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Home , Edmund Landau, Emil Artin, Ernst Witt, Felix Klein, Gustav Herglotz, Hans Lewy

Mathematics at Göttingen under the Nazis

The Mathematical Institute in Göttingen in 1931 losophy on the Basis of Modern Science”. His suc- had an outstanding tradition: Gauss, Riemann, cessor, , lectured widely on dif- Dirichlet, , Minkowski and Hilbert. It ferential , and on the was located in a new and ample building (thanks philosophy of (on which I wrote up to the , which had also lecture notes). From his seminar on rep- provided such a building for mathematics at resentations, I learned much (e.g., on the use of ). The library was ample, linear transformations), but I failed to listen to and included a famous thesis his urging that algebraists should study the filling a trunk and giving an ex- structure of Lie algebras. I also was not con- ...a dynamic plicit construction “by ruler and vinced by his assertion that involved compass”. The faculty was too much “sand”. (professor and small (by present standards) since 1909) lectured to large audiences with his but superb, with a large repre- accustomed polished clarity—and with assis- successful sentation of young people. tants to wash off used (rolling) blackboards. model of a Before my time, many Amer- , administrative head of the In- ican (most re- stitute, lectured and managed the many assis- top cently H. B. Curry) had studied tants working on the manuscript of the Courant- in Göttingen. Here I will sum- Hilbert book. delivered mathematical marize my own experiences eloquently his insightful lectures on a wide va- there, quoting at some length riety of topics: Lie groups, , geomet- center... from a few letters which I wrote rical optics, functions with a positive real part. at the time (1933), since they Felix Bernstein taught statistics, but left in De- record my reactions on the spot. cember 1932 before the deluge struck. These In 1931, after graduating from Yale and spend- were then the ordentliche professors in Göttin- ing a vaguely disappointing year of graduate gen. study at Chicago, I was searching for a really first- The ausserordentliche Professoren (with much class mathematics department which would also less prestige) included , Paul Hertz include . I found both in Göt- and . Hertz lectured on causality tingen. and (the famous Physical Institutes, with Hilbert had retired from his professorship, but , Richard Pohl and were still lectured once a week on “Introduction to Phi- right next door). Paul Bernays worked with Hilbert in logic and on the preparation of the prospective Hilbert-Bernays book Grundlagen Saunders Mac Lane is Max Mason Distinguished Service der Mathematik. He also taught (with less en- Professor Emeritus of the . thusiasm) the famous Felix Klein course Ele-

1134 NOTICES OF THE AMS VOLUME 42, 10 mentary Mathematics from the Higher Stand- In 1931, faced massive economic (intended chiefly for future gymnasium and political problems. The Great Depression had teachers). Emmy Noether (whom Weyl regarded caused much unemployment in Germany, and as his equal) taught enthusiastic but obscure many Germans still recalled clearly the painful courses on her current research interests (e.g., postwar inflation. The German chancellor (Brun- on group representations and on algebras). Her ing) did not have a secure majority in the Re- inspired students included Ernst Witt and Oswald ichstag, so he ruled by emergency decrees. The Teichmüller. people I knew were concerned by these issues There were many young Privatdozenten and and often had liberal or left-leaning sympathies, Assistenten, including , from whom I but I recall no one who correctly foresaw the fu- learned about P.D.E., Otto Neugebauer (history ture. I arrived in Germany first in to learn of mathematics) and Arnold Schmidt (logic), as German and to absorb the culture (e.g., Bertold well as , , Franz Brecht and the Drei Groschen Opera). There com- Rellich and Wilhelm Magnus. Often we went to munists and social democrats competed with the fine restaurant at the nearby railroad station Nazi storm troopers (the SA). I carefully studied for good food and discussion. There were many a pamphlet The Twenty-seven Political Parties of eager students, including Gerhard Gentzen Germany; the had managed to (logic), Fritz John, Peter Scherk, Olga Taussky, get politics badly fragmented. Once I settled in and Ernst Witt. Göttingen, I could note every Sunday the young The social life included a one-time dancing students with bandaged faces—they came from party at Professor Weyl’s apartment. If on a Sun- practice duels of the “color” (corps) fraternities; day you called at the palatial home of Edmund perhaps they anticipated general admiration for Landau to leave your card, that action would professors of law who sported impressive du- ensure an invitation to a subsequent Landau eling scars. Once in the winter, I defended a party, complete with competitive games. At one street urchin who had unwisely lobbed a snow- point, Landau had invited G. H. Hardy for a visit, ball at a corps student. The student thereupon so Landau went to the train to meet him. Hardy, challenged me (“Your card, please”). I had no call- in a trench coat and dark glasses, stepped down ing card on me, so declined the challenge. The from his car. Landau pounced on him and asked student responded, “Mit solchen Leuten for the latest results on the “minor arcs” used verkehren wir nicht”—“We do not associate with in analytic ; Hardy responded, to such people”—and indeed he did not, passing me Landau’s dismay, that he had lost all interest in often on the street with wordless disdain. Per- the subject. It turned out that the dark glasses haps I was lucky. Martin Kneser told me that in hid not Hardy, but a Landau student anxious to 1912 George Polya was in Göttingen, was chal- play a trick. lenged by a student, declined—whereupon the There were many other visitors. Paul Alexan- rector advised him to leave the university. I man- droff came to present the latest formulations of aged to stay, to my great profit. algebraic topology (as in his slim volume Ein- In 1932, German politics was turbulent with fachste Grundbegriffe). came from street battles in Berlin and elsewhere between to expound the obscure beauties of the Nazi storm troopers and communist groups. class theory. lectured (at one Then in January 1933, there was an election in meeting of the weekly colloquium) on projective which the Nazis made common cause with the relativity theory. As always, the colloquium was German National Party (led by von Papen); these preceded by tea and a display of the latest issues Nationalists probably thought that they could of journals. Richard von Mises was then a pro- control Hitler; the combined vote was sufficient fessor at Berlin (the long-time rival of Göttingen to make Hitler Reichschancellor. His speeches mathematics). He gave an evening lecture on his and his picture appeared everywhere. (somewhat ambiguous) foundation of probabil- On February 12, 1933, I took a study break to ity theory on his notion of a Kollektiv. The whole visit Weimar. On arrival, I went to the Opera Göttingen establishment listened, and then House, but tickets for the next day were all sold (Hilbert, Bernays, Bernstein, and others) de- out (it was the 50th anniversary of the death of nounced his approach. In brief, new ideas were Wagner). Fortunately, by standing outside the forcefully presented and discussed. There was Opera House the next morning, I managed to get plenty of personal contact; for example, for a pe- a ticket; the first half of the opera (Wagner, of riod I lived in Courant’s house in order to teach course) was splendid. In the intermission, I him the use of English in preparation for his walked out to the lobby. There, twenty-five feet planned visit to the U.S.A. away, stood Hitler and Göring (easy to recognize Thus the Mathematical Institute at Göttingen from their newspaper pictures). At that time (as in 1931–1932 was a dynamic and successful I did some months later), I did not fully realize model of a top mathematical center. the prospects of evil. In later years, I vividly re-

OCTOBER 1995 NOTICES OF THE AMS 1135 called the sight of Hitler, but thought that it a new law about such officials summarily dismissed took place later, in May 1933. It thus later seemed all those who were Jewish, except for those ap- to me to be the one occasion where (had I car- pointed before 1914 and those who served as sol- ried a weapon) I might have personally changed diers in the First World War. In addition, dis- history. missal awaited “all those officials who are not On March 5, 1933, the government coalition at every time completely committed to the Na- held a second election, preceded by a vast pro- tional Socialist State”. paganda effort. It produced a much larger vote The effect on the Mathematical Institute was for the government. The resulting situation is de- drastic. Courant, Noether, and Bernstein were im- scribed in two letters which I wrote my mother— mediately dismissed (on April 25). In Courant’s one dated March 10, 1933, and the other un- case, his service in the First World War did not dated. (The author will provide copies of these spare him; evidently his earlier political views letters on request.) and his wide mathematical influence (inherited The first letter (10.III.33) is a tongue-in-cheek from Felix Klein) made him disliked. With his de- praise of propaganda. I had never before seen parture, Neugebauer was made acting head of what official propaganda could do to alter opin- the Institute, but he lasted only one day, when ion. By the time I left Germany in August, I felt he too was dismissed, apparently because of so misled by continued propaganda that I did not his political sympathies, but perhaps because he know what was really going on in the world. failed to mow his lawn! On April 27, Bernays, In the second undated letter (“address omit- Hertz and Lewy were dismissed. Landau was ted”), I seem to be worried that my mail might advised not to lecture in the coming summer se- be censored. I now think that this worry was mester; he followed the advice. As a result of this, groundless. But I was a bit concerned about my my letter of May 3 to my mother read (in part): copy of Das Kapital; I recall that I carefully hid So many professors and instructors it in a drawer under some shirts. Actually, there have been fired or have left that the was a book-burning in Göttingen on May 10, mathematics department is pretty 1933. At about that time the copies of the Lit- thoroughly emasculated. It is rather erary Digest which my mother sent me were no hard on mathematics, and we have longer allowed to come. but the cold comfort that it is the After writing those letters, I went on a student- best thing for the Volk. organized two-week skiing trip to Oberstdorf in the Tyrol. We returned (on a group ticket) by For that summer semester, things struggled train, stopping for three hours in Nurenberg. along somehow. All the students who could do This was the day for which Hitler had decreed so hurried to finish up degree requirements. I a peaceful boycott of all Jewish stores. Leaving had lost my thesis advisor (Paul Bernays); Her- my skis and baggage on the train, I went to ex- mann Weyl took his place, and subsequently plore the town. There, at a big shoe store, I saw gave me a tough oral examination. I managed, a seedy-looking man peering into the display but in the definition of a Hausdorff , I for- window. The store was closed, but nevertheless got the separation axiom but did not dare men- the police spotted the man and at once hustled tion the fact that Weyl had once forgotten it in him off. Since I had supposed the boycott to be print. For another oral exam, I took a course on peaceful, I was curious and followed along. Soon the philosophy of mathematics with Professor I too was arrested. The earnest policeman as- Moritz Geiger. Though Jewish, he had served in sumed that I was one of the Anglo-Saxon re- the First World War, so was still left in office. porters who were collecting lies about the Reich; However, in every lecture I could notice his ner- he upbraided me. I tried to assure him that I was vous anxiety about the future—a justified anx- not a reporter, but only a student. He thereupon iety. observed that if he were visiting the U.S.A., he On July 14, I wrote my mother: would not intrude on the police. I tried my best to report that all my possessions were about to leave on a train—I was let go just in time to Just recently it has been proclaimed catch it. I returned to Göttingen to my lodgings that the German revolution is now at at 28 Lötze Strasse (not far from the Math- an ; now things must proceed in ematical Institute). There my landlady regularly in a strictly legal fashion. provided me with evening tea and talk; I rapidly That somehow gives the impression discovered that two weeks of propaganda had that up to the present everything has converted her from mild conservative views to not proceeded in a strictly legal fash- ardent Nazi discipleship. ion, or at least that the SA (the Sturm In Germany, professors, Privatdozenten and as- Abteilung) has on occasion taken sistants are all government officials. On April 7, 1933, unto itself the rights and privileges

1136 NOTICES OF THE AMS VOLUME 42, NUMBER 10 of the police. How far that has hap- Herglotz: What is the group for complex analy- pened I cannot very well tell. sis? SM: The conformal group. My fiancée, Dorothy Jones, had come to Göt- That sufficed to start Herglotz on a splendid tingen from New York to help me finish my the- lecture on geometric theory in terms of sis. She learned much about the political situa- the conformal group. tion.When she and I went to the Standesamt to My thesis was done, and I was through. get a wedding license, we were surprised to find there my fellow student Fritz John and his friend Charlotte. They were troubled to have us discover their presence. He was Jewish, she was not; they were anxious to get married quickly because he feared the prospect of a law which would pro- hibit such intermarriages. We agreed to secrecy; they invited us to their feierliches Abend after their wedding. Among the other guests were a blond German youth and his evidently Jewish girlfriend. Dorothy wrote my mother, “There is adventure amid romance in such a marriage.” On July 25, I wrote my mother:

Politics continue to be as absorbing as ever. Friday night Dorothy and I went to a Nazi speech on the new order of things in the German uni- versities. It turned out to be a most sensible speech. The speaker (a prominent Nazi professor in Berlin) did not demand that Wissenschaft The pleasant hills near Göttingen made excursions possible and at- be completely bound down by poli- tractive. One day, at her lecture, Professor Noether observed with dis- tics. He said that Wissenschaft should taste that the Mathematical Institute would be closed at her next lec- be independent but not au- ture, in honor of some holiday. To save mathematical research from tonomous…. After the meeting, we this sorry interruption, she proposed an excursion to the coffee went downtown and drank coffee house of Kerstlingeroden Feld, up in the hills. So on that day we all with my friend Gebhardt (whom we met at the doors of the Institute—Noether, Paul Bernays, Ernst Witt, had met at the meeting). There again etc. After a good hike we consumed coffee, talked algebra, and hiked we discussed politics, the influence back, to our general profit. There were other such excursions, as on of Catholicism (blind obedience) upon the occasion of the visit by Oswald Veblen. The picture above (cour- Hitlerism, and so on far into the night. tesy of Martin Kneser), with some uncertain identifications (was I I have recently become impressed really there?) may now testify to this. with the great variety of opinions —Saunders Mac Lane within the Nazi movement. All Nazis Standing: Paul Bernays, Hans Lewy(?), O. F. G. Schilling, Schw- do not think alike, even though it ertfager(?). Woman facing right may be Olga Taussky, then Erna may externally seem as if they did! Barrow, Emmy Noether (almost hidden), Paul Alexandroff (?), (?). (Note, 1995: I no longer recall the discussion Seated, front row: Ernst Witt, (?), Mac Lane(?), (?), (?). of Catholicism; I was then largely ignorant of Ger- man Catholicism and a great admirer of my grandfather’s powerful sermon favoring toler- ance.) But for the Institute, there were added losses. My oral exam still threatened—one on geo- Hermann Weyl was not Jewish, but his wife was; metric function theory with that redoubtable this meant then that their two sons were so professor Gustav Herglotz. I consulted my ex- counted. So at the end of the summer semester perienced friends: what to do? They reminded 1933, Weyl left for a professorship at the Insti- me that he loved to lecture. This I bore in mind tute for Advanced Study in Princeton. All told, during the exam: in 1933 eighteen mathematicians left or were dri- ven out from the faculty at the Mathematical In- stitute in Göttingen. This included Landau; he Herglotz: What is the Erlanger Program? was not officially dismissed, but when he again SM: Everything depends on the group. started to lecture in the winter semester of 1933,

OCTOBER 1995 NOTICES OF THE AMS 1137 the students organized a complete boycott of his Eventually, the four professorships at Göt- lecture. He thereupon resigned and retired to tingen were again occupied (Hasse, Herglotz, Berlin. Kaluza, Siegel), but even with Karl Ludwig Siegel Mathematics at the University of Berlin was the former glory was not restored. At one point, also seriously disrupted; there twenty-three fac- Hasse hoped to increase his influence with the ulty members (including , Max authorities. So, according to his son-in-law, Mar- Dehn, Hans Freudental, B. H. Neumann, Hanna tin Kneser, he applied for membership in the Neumann, and Richard von Mises) left. The spe- Nazi Party, but it turned out that one of his cific (and often less extensive) effects at other grandmothers might have been a Jew; his ap- German universities have been carefully tabu- plication was put on hold till after the war. After lated by Maximilian Pinl in four articles. Detailed the war, Hasse was dismissed as part of the de- analysis of the situation at Göttingen has been nazification. Since then, the Göttingen Math- presented by Schappacher as part of a book on ematical Institute has been gradually reconsti- Göttingen under the Nazis. tuted as one of several such institutes at other One observer has summarized the effect on German universities. But it has not succeeded in mathematics in the following words: reclaiming its original brilliant dominance. As Dorothy and I left in August of 1933, I car- Within a few weeks this action would ried with me, as a treasure, something of the vi- scatter to the winds everything that sion of the earlier Göttingen as the unique model had been created over so many of a great mathematics department. I mourned decades. One of the greatest tragedies the loss, but not only for the sake of science. I experienced by human culture since did not foresee the holocaust, but I was aware the time of the Renaissance was tak- of the power of state propaganda and I was ac- ing place—a tragedy which a few tively fearful of the prospects for a world war, years before would have seemed an although prevention seemed beyond my powers. impossibility under twentieth cen- Now in retrospect, the whole development is a tury conditions. decisive demonstration of the damage done to There were attempts to rebuild mathematics academic and mathematical life by any subor- at Göttingen. The eminent algebraist Helmut dination to populism, political pressure and pro- Hasse became professor and director of the In- posed political principles. stitute; for a period he had difficult dealings with several mathematicians with Nazi enthusi- References asm: Oswald Teichmüller, Werner Weber, Ed- [1] S. Mac Lane (1981). Mathematics at the Univer- ward Tornier. Tornier was briefly co-director of sity of Göttingen, 1931–1933, in Emmy Noether, the Institute; at one point he hoped to get Hasse A Tribute to Her Life and Work, (J. K. Brewer and M. K. Smith, eds.), Marcel-Dekker, New York, 1981, removed from the directorship. Tornier favored pp. 65–78. the party; for example, he later wrote in the then [2] ———, Mathematics at the University of Chicago, new journal Deutsche Mathematik, 1936, vol. 1, in A Century of Mathematics in America, Vol. II, page 2 (my translation): Amer. Math. Soc., Providence, RI, pp. 128–151. [3] M. Pinl, Kollegen in einer dunklen Zeit, Jahresber. Pure mathematics too has real ob- Deutsch. Math.-Verein. 71 (1969), 167–288; jects—whoever wishes to deny this is (1970/71), 165–189; 73 (1971/72), 153–208; 75 a representative of Jewish-liberal (1973/74), 160–208. thought, like philosophical sophisti- [4] N. Schappacher and E. Scholz, Oswald Teich- cates…. Every theory of pure math- müller—Leben und Werke, Jahresber. Deutsch. ematics has the right to exist if it is Math.-Verein. 94 (1992), 1–35. really in a position to answer con- [5] N. Schappacher, Das Mathematische Institut der crete questions which concern real Universität Göttingen 1929–1950, Die Universität objects like whole or geo- Göttingen unter dem Nationalsozialismus. Das metric figures—or if at least it serves Bedrängte Kapital ihrer 250–Jährigen Geschichte, Munich K. G. Saur, 1987, pp. 345–373. for the construction of things which happen there. Otherwise it is incom- plete, or else a document of Jewish- liberal confusion, born from the brains of rootless artists who by jug- gling with object-less definitions mis- lead themselves and their thoughtless public…. In the future, we will have German mathematics.

1138 NOTICES OF THE AMS VOLUME 42, NUMBER 10