator: 380, 383, 412-13 Polish-Russian math.: 334 Mendeleev, Dmitri I. 1834–1907, Russian Möbius, August Ferdinand 1790–1868, chemist: 363 math.: 37, 104, 114, 140, 208, 215, Merkel, Friedrich 1845–1919, anatomist: 217, 237, 248, 257, 301, 310-312, 478, 115, 117, 479 629, 653 Mertens, Franz [Franciszek] 1840–1927, Mohrmann, Hans 1881–1941, math., DMV, Polish Austrian math.: 613, 616 Enc: 433, 537 Merz, John Theodore 1840–1922, German Molien, Theodor 1861–1941, German- British chemist, historian, industrialist: Baltic/Soviet math., DMV: 231, 251, 480, 484, 640 293, 311 Metzler, G.F., listener with Klein: 399 Molk, Jules 1857–1914, French math., Metzner, Carl 1876–1939, teacher, Prussian DMV, Enc(f): 429, 613, 616, 628, 630 official: 556, 590 Mollier, Richard 1863–1935, applied Meyer, Diedrich, building officer, VDI physicist, eng.: 424 director: 565, 616 Mommsen, Theodor 1817–1903, historian: Meyer, Eugen 1868–1930, techn. physicist, 366, 642 DMV: 424, 616 Monge, Gaspard 1746–1818, French math.: Meyer, Franz 1856–1934, math., DMV, 37, 44, 224, 625 Enc: 4, 12, 108, 193-94, 204, 243, 299, Moore, Eliakim Hastings 1862–1932, Ame- 305, 369-70, 372, 392, 395, 426, 430, rican math., DMV: 313, 399, 402-04, 433-34, 616 413, 613, 616, 619, 640, 641 Meyer, Georg, math. teacher in Bremen, Morera, Giacinto 1856–1909, Italian math.: DMV: 369-70 156, 231, 247-48, 293, 311 Meyerstein, Moritz 1808–1882, mech.: 120 Morgan, Augustus de 1806–1871, British Michelson, Albert Abraham 1852–1931, math: 151-52, 354, 586 American physicist: 395 Morley, Edward Williams 1838–1923, Mie, Gustav 1868–1957, physicist, DMV: American chemist: 417 307 Morrice, George Gavin 1859–1936, British Mill, John Stuart 1806–1873, British philo- scientist, transl.: 290 sopher, economist: 36 Mügge, Otto 1858–1932, mineralogist, Enc: Miller (ab 1875 von), Oskar 1855–1934, 356, 522, 616 civil eng.: 516, 613 Mühler, Heinrich von 1813–1874, Prussian Minding, Ferdinand 1805–1885, German- Minister of Culture: 39, 82, 593 Russian math.: 136 Müller, Conrad Heinrich 1878–1953, math., Minkowski, Hermann 1864–1909, math., math.hist., PhD with Klein, DMV, Enc: DMV, Enc: viii, 57, 236, 279, 286, 390, 394, 429, 457, 470, 479, 515, 537, 327, 331, 346, 358, 369-70, 377, 391, 588, 613, 616 Index of Names 669

Müller, Felix 1843–1928, math., teacher, 42, 576, 578, 581, 584, 591, 637, 641, DMV: 118, 120 644-45, 650, 651 Müller, Georg Elias 1850–1934, psychol.: Noether, Fritz 1884–1941, math., DMV: 50, 258, 317, 484-85, 490, 492, 616 462, 616, 637 Müller, Hans math., PhD Göttingen (1903), Noether, Max 1844–1921, math., DMV: 10, DMV: 394 13, 47, 49, 50, 53, 57-59, 64-65, 68-71, Müller, Reinhold 1857–1939, math., DMV: 77, 79, 84, 103, 107, 113, 118-20, 124, 370 147-48, 155, 158-62, 178, 182, 188-89, Müller, Wilhelm 1812–1890, Germanist: 204, 208, 236, 248-49, 278, 285, 296, 600 323, 334, 341, 351, 354, 357, 366, 372, Müller-Breslau, Heinrich 1851–1925, struc- 402, 406, 417, 462, 481, 576, 578, 606, tural eng.: 304, 468, 634 613, 616, 618, 643 Nachtweh, Alwin 1868–1939, eng.: 168-69, Nohl, Herman 1879–1960, philosopher, 616 pedagogue: 534 Naumann, Otto 1852–1925, Prussian Ocagne, Maurice d’ 1862–1938, French official: 391, 526, 528, 530, 541 math., Enc(f): 302, 402, 645 Neesen, Friedrich 1849–1923, math., Ohrtmann, Carl 1839–1885, math., teacher: physicist: 34, 96-97, 108-09, 113-15, 118, 120 120, 166-67, 208, 345 Olbricht, Richard 1859–1912, math., school Nekrasov, Pavel A. 1853–1924, Russian director, PhD with Klein: 230, 616 math.: 355, 603-04 Oliver, James Edward 1829–1895, Ameri- Nelson, Leonard 1882–1927, philos.: xx, can math.: 404, 406 481, 489-91, 568, 584, 616 Osgood, William Fogg 1864–1943, Ameri- Nernst, Walther 1864–1941, physical che- can math., DMV, Enc: 249, 280, 334, mist: 385, 413, 422-23, 502, 516, 522, 340-41, 405-06, 585, 613, 616, 625 528, 637, 640 Ostrowski, Alexander M. 1893–1986, Ukrai- Netto, Eugen 1848–1919, math., DMV, Enc: nian-Swiss math., DMV: 442, 478, 66, 67, 120, 402 524, 536, 545-46, 579, 641 Neugebauer, Otto 1899–1990, Austrian- Ostwald, Wilhelm 1853–1932, physical American math.hist., DMV: 480, 537, chem.: 2, 426, 492, 513, 528, 546, 637 539, 642 Ovidio, Enrico d’ 1842–1933, Italian math.: Neuhäuser, Joseph 1823–1900, philosopher: 153-54, 247, 613, 616 30-31 Padé, Henri Eugène 1863–1953, French Neumann, Carl 1832–1925, math., DMV: math.: 130, 334 46-48, 53-55, 63, 108, 140, 215, 221- Padova, Ernesto 1845–1896, Italian math.: 23, 227, 229, 253-56, 262, 306, 311, 157 321, 323, 569, 596, 652 Painlevé, Paul 1863–1933, French math., Neumann, Franz 1798–1895, physicist: 47 Enc: 333, 452, 471-72, 588 Newcomb, Simon 1835–1909, Canadian- Paladini, Bernardo 1863–?, Italian math.: American math., astronomer: 246, 407 402 Newton, Isaac 1642–1727, British math., Papperitz, Erwin 1857–1938, math., PhD physicist: 31, 491, 594 with Klein, DMV, Enc: 231, 280, 369- Nielsen, Jakob 1890–1959, Danish math., 70, 616 DMV: 536 Parseval, August von 1861–1942, airship Nimsch, Paul *1860, math., PhD with Klein: designer: 453 230, 293 Pascal, Blaise 1623–1662, French math.: Noble, Charles Albert 1867–1962, Amer. 139 math.: 399, 556 Pascal, Ernesto 1865–1940, Italian math.: Nöggerath, Johann Jakob 1788–1877, mine- 156, 334, 341, 366, 613, 616, 634 ralogist, geologist: 31-32 Pasch, Moritz 1843–1930, math., DMV: Noether, Emmy 1882–1935, math., DMV: 100, 120, 482, 491, 606, 645 ix, 50, 160, 178, 359, 417-18, 536, 539- 670 Index of Names

Pasquier, Ernest 1849–1926, Belgian math.: 53, 58-62, 65-69, 71, 80, 88-89, 92-93, 120, 127-28 96, 111, 113-14, 126, 128-29, 134, 138- Pasteur, Louis 1822–1895, French micro- 39, 151, 154-55, 206, 208, 216, 233, biologist: 36 300, 301, 309, 330, 345, 477-78, 510, Pauli, Wolfgang Ernst 1900–1958, Austrian 536, 569-70, 575, 596-97, 599, 609, physicist, Enc: 536, 541, 632 627-29, 642, 653 Peano, Giuseppe 1858–1932, Italian math.: Pockels, Agnes 1862–1935, physico-che- 483, 491, 647 mist: 345 Peipers, Johann Philipp David 1838–1912, Pockels, Friedrich 1864–1913, math., physi- philosopher: 116-17 cist, DMV, Enc: 302, 344-45, 455, 616 Perry, John 1850–1920, Irish eng., math.: Poincaré, Henri 1854–1912, French math.: 169, 302, 502, 507, 509, 584, 641 viii, 4-6, 102, 130, 189, 215, 245, 250, Pervushin, Ivan M. 1827–1900, Russian 252-53, 258, 267-85, 295, 340, 342, math.: 402 352, 357, 381, 387, 394-95, 403, 410, Pestalozzi, Johann Heinrich 1746–1827, 456, 458, 467, 485, 495, 512-13, 519, Swiss pedagogue: 531 541, 571-73, 579, 582, 587, 610, 613, Petermann, August Heinrich 1822–1878, 631, 640, 642-43, 646, 651, 652 cartographer: 36 Poinsot, Louis 1777–1859, French math.: Petzoldt, Joseph 1862–1929, philos.: 490 177, 595-96 Pfaff, Friedrich 1825–1886, geologist, mine- Poisson, Siméon Denis 1781–1840, French ralogist: 145 math., physicist: 595 Pfaff, Hans Ulrich Vitalis 1824–1872, Pokrovsky, Petr M. 1857–1901, Russian math.: 124, 145, 163 math., DMV: 355 Pfeiffer, Friedrich 1883–1961, math., DMV: Poncelet, Jean-Victor 1788–1867, French 470-71, 616 math., eng., physicist: 1, 37-38, 68, 70, Pfitzer, Ernst 1846–1906, botan.: 32 127, 569 Picard, Charles Émile 1856–1941, French Pontani, Bernhard *27.10.1845, teacher: 29 math.: 131, 253, 268, 292, 333, 340, Poske, Friedrich 1852–1925, pedag.: 494, 342-43, 352, 357, 410, 456, 459, 495, 550, 553, 616 512, 529, 531, 583, 613, 616 Prandtl, Ludwig 1875–1953, eng., mech., Pick, Georg 1859–1942, Austrian math., DMV, Enc: viii, 4, 7, 307, 327, 391, DMV: 10, 248, 293-97, 321, 330, 341, 449-53, 465-66, 468, 470-71, 522, 524, 460, 576 562-63, 565-66, 577, 581, 588, 616, Pickering, Edward Charles 1846–1919, 623, 628, 637 American astronomer: 406 Prange, Georg 1885–1941, math., DMV, Pieri, Mario 1860–1913, Italian math. Enc: 114 Enc(f): 130, 639 Pringsheim, Alfred 1850–1941, math., Pietzker, Friedrich 1844–1916, teacher, DMV, Enc: 204, 509-10, 616 DMV: 400, 503, 616 Pringsheim, Nathanael 1823–1894, botanist: Pincherle, Salvatore 1853–1936, Italian 36 math., DMV, Enc: 402, 635 Prym, Friedrich 1841–1915, math., DMV: Planck, Gottlieb 1824–1910, lawyer: 327 65, 237, 256, 264, 457 Planck, Max 1858–1947, physicist, DMV: Puiseux, Victor 1820–1883, French math.: 14, 177-78, 204, 327, 415, 440, 457, 108 489, 513, 528-30, 541, 583, 587, 632 Pulfrich, Carl 1858–1927, physicist: 35 Plato ca. 428–348 BC, Greek philos.: vii, Pupin, Mihajlo Idvorski 1854–1935, Ser- 35-36, 117, 143 bian-American physicist: 467-68 Plücker, Albert, son of Julius P.: 39 Rabinowitsch-Kempner, Lydia 1871–1935, Plücker (née Altstätter), Antonie, Julius P.’s bacteriol.: 505, 506 wife: 40, 97, 111, 477 Radicke, Gustav 1810–1883, physicist: 32 Plücker, Julius 1801–1868, math., physicist: vii, 2, 9-10, 17, 22, 28-42, 46-48, 52- Index of Names 671

Rados (Raussnitz), Gusztáv 1862–1942, Riedler, Alois 1850–1936, Austrian eng., Hungarian math., DMV: 103, 231, professor in Germany: 401, 424, 443 248-50, 616 Riemann, Bernhard 1826–1866, math.: vii, Ranke (as of 1865 von), Leopold 1795– 2, 4-6, 9, 45, 48-49, 51, 53, 58, 65, 68, 1886, historian: 116, 164-65, 427-28, 72-73, 92, 95, 98, 101, 103, 126, 128- 475, 477 29, 135-36, 139-43, 149, 153-54, 156- Raphael 1483–1520, Italian painter: 566 57, 178-81, 184-86, 194, 203, 217, 222- Rathenau, Walther 1867–1922, industrialist, 23, 228, 237, 249, 252-53, 255-60, 262- liberal politician: 584 65, 268, 270-74, 276-78, 280, 282-85, Rausenberger, Otto 1852–1931, math., 288, 294-95, 338, 340, 342-44, 352, teacher: 274-75 354, 357, 360, 366, 379, 389, 393, 406, Rayleigh (Lord), Strutt, John William 1842– 409-10, 417, 452, 457, 461, 464, 478, 1919, British physicist.: 151-52, 345, 479, 547, 549, 570, 572, 586, 600, 607- 431 08, 610, 621, 631, 634, 638, 640, 643- Reeß, Maximilian 1845–1901, botanist: 135 44, 646, 648, 651, 653 Reger, Maximilian (Max) 1873–1916, com- Rieppel (as of 1906 von), Anton 1852–1926, poser: 167 eng.: 439-40, 444-45, 469, 471, 616 Reich, Max 1874–1941, physicist: 562 Ritter, August 1826–1908, astrophysicist, Reichardt, Hans 1908–1991, math., DMV: prof. of mechanics, DMV: 370 73, 548, 642 Ritter, Ernst 1867–1895, math., PhD with Reichardt, Willibald A. 1864–1924, math., Klein, DMV: 331, 387-88, 393, 406, PhD with Klein: 231, 311, 337, 616 413, 435 Rein, Wilhelm 1847–1929, pedag.: 492 Rockefeller, John D. 1839–1937, American Reinke, Johannes 1849–1931, botanist: 501 entrepreneur: 564, 647 Reissner [Reißner], Hans 1874–1967, eng., Rodenberg, Carl Friedrich 1851–1933, math., physicist, DMV, Enc: 468, 565, math., DMV: 97, 108, 309, 370 616 Rohn, Karl 1855–1920, math., PhD with Repsold, Johann A. 1838–1919, instrument Klein, DMV, Enc: 193-94, 204, 206- maker: 363, 366 07, 220-23, 226, 236, 298, 308-09, 311, Réthy, Mór (Moritz) 1846–1925, Hungarian 433, 613, 616 math., DMV: 120 Rohns, Christian Friedrich Andreas 1787– Reye, Karl Theodor 1838–1919, math., 1853, architect: 169, 327 DMV: 69, 73, 78, 87, 120, 208, 215, Rohr, Moritz von 1868–1940, math., inven- 240, 371, 596, 618 tor: 114, 650 Reynolds, Osborne 1842–1912, British Rosanes, Jacob 1842–1922, math., DMV: physicist: 354 374, 375, 616 Ricci-Curbastro, Gregorio 1853–1925, Rosemann, Walther 1899–1971, math.: 257, Italian math., DMV: 199-200 547, 636 Richardson, Roland George Dwight 1878– Rosenbach, Friedrich Julius 1842–1923, 1949, Canadian-American math., physician, surgeon: 384 DMV: 346-47, 619 Rosenhain, Johann Georg 1816–1887, Richelot, Friedrich Julius 1808–1875, math.: math.: 236 47, 119, 223, 379 Rosenthal, Arthur 1887–1959, math., DMV, Richert, Hans 1869–1940, teacher, education Enc: 381, 421, 430, 616 politician: 556 Rost, Georg 1870–1958, math., DMV: 457 Richter, Otto math. student: 231 Rothe, Rudolf 1873–1942, math., DMV: Riecke, Eduard 1845–1915, physicist, 550 DMV: 96, 110-17, 120, 161, 235, 305, Routh, Edward John 1831–1907, British 316-20, 325, 332, 336, 363, 366, 400, math.: 302, 431 420, 423-24, 434, 439, 450, 473-74, Roux, Karl 1826–1894, painter: 210 519, 522, 546, 560, 611-12, 616, 636, Rudio, Ferdinand 1856–1929, German- 643 Swiss math.: 317, 479, 613, 616 672 Index of Names

Rüdenberg, Reinhold 1883–1961, eng.: 466, Schimmack, Rudolf 1881–1912, math., 616 didactics, DMV: 302, 390, 446, 504- Ruer, Wilhelm 1848–1932, judicial counci- 05, 515, 517, 588, 613, 616, 635, 645 lor, poet, Klein’s classmate: 27, 616 Schläfli, Ludwig 1814–1895, Swiss math.: Runge, Carl 1856–1927, math., DMV, Enc: 140-41, 257, 309, 633 viii, 25, 62, 89, 168, 177-78, 229, 261, Schlegel, Victor 1843–1905, math., teacher, 303, 327, 391, 421, 445, 448-49, 452- DMV: 313, 402 53, 465, 469-70, 473, 476, 489, 506, Schlesinger, Ludwig 1864–1933, Hunga- 512, 517, 522-24, 528, 532, 537, 539, rian-German math., DMV: 344, 478, 558-60, 566, 587, 613, 616, 632, 643 616 Runge, Iris Anna 1888–1966, math., chem., Schlömilch, Oscar 1823–1901, math., DMV: physicist: 418, 448, 466, 506-07, 517, 303 523, 537, 546, 650 Schmeidler, Werner 1890–1969, math., Russell, Bertrand 1872–1970, British DMV: 536 philosopher, polymath.: 353, 572 Schmidt, Carl, theologian: 155 Sachs, Eva Henriette 1882–1936, classical Schmidt, Erhard 1876–1959, math., DMV: scholar, teacher: 35 394 Sachs, Julius 1832–1897, botanist: 36 Schmidt (as of 1920 Schmidt-Ott), Friedrich Sagorski, Ernst 1847–1929, Klein’s fellow 1860–1956, science politician: 303, student, teacher: 29, 35, 44 401-02, 413, 444, 450, 453, 530, 533, Salmon, George 1819–1904, Irish math.: 557, 559, 560, 563-64, 645 40-41, 47, 71, 87, 102, 248, 596, 645 Schmitz, Wilhelm 1846–1900, manager in Sanden, Horst von 1883–1965, math., DMV: the company Krupp: 444 453, 616 Schmoller (since 1908 von), Gustav 1838– Sartorius Freiherr von Waltershausen, 1917, economics scholar: 501 Wolfgang 1809–1876, geol.: 90 Schneider, Jakob 1818–1898, F. Klein’s Sauppe, Hermann 1809–1893, classical phi- math. teacher: 25 lologist: 317, 364-66 Schoenflies (Schönflies), Arthur 1853–1928, Scheffers, Georg 1866–1945, math., DMV: math., DMV, Enc: 4, 10, 96, 103-04, 447 154, 296, 329-32, 335-36, 356, 359-60, Scheibner, Wilhelm 1826–1908, math., 380, 383-84, 387, 392, 402-03, 422, DMV: 206, 215-16, 222, 229-30, 233, 447-78, 502, 538, 591, 605-06, 617, 237, 239, 308, 311-12, 321 633, 640, 642, 646 Schell, Wilhelm 1826–1904, math., mech., Scholze, Peter *1987, math., DMV: 460 DMV: 596 Schotten, Heinrich 1856–1939, teacher, Schellbach, Karl Heinrich 1805–1892, DMV: 494, 613, 617 math., pedagogue: 63, 65 Schottky, Friedrich 1851–1935, math., Schering, Ernst Christian Julius 1833–1897, DMV: 234, 256, 265, 270, 283, 375, math., astr., DMV: xvii, 11, 92, 93, 95, 377, 392, 428, 457, 587, 609, 611 98, 120, 235, 236, 317, 318, 325, 335, Schouten, Jan Arnoldus 1883–1971, Dutch 363, 366, 367, 377, 378, 380, 384, 392, math., DMV: 131, 302, 646 434, 478, 598, 600, 601, 602 Schröder, Edward 1858–1942, Germanist, Schering (née Malmstén), Maria Heliodora mediaevalist: 577 1848–1920: 367 Schröder, Ernst 1841–1902, math., DMV: Schiller, Friedrich 1759–1805, poet, play- 120, 369-70 wright: 25, 454 Schröder, Johannes 1865–1937, math., Schilling, Carl 1857–1933, math., DMV: teacher, PhD with Klein, DMV: 339, 370, 616 418 Schilling, Friedrich (Fritz) 1868–1950, Schrödter, Emil 1855–1928, eng.: 422 math., DMV: 302, 386-87, 391, 393- Schroeter, Heinrich Eduard 1829–1892, 94, 440, 447, 449, 616, 636, 645 math., DMV: 64, 87, 373, 375-76 Schilling, Martin publisher: 175 Index of Names 673

Schubert, Hermann Cäsar Hannibal 1848– Siedentopf, Henry 1872–1940, physicist: 1911, math., DMV, Enc: 50, 67, 100, 399, 466 119-20, 241, 368-71, 581 Siemens, Werner von 1816–1892, eng., Schüler, Wilhelm, math.: 172, 176-77, 577 entrepreneur: 438-39, 442, 451 Schütz, L., a student in Klein’s courses: 399 Simon, Hermann Theodor 1870–1918, phy- Schur, Friedrich 1856–1932, math., DMV: sicist: 306, 447, 449, 466, 518, 562, 219, 223, 233-34, 236, 251, 308, 311, 617 323, 613, 617 Simon, Max 1844–1918, math., hist., DMV: Schur, Issai 1875–1941, math., DMV: 523, 67, 120, 509, 617 557, 558, 559, 560 Simony, Oscar 1852–1915, Austrian math.: Schur, Wilhelm 1846–1901, astronomer, 208 DMV: 325, 335, 363, 434 Sintsov (Sinzow), Dimitrii M. 1867–1946, Schwalbe, Bernhard 1841–1901, math., Russian math. DMV: 130, 251, 372, teacher, DMV: 500 613, 617 Schwarz, Hermann Amandus 1843–1921, Sitter, Willem de 1872–1934, Dutch astr.: math., DMV: 11, 13, 65, 69, 98, 120, 542-43, 643 181, 185, 207, 212, 233, 235-36, 238, Slaby, Adolf 1849–1913, eng.: 424, 443, 256, 261-62, 266, 269, 276, 280, 282- 451, 499-502, 635 83, 295-96, 317, 318-23, 325-26, 328- Slodowy, Peter 1948–2002, math., DMV: 5, 32, 334-36, 342-43, 356, 358, 360, 363, 179, 290, 634, 648 365, 372, 374-78, 381, 383-84, 387, Smend, Rudolf 1851–1913, theologian: 434 393, 412, 428, 456-57, 499, 522, 587, Smith, David Eugene 1860–1944, American 597-98, 601-02, 605-07, 611, 623, 640 math., hist., pedag., DMV: 396, 399, Schwarzschild, Karl 1873–1916, astrono- 493-94, 517, 549-50, 613, 617, 635 mer, DMV, Enc: 394, 420, 453, 461, Smith, Henry John Stephen 1826–1883, 465, 467, 617, 636 British math.: 148-52, 183, 192, 196, Scott, Charlotte Angas 1858–1931, British- 199, 244, 314, 586 American math., DMV: 258, 416-17, Smith, William Robertson 1846–1894, Scot- 639 tish orientalist, Old Testament scholar: Seeger, Johannes, physicist: 44 96, 105, 123, 147, 183, 353 Seeliger (Ritter von), Hugo 1849–1924, Snyder, Virgil 1869–1950, American math., astronomer, DMV: 222, 304 PhD with Klein, DMV: 372, 399, 406, Segre, Corrado 1863–1924, Italian math., 417, 550, 613, 617-19 DMV, Enc: 6, 41-42, 130, 154, 431, Sohncke, Leonhard 1842–1897, physicist: 483, 613, 617-18, 626, 644, 647 356 Seidel (as of 1882 Ritter von), Ludwig Sommerfeld, Arnold 1868–1951, math., 1821–1896, math., DMV: 173, 193-94, physicist, DMV, Enc: 4, 7, 11, 50, 253, 206, 209, 241, 373, 379, 381, 598 256, 303-04, 331, 345, 388-89, 391, Selenka, Emil 1842–1902, zoologist: 135 393, 395, 426, 431-32, 435, 453, 455, Selling, Eduard 1834–1920, math., DMV: 459, 462-63, 472, 539, 544, 564, 613, 392 617, 628, 636, 648 Serret, Joseph Alfred 1819–1885, French Sommerfeld (née Höpfner), Johanna 1874– math.: 232, 596 1955: 389 Severi, Francesco 1879–1961, Italian math: Sonin, Nikolay Y. 1849–1915, Russian 49, 618, 640 math., DMV: 251, 372, 487 Seyfarth, Friedrich 1891–1960, math., Speiser, Andreas 1885–1970, Swiss math., teacher, DMV: 538, 548, 556, 636 DMV: 459 Shafarevich, Igor R. 1923–2017, Russian Spiegel-Borlinghausen, Adolph von 1792– math.: 47, 50, 647 1852, officer, Prussian official: 18 Sibley, Hiram 1807–1888, American entre- Spiess, Otto 1878–1966, Swiss math., hist.: preneur: 406 537 674 Index of Names

Spiro, Eugen (Eugene) 1874–1972, German- Stresemann, Gustav 1878–1929, politician: American painter: ix 555 Spitzer, Simon 1826–1887, Austrian math.: Stringham, Irving W. 1847–1909, American 208 math.: 10, 230, 245, 575 Springer, Anton 1825–1891, art hist.: 30-31 Struik, Dirk 1894–2000, Dutch-American Springer, Julius 1880–1968, publisher, math., hist., DMV: 537, 539 DMV: 57, 301, 307, 543, 635 Struve, Ludwig von 1858–1920, German- Stäckel, Paul 1862–1919, math., hist., DMV, Baltic math., astronomer: 231 Enc: 302, 304-05, 349, 427, 443, 471, Studt, Konrad von 1838–1921, Prussian 476-78, 494, 499, 613, 617 Minister of Culture: 499-501 Stähelin, Helene 1891–1970, Swiss math.: Study, Eduard 1862–1930, math., DMV, 535, 537 Enc: 50, 87, 131, 224, 233, 240, 242- Stahl, Hermann von 1843–1909, math., 44, 246, 323, 330, 339, 351, 357, 369, DMV: 457 402, 404, 542, 577, 617, 627, 631, 637 Staiger, Robert 1882–1914, musicologist, F. Stumpf, Carl 1848–1936, philosopher: 115- Klein’s son-in-law: x, 166-68, 527 16, 485-86, 489, 648 Stark, Johannes 1874–1957, exp.physicist: Sturm, Rudolf 1841–1919, math., DMV: 474, 542, 560 42, 120, 208, 369-70, 375, 596 Starke, Dorothea 1902–1943, math. 471 Süchting, Friedrich (Fritz) Wilhelm 1874– Staude, Otto 1857–1928, math., PhD with 1969, eng., F. Klein’s son-in-law: 166- Klein, DMV, Enc: 71, 100, 221, 228, 67, 169, 516, 641 230, 233, 236-37, 264-65, 311-12, 428, Sylow, Ludwig 1832–1918, Norweg. math.: 505, 617, 632 240, 569 Staudt, Karl Georg Christian von 1789– Sylvester, James Joseph 1814–1897, British 1867, math.: 70, 73, 79, 97, 103, 123- math.: 37, 47-48, 87, 148, 151-52, 245, 24, 126, 138, 141, 215, 585, 609, 640 246, 314-316, 360, 395, 401, 407, 409, Steckel, Fritz 1884–1915, teacher: 491 412, 575, 586, 641 Steindorff, Ernst 1839–1895, hist.: 116-17 Tägert, Friedrich 1863–1950, math. teacher: Steiner, Jakob 1796–1863, math.: 37, 47 398, 635 Steinitz, Ernst 1871–1928, math., DMV, Tait, Peter Guthrie 1831–1901, Scottish Enc: 42 math., physicist: 94, 96, 105, 147-48, Steklov (Steckloff), Vladimir A. 1863–1926, 256, 570 Russian math.: 613, 617 Takagi, Teiji 1875–1960, Japanese math., Stéphanos, Cyparissos 1857–1917, Greek DMV: 488 math., DMV: 130, 495, 613, 617, 642 Tannery, Jules 1848–1910, French math.: Stern, Alfred 1846–1936, hist.: 116-17, 564 75-76, 302, 474 Stern, Antonie 1892–after 1967, math., Taussky-Todd, Olga 1906–1995, Austrian, DMV: 536 later Czech-American math., DMV: Stern, Moritz Abraham 1807–1894, math., 417, 460 DMV: 51-52, 92-95, 107, 116, 120-21, Taylor, Brook 1685–1731, Engl. math.: 487 127, 132, 235, 317, 329, 364, 564, 598, Tedone, Orazio 1870–1922, Italian math., 601-02, 646 DMV, Enc: 470 Still, Carl 1868–1951, eng., entrepreneur, Teixeira, Francesco Gomes 1851–1933, Por- DMV: 563 tuguese math., hist.: 495, 613, 617 Stöhr, Friedrich, student: 230 Tellkampf, Adolph 1798–1869, math., Stokes, George Gabriel 1819–1903, Irish pedag.: 503, 629 math., physicist: 353, 431, 569 Terquem, Orley 1782–1862, French math.: Stolz, Otto 1842–1905, Austrian math., 304 DMV: 6, 14, 61, 66-67, 69-71, 100, Thaer, Albrecht 1855–1921, math., pedag., 107, 116, 119-20, 123, 128, 138-39, DMV: 494, 613, 617 161, 183, 208, 210, 213, 218, 221, 295- Thomae, Johannes 1840–1921, math., 96, 623, 625 DMV: 124 Index of Names 675

Thomas de Colmar, Charles Xavier 1785– Van Vleck, Edward Burr 1863–1943, Ame- 1870, French inventor: 145-46 rican math., PhD with Klein, DMV: Thomas, Sidney Gilchrist 1850–1885, Engl. 334, 346, 372, 404, 406, 613, 617 inventor: 422 Van Vleck, John Monroe 1833–1912, Ame- Thompson, Henry Dallas, American math., rican astronomer: 407 PhD with Klein: 334, 339, 407, 607 Varićak, Vladimir 1865–1942, Serbian Thomson, Joseph John 1856–1940, British math., DMV: 473 physicist: 431, 448-49 Vasilev [Wassiliew], Alexander V. 1853– Thomson, William (Lord Kelvin) 1824– 1929, Russ. math., DMV: 251, 350, 1907, British physicist: 94, 96, 146-47, 355, 372, 408, 495, 511, 533, 613, 617, 205, 256 635 Tietjen, Friedrich 1834–1895, astron.: 376 Vermeil, Hermann 1889–1959, math., Tietze, Heinrich 1880–1964, Austrian math., DMV: 107, 535-36 DMV, Enc: 433, 617 Veronese, Giuseppe 1854–1917, Italian Tikhomandritsky, Matvey A. 1844–1921, math., DMV: 154, 230, 246-47, 351, Russian math.: 250 613, 617-18 Tilly, Joseph Marie de 1837–1906, Belgian Vietoris, Leopold 1891–2002, Austrian math.: 348 math., DMV, Enc: 433 Timerding, Heinrich Emil 1873–1945, Virchow, Rudolf 1821–1902, physician: math., DMV, Enc: 4, 476-77, 550 205, 653 Timoshenko, Stephen P. 1878–1972, Vögler, Albert 1877–1945, entrepreneur: Ukrain.-Amer. mechan.: 466, 471, 649 561-62, 637 Timpe, Aloys 1882–1959, math., PhD with Voellmy, Erwin 1886–1951, Swiss math., Klein, DMV, Enc: 302, 390, 470, 480, teacher, DMV: 537 617 (Trimpe=Timpe) Voigt, Woldemar 1850–1919, theor. physi- Toeplitz [Töplitz], Otto 1881–1940, math., cist, DMV: 317, 325, 335, 345, 363, DMV, Enc: 14, 346, 490, 510, 617, 630 434, 439, 461, 466, 522, 562, 613, 617 Tollens, Bernhard 1841–1918, chemist: Volhard, Jakob 1834–1910, chemist: 597 115, 117 Von der Mühll (VonderMühll), Karl 1841– Treitschke, Heinrich von 1834–1896, hist.: 1912, Swiss math., DMV: 47, 53-55, 117 57, 120, 215, 219, 222, 227, 613, 617 Treutlein, Peter 1845–1912, math., pedag., Voss [Voß], Aurel 1845–1931, math., DMV, DMV: 494, 514, 613, 617, 638 Enc: 4, 41, 51-52, 54, 59-60, 94-95, Troschel, Franz Hermann 1810–1882, 97, 100, 108, 119-20, 124, 132-33, 136, zoologist: 31-32 138, 146, 158, 160, 163, 258, 301, 317- Trueblood, Mary Esther 1872–1939, 19, 321-23, 339, 365, 372, 384, 419, American math.: 487 453, 476-77, 492, 529, 546, 576, 584, Tyler, Harry Walter 1863–1938, American 599-600, 602, 613, 617, 652 math., DMV: 249, 334, 404, 613, 617 Vries, Gustav de 1866–1934, Dutch math., Uffrecht, Bernhard 1885–1959, math., DMV: 432 pedagogue: 491 Waelsch, Emil 1863–1927, Czech math., Ulrich, Georg Karl Justus 1798–1879, DMV: 231, 248-49, 613, 617 math.: 92-94, 120 Waerden, Bartel Leendert van der 1903– Uppenkamp, August 1824–1909, teacher: 1996, Dutch math., DMV: 241, 359 23 Wagner, Ernst Leberecht 1829–1888, phy- Urysohn, Pavel S. 1898–1924, Russian sician: 258 math.: 533, 538 Wahrendorff, Ferdinand 1826–1898, physi- Valentiner, Herman 1850–1913, Danish cian: 324 math.: 189, 247 Waitz, Georg 1813–1886, hist.: 89, 116-17, Valentiner, Theodor 1869–1952, lawyer, 164, 546 univ. curator: 555 Walker, Gilbert 1868–1958, British math., physicist, meteorologist: 431-32 676 Index of Names

Wallach, Otto 1847–1931, chemist: 115, Weitzenböck, Roland 1885–1955, Austrian 439, 522, 617, 625 math., DMV, Enc: 433 Walter, Max 1857–1935, eng.: 563, 617 Welcker, Friedrich Gottlieb 1784–1868, Waltershausen, Wolfgang Sartorius von class. philologist, archeologist: 35 1809–1876, geol.: 90 Wellhausen, Julius 1844–1918, biblical Walther, Alwin 1898–1967, math.: 487 scholar, orientalist: 147, 380 Wangerin, Albert 1844–1933, math. DMV, Wellmann, H. math. teacher, DMV: 369-70 Enc: 419 Wende, Erich 1884–1966, lawyer, adminis- Warnstedt, Adolf von 1813–1897, lawyer, trator: 526 univ. curator: 318 Wenker, Albert †1871, F.Klein’s school Weber, Carl Maria von 1786–1826, com- friend: 26, 60-61, 85-86, 89 poser: 35 Wernicke, Alexander 1857–1915, math., Weber, Eduard Ritter von 1870–1934, mech., pedagogue, DMV: 496, 617 math., DMV, Enc: 393 Westphal, Wilhelm 1882–1978, physicist: Weber, Ernst Heinrich 1795–1878, physi- 563 cist, physician: 308 Weyl, Hermann 1885–1955, math., DMV: Weber, Heinrich 1842–1913, math., DMV, 2, 131, 142, 243, 480, 491, 517, 544, Enc: 11, 47, 51, 57, 249, 282, 304, 565, 617, 645-46, 648 366, 369-70, 372, 374, 376, 378-80, Weyr, Eduard 1852–1903, Czech Austrian 383-84, 392-93, 396, 402, 426, 434, math.: 402 436, 476, 509, 613, 617, 643, 645 Weyr, Emil 1848–1894, Czech Austrian Weber, Moritz 1871–1951, eng., DMV: math., DMV: 76, 248, 340 390-91 White, Henry Seely 1861–1943, American Weber, Wilhelm Eduard 1804–1891, physi- math., PhD with Klein, DMV: 334, cist: 89, 92-94, 97, 111-12, 120, 235, 340-41, 372, 377, 402 317, 326-27, 365, 439 Whitehead, Alfred North 1861–1947, British Wedekind, Ludwig 1843–1908, math., PhD math., philosopher: 244, 572, 639 with Klein: 129, 133-37, 139, 147, Wiechert, Emil 1861–1928, geophysicist, 191, 401 DMV, Enc: 440, 447-52, 466, 555, Weichold, Guido *1857, math., PhD with 617, 636 Klein: 230, 261-62, 264-65 Wiedemann, Eilhard 1852–1928, physicist: Weierstraß, Karl 1815–1897, math., DMV: 222 9, 13, 35, 41, 48, 50-51, 56, 61, 63-69, Wieghardt, Karl 1874–1924, math., PhD 71-72, 97, 119, 139, 142, 151, 183, with Klein, DMV, Enc: 391, 469, 617 192, 197-200, 204, 207, 212, 217, 222, Wiener, Christian 1826–1896, math., DMV: 229, 233, 235, 237-38, 249, 256, 260- 48-49, 118, 239 61, 263-66, 268, 291-92, 294-95, 298- Wiener, Hermann 1857–1939, math., DMV: 99, 318-19, 321-23, 328, 329-30, 339- 231, 233-34, 239, 369-70, 617 40, 342, 354, 357, 365, 368, 371-74, Wiener, Norbert 1894–1964, American 376-77, 410-12, 457, 483, 486, 509-10, math., DMV: 437, 566 569-70, 586, 591, 602, 607, 623-26, Wigger, Julius 1871–1934, teacher: 399 632-33, 637, 644-45, 647, 652 Wilamowitz-Moellendorff, Ulrich von Weiler, Adolf 1851–1916, Swiss math., PhD 1848–1931, class. philologist: 35, 366, with Klein, DMV: 42, 97, 108, 110, 437, 528, 626 132-34, 137 Wilbrandt, Adolf von 1837–1911, writer: Weingarten, Julius 1836–1910, math., 362 DMV: 100, 200 Wiles, Andrew *1953, British math.: 381 Weinreich, Hermann 1884–1932, math., Wilhelm I 1797–1888, German Emperor and pedagogue, DMV: 302, 496 Prussian King: 84, 320 Weiß, Wilhelm 1859–1904, Austrian math., Wilhelm II 1859–1941, German Emperor DMV: 40, 54, 177, 231, 248-49 and Prussian King: 363, 401, 416, 437, 443-44, 451-52, 487, 497, 499 Index of Names 677

Williams, Ella Cornelia, American math. Young, William Henry 1863–1942, British teacher: 412 math., DMV: 302, 429, 522, 538, 631, Wiltheiss, Eduard 1855–1900, math., DMV: 640, 653 370 Zacharias, Max 1873–1962, math., DMV, Wiman, Anders 1865–1959, Swedish math., Enc: 433 DMV, Enc: 99, 189, 247, 288, 338, Zarncke, Friedrich 1825–1891, philologist: 613, 617 (Wimmer=Wiman) 30, 220 Windau, Willi 1889–1928, math., DMV: Zeiss, Carl 1816–1888, scientific instrument 536 maker: 10, 35, 114, 438, 442, 447, 471, Winkelmann, Max 1879–1946, math., PhD 558, 565-66, 590, 649 with Klein, DMV: 418, 463, 471, 548, Zemplén, Győző 1879–1916, Hungarian 617 physicist, Enc: 468, 613, 617 Winston (md. Newson), Mary Frances Zeppelin, Ferdinand Graf von 1838–1917, 1869–1959, American math., PhD with general, inventor: 451, 617 Klein: 346, 404, 413, 415-16, 462, Zermelo, Ernst 1871–1953, math., DMV, 547, 576, 632 Enc: 307, 394, 456, 490, 514 Wirtinger, Wilhelm 1864-1945, Austrian Zeuthen, Hieronymus Georg 1839–1920, math., DMV, Enc: 4, 131, 141, 184, Danish math., Enc: 47, 50, 54, 68, 120, 280, 292, 340, 341, 366, 371, 417, 429, 242, 309, 395, 476-77, 479, 613, 617 457, 482, 575, 576, 577, 613, 617, 628, Zhukovsky, Nikolay Y. 1847–1921, Russian 630, 643, 653 math., mech.: 372, 450, 453, 463, 466 Wirtz, Karl 1861–1928, prof. of electrical Zindler, Konrad 1866–1934, Austrian math., engineering: 231, 617 DMV, Enc: 41-42 Witting, Alexander 1861–1946, math., PhD Ziwet, Alexander 1853–1928, Polish-Ger- with Klein, DMV: 231, 338, 617, 653 man-American eng., math., DMV: 404, Wöhler, Friedrich 1800–1882, chemist: 45 495, 634 Wolff, Karl Georg 1886–1977, math., Zoepffel, Richard 1843–1891, church teacher, DMV: 550, 640 historian: 116 Wolfskehl, Paul Friedrich 1856–1906, Żorawski, Kazimierz 1866–1953, Polish physician, math., DMV: 381, 395, 538 math., DMV: 335, 613, 617 Woods, Frederick Shenstone 1864–1950, Zorn, Philipp 1850–1928, prof. of canon and American math., PhD with Klein: 334, constitutional law: 500 613, 617 Zühlke, Paul 1877–1957, math., pedagogue, Wright, Orville 1871–1948, American DMV: 505, 617 aviation pioneer: 450, 452, 640 Wright, Wilbur 1867–1912, American aviation pioneer: 450, 452, 640 Wüllner, Adolf 1835–1908, physicist: 29, 648 Wulff, George V. 1863–1925, Russian crystallographer: 356 Wundt, Wilhelm 1832–1920, psychol., philos.: 219, 229, 310, 492, 528 Wußing, Hans 1927–2011, math.hist.: ix, 5, 78, 126, 653 Yoshiye (Yoshie), Takuji (Takuzi) 1874– 1947, Japanese math.: 394, 487-88, 494, 613, 617 Young, George Paxton 1818–1889, British- Canadian theol., logician: 25 Young (née Chisholm), Grace, see Chisholm