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Corrections on Mac Lane’s In this context it is not worth men- (iii) Max Dehn was never in Berlin Article tioning the missing accents on Brün- as a professor, but was “habilitated” Saunders Mac Lane’s memories of ing and Pólya or the curious spelling in Münster, and then was successively mathematical life in Göttingen imme- “Bertold” for Bertolt (Brecht). in Kiel, Breslau, and Frankfurt (where diately after January 30, 1933 (Notices, Mac Lane also gets some historical he succeeded Bieberbach in 1921). He vol. 42, October 1995, 1134–1138), things wrong. fled in 1939, first to Denmark, and in when he was a foreign student there, (i) Moritz Geiger did not serve in the a very arduous way finally came to the are inevitably interesting, as he is one First World War—he was dismissed on United States. of the few surviving mathematicians September 26, 1933 (one month after (iv) Richard Brauer was not in from that time. However, either Pro- Mac Lane’s departure). Berlin; his elder brother, Alfred (a well- fessor Mac Lane, or more likely the (ii) Mac Lane must have misunder- known number theorist, though not as Notices editor responsible, should have stood Martin Kneser about his father- famous as his younger brother), was. When Richard emigrated in October done a better job of editing these rem- in-law. It was a great-great-grand- 1933, he was a professor at Königs- iniscences. To wit: mother of Hasse who was Jewish (her berg. Mac Lane may have been con- “Richard Pohl” should be Robert name was Itzig). I was shown this doc- fused by the fact that both Alfred and Pohl. umentation by Martin Kneser in 1988. Richard did doctoral dissertations in “Hans Freudental” should be Hans The “non-Aryan rules” for being a Freudenthal. Berlin. member of the NSDAP were far “Edward Tornier” should be Erhard (v) I believe Hans Freudenthal left stricter than for anything else and re- Tornier. Berlin in 1931. He certainly did only quired no non-Aryan ancestor alive in “Karl Ludwig Siegel” should be Carl narrowly escape the Nazis, but that 1800. Hasse’s great-great-grand- Ludwig Siegel. was in Holland. Under the picture (p. 1137) “Schw- mother in question was born in 1775. (vi) Hanna Neumann was not Jew- ertfager” should be Schwerdtfeger (his The story of Hasse’s application for ish (her maiden name was vonCaem- first name was Hans). Nazi Party membership is very com- merer). In January 1933 she met Bern- “Erna Barrow” should presumably plicated. Suffice it to say here that he hard Neumann, who was Jewish and be Erna Bannow, who, incidentally, had a brother, Albrecht Hasse, living who emigrated in August of that year later followed Witt to Hamburg, be- in Berlin who had been allowed to to England. She became secretly en- came his first doctoral student (de- join the Party, and so Helmut Hasse gaged to him in 1934; she passed the gree awarded in 1939), and married had reason to believe he might be Staatsexamen while still at Berlin and him in 1940. able to do so as well. in 1937 actually started work on a

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doctorate at Göttingen, to be super- that his “good friend” Gerhard I propose that the AMS take a vised by Hasse. She did not leave Ger- Gentzen “disappeared” when the Rus- stronger, more visible role in the dis- many until July 1938 and married sians arrived in Prague. In fact cussion of the problems of teaching Bernhard secretly later that year. For Gentzen refused to voluntarily give up mathematics. I suggest the following more detail, her obituary in volume his university position in early April action: 17 of the Journal of the Australian 1945; arrested in May, he was placed 1. The Notices editorial board Mathematical Society should be con- in a detention camp, where appar- should invite a series of feature arti- sulted. ently he was murdered by Czech (not cles highlighting the kinds of change (vii) Concerning the story about Russian) soldiers. which are being implemented. There Pólya, since various versions of it cir- are many serious mathematicians who culate (e.g., see also p. 26 of the recent Sanford L. Segal have taken a deep interest in this ac- book George Pólya, Master of Discov- University of Rochester tivity in recent years. Why have they ery, by Harold and Loretta Taylor), the done that? Why do they continue to do (Received December 13, 1995) truth is perhaps worth presenting. On it? Is it, as Professor Krantz suggests, P.S. In Mac Lane’s recent piece in January 18, 1921, Pólya wrote Bieber- because that’s where the big bucks the Mathematical Intelligencer (vol. 16, bach (then in Frankfurt) a lengthy let- are? I don’t think so. Let’s find out. no. 3 (1994), 9–10) an error relevant ter from Zürich (a copy is in my pos- 2. The Society should schedule me- to this letter also occurs. The “math- session) in which the incident alluded diated discussions at AMS meetings on ematical anti-Semite” who said to by both Mac Lane and the Taylors the issues of change. The participants “Princeton ist ein kleines Negerdorf” (following a taped interview with should represent various positions on was not in Berlin and was not in- Pólya’s nephew) is described. Inci- the questions of change, and these significant. He was the great geome- dentally, the context of this letter is should not simply be panel discus- ter Wilhelm Blaschke, who was in that Pólya might be considered (the sions. They should also not degener- Hamburg. chance, in fact, was very remote) as ate into debates, since debate implies Bieberbach’s successor when he went confrontation, and in debate, victory to Berlin. Presumably Pólya in 1921 is tends to go to the glib participant. rather more accurate about something Innovations in Mathematics The goal should be information for that happened in 1913 than other peo- Education the membership. I suggest discussion ple’s secondhand memories many The AMS has been presented with an mediated by persons who are trained years later. So far as I know this is the opportunity for positive action and for that activity. first time this story has become pub- change by Steven Krantz. He has pre- 3. The Committee on Education lic. Christmas 1913, Pólya was travel- sented readers of AMS publications should better highlight the Society’s ling from Zürich to Frankfurt and had with a collection of singularly unpro- activities related to education at its an exchange of words with the young fessional diatribes opposing change in Web site, and the Committee on Edu- man sitting opposite him in the train the way we teach mathematics and cation should attempt liaison with compartment over Pólya’s trunk, attacking those who promote change. other organizations interested in the which had fallen down. Pólya, who was The most recent, in “Math for Sale”, same problems. in an “overly irritated state”, chal- the editorial in the October 1995 issue Seven years ago Jerry Uhl and Ho- lenged the fellow to a duel. He refused, of the Notices, carries the authority of racio Porta decided to try using new where upon Pólya punched him. It the Society, since it was written by an tools and ideas in teaching calculus to turned out that his unwilling oppo- editor and published by the Society. undergraduates. The Calculus&Math- nent was the son of an important man Do you know that the Society has ematica project was born. I came along and a student in Göttingen. Pólya had a Committee on Education? Do you shortly after they started. We tried to leave Göttingen as a consequence. know what it is doing? You can find these things and were very excited by Pólya says, “privately the story is also out by going to the AMS home page what we saw: first-year undergrads not worth a defense.” Thus, there were on the World Wide Web. Do you know (and not just honors students) talking no anti-Semitic remarks as in the Tay- that the Society has a listserv for dis- about mathematics in ways we hadn’t lors’ version, and Pólya was the one cussion of calculus reform issues? seen before, students taking charge of who demanded a duel rather than the Will you find reference to it on the their own explorations into mathe- other way around. Pólya blames him- AMS home page? Not as this is being matics, and students who could and self completely for the incident. Inci- written. Is the Society serious about did explain in their own terms what dentally, Pólya does mention anti- addressing problems in the teaching the calculus does and is. We were Semitism elsewhere in the letter, so of mathematics? hooked. We have continued to invent there is every reason to believe this ver- I believe that the Society and its and pursue change, and we are still ex- sion. Of course, neither Mac Lane nor membership have a vital interest in cited by what we see happening. Martin Kneser could have known about questions about teaching mathemat- Changing the way we teach math- this. ics. The questions are difficult, and ematics is a serious enterprise and In this connection, one must also points of view vary, but there is strong should not be demeaned by an opin- mention Mac Lane’s letter in the same evidence to suggest that general im- ionated, uninformed member of the issue of the Notices, when he hints provement is possible. Notices editorial board. Much of what

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is going on is being done by mathe- munistischen Machtergreifung unter guished place in the history of their maticians with long and respected ser- Tito in Jugoslawien auch für die Fam- subject. vice to the profession and to the So- ilie Avakumovi´c tiefgehende Ein- 4. With no visible relation to their ciety. Those people deserve the schnitte” [4, p. 145]. Lorch does not respective arguments, both Booss and support and respect of the organiza- quote, however, the explanation that Lorch feel obliged to remark that tion, not what Steve Krantz would give follows: “Der Vater starb, die Familie J. Brüning had some presumably im- them. verlor durch Enteignung den größten portant task in the restructuring of sci- Teil des Besitzes, der Bruder emigri- ence in [the] former GDR after 1990, William J. Davis erte nach London.” We maintain that entrusted to him by the German fed- The Ohio State University expropriation of the family, emigra- eral government. Booss describes this tion of the brother, and denial of the (Received January 1996) task as “the liquidation of the academy right to emigrate to Avakumovi´c’s wife of sciences of the former GDR.” Lorch and children could be rightly termed “deep incisions in the life of the fam- refers to Booss (in a postscriptum) Comments on Lorch’s Letter ily”, but it escapes us how this could but does not hesitate to magnify the Obituaries published in JDMV have be read as “derision of the post-war “official responsibilities” into a full- recently become a topic in letters pub- Tito regime in Yugoslavia.” fledged “restructuring of the former lished in the Notices of the AMS and The second remark mentions “die German Democratic Republic.” Well, the Mathematical Intelligencer [1], [2], weltoffene Liberalität, die er (Avaku- the fact is that the academy was in- [3]. We do not want to contribute to movi´c) seiner noch von der Donau- deed dissolved but, in its substance, this discussion, which appears overly monarchie geprägten Erziehung ver- by no means liquidated (a strong and emotional and, by the quality of the dankte.” We have experienced lively Karl-Weierstrass-Institut, as its arguments used, not suited for pub- Avakumovi´c’s “weltoffene Liberalität” mathematical part, exists to this very lications addressing a scientific com- many times in personal encounters, day), and it is also a fact that Brüning munity. Since our obituary [4] for Vo- and this personal trait could easily jislav G. Avakumovi´c has been dealt had no part in these decisions. He was and convincingly be related to his ed- with at length, we feel obliged, how- serving, though, on a committee ap- ucation, which happened to take place ever, to explain at least a few relevant pointed by the state of Berlin to re- in the days of the Habsburg monar- facts. build the mathematics department of chy—that is what we are saying, and 1. Lorch [3] criticizes the fact that Humboldt-Universität. Every colleague we do not see what is wrong here. we do not supply information on the can easily inform himself about the 3. Lorch’s criticism culminates in life circumstances of Avakumovi´c dur- outcome. the passionate question, “What im- ing the German occupation of Yu- One wonders about the motives of pression of history are the authors goslavia. The reason for this is very scientists who find it necessary to attempting to convey?” This reveals a simple: we do not know anything sub- abuse the facts—readily available as stantial about this period of his life basic misconception of what an obit- uary should be about: we see it as in- they are—in such an irresponsible nor does any friend or family member way. we were able to ask; all of them, in- formation for the mathematical com- munity, concentrating on math cluding his wife, met Avakumovi´c only References after the war. He himself talked about ematical achievement and leaving a [1] L. Lorch et al., Notices AMS 41 (1994), his life at various occasions, but he did little room for homage paid by the 571—572 and 1101. not mention this particular period ei- authors, usually friends or students. Correctness of the facts communi- [2] B. Booss-Bavnbek, Memories and memo- ther. Thus, all we can say is that rials, The Mathematical Intelligencer 17 Avakumovi´c moved from the family cated is a necessity; a critical evalua- tion of life and achievement in the (1995), 15—20. estate in Semlin to Belgrad, where he [3] L. Lorch, Letter to the Editor, Notices context of the scientific and political lived in [the] house [owned by his AMS 42 (1995), 845—846. background of the century certainly brother], who was then ambassador of [4] J. BrÜning and W. Eberhard, Zum [is] not—it is beyond what a mathe- Yugoslavia to the United States. We Gedenken an Vojislav Gregor Avaku- matician can usually do and must be can infer, though, that he was suffer- movi´c, Jber. d. Dt. Math.-Verein. 95 ing like everybody else under the Ger- left to the professional historian. In (1993), 141—152. man occupation—a well-known fact this respect we fully subscribe to the [5] James A. Jenkins, Letter to the Editor of history which we have no intention sober statements in [5]. (with Editor’s Note), Notices AMS 42 to defend. Concerning Avakumovi´c’s mathe- (1995), 847. 2. Lorch finds “quite a few personal matical achievements we feel it nec- and political remarks” in our text. essary to emphasize again that we J. Brüning Those which could be called “political” hold them in high esteem. Of his 31 Berlin in the widest sense of the word are ex- papers, published between 1935 and W. Eberhard 1956, at least two (reference numbers actly two. The first one mentioning Duisburg Tito is quoted by Lorch as follows: 11 and 30 in [4]) have been truly in- “Das Kriegsende brachte mit der kom- fluential and have earned a distin- (Received January 5, 1996)

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From Barbados on Ethnicity tion to a student’s mathematics edu- dents, will definitely enhance my un- I wish to applaud Raymond Johnson cation. For a variety of reasons derstanding of and sensitivity to just for his informative and thought-pro- though, very few mentees seek out a how important the notion of com- voking article “Conference for African mentor who works in the natural sci- munity really is. American Researchers in the Mathe- ences, and fewer yet in mathematics. matical Sciences at MSRI” (AMS No- A participant at the conference at Raymond Grinnell tices, December 1995). The socio-math- MSRI, when commenting on one of University of the West Indies its successes, revealed that, “…meet- ematical agenda of the conference and (Received January 17, 1996) the personal commitment on the part ing people who could help me attain of the participants are a source of en- my goals of becoming a Ph.D. in math- couragement and inspiration. There ematics. Gaining inspiration from those who have succeeded” (p. 1497). Teaching from a Twentieth- are interesting similarities and differ- Century Perspective ences in a number of university/math- I ask again whether mathematics stu- dents here experience an “osmosis Recent letters and articles in the No- ematical issues here in Barbados and effect” with regard to motivating their tices seem to imply that calculus re- some of those highlighted in the arti- potential in mathematics by way of form is the work of mathematical cle. At the outset, I hope my letter any of their interactions with me? If charlatans after soft money and su- makes a small contribution to sus- they don’t, are any of the reasons for perficial results. In your January 1996 taining the positive momentum gen- this due to my ethnicity? issue, we were told by Greenman that erated at the conference. There are a number of indicators “Mathematics is losing its soul. Its Upon hearing the country name suggesting that Barbados will mature priests are pawning it off to a dif- “Barbados”, one probably imagines a sufficiently over the next few years ferent god.” In an editorial in an ear- tropical, sundrenched island paradise. and hence attain formal developed-na- lier issue of the Notices, Krantz de- While this picture is quite accurate, tion status within a decade or so. Im- clared that “It is time for pure there are a few facts about the coun- plicit in this assertion is the necessary mathematicians to close ranks and try which are of particular significance. consumption of computer technol- stand up for the integrity of our dis- Upwards of 90 percent of the total ogy and ultimately a greater depen- cipline.” Indeed, as evidenced by the population here is of African descent, dence on the expertise of its people renewed popularity of traditional and essentially all of my students in basic sciences and mathematics. textbooks, the ranks may be closing share this identical lineage. It is not at In this sense and numerous others, already—reform might soon become all uncommon to hear the label “Afro- the reality here and that in North a thing of the past. Caribbean” when they are referring to America are vastly different. How- If so, then McCallum’s letter in themselves. As in North America, there ever, the issue of the environment in your January 1996 issue may be exists a pervasive quest, particularly which one learns mathematics is uni- prophetic where it states that “the in young people, to seek identity, com- versal. In Johnson’s paraphrasing of academic mathematical community is munity, and affirmation in a rapidly some questions due to Lenore Blum, in danger of having many of its re- changing society. Of course, such a he recounts a particular aim of the sponsibilities taken away from it, par- desire is by no means unique to math- conference (p. 1496). I also paraphrase ticularly its teaching responsibilities.” ematics students. The “community by suggesting, as they do, that we Our students understand less and concept” (p. 1496) is positive, defining, “…create an environment where [West less of our traditional curriculum, and a prominent feature of both the Indians] have a chance to do and learn and our graduates are less and less very small mathematics group at this mathematics in a way that most suc- able to find meaningful work. More campus and the almost infinitely cessful [white] male mathematicians and more, the mathematical ideas larger group of African American stu- take for granted” (p. 1496). used by scientists, businessmen, and dents and researchers in North Amer- Each year a few of our final-year engineers are being taught by scien- ica. I find it encouraging that my ob- students make plans to pursue grad- tists, businessmen, and engineers. If servations in Barbados on this issue uate studies in mathematics and com- our response is to bury our heads in were distantly confirmed by partici- puter science at a North American the sand, then it is only a matter of pants at the conference. university. I was surprised, and felt time before society buries the rest Johnson writes about the mentor- somewhat naïve, when several of of us as well. ship concept (p. 1498). As a white these students revealed that an im- The problem is that mathematics Canadian male mathematician, the in- portant factor that would influence has refused to change for so long formation I read on this topic has their choice of school is its reputation that it now must regard progress as made me wonder to what extent and as a “black university”. The impor- a crisis rather than as an opportunity. on what personal level my students tance of an ethnically similar and ac- In a world that has been revolution- can identify me as a mentor. Our cam- cepting [university] community is em- ized by twentieth-century mathe- pus is small, and as a country Barba- phasized in several places in matics and science, mathematicians dos is minuscule. It is not difficult to Johnson’s article and in mine. The are committed to ignoring the math- imagine that the mentorship program comments on this issue from the con- ematics and science of the twentieth here could well make a fine contribu- ference, as well as from my own stu- century. Economics has benefitted

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greatly from game theory, but have ern perspective. Even freshmen seem Erratum our undergraduates? An undergradu- to prefer Lesbegue’s definition, even The March 1996 issue of the Notices ate chemistry curriculum would be though it really “blows them away”. carried an article entitled “Downsiz- laughable if it did not include spec- They like iteration and fixed point ing at Rochester: Mathematics Ph.D. troscopic methods, but even the sim- theorems. They can handle supre- Program Cut”. On page 303, the ar- plest concepts of spectral theory are mums and infimums, and they prefer ticle states that, as part of the for- withheld from our students. In fact, them to epsilons and deltas. They mulation of the Rochester Renais- even get excited about integration by our students graduate having never sance Plan, administrators parts when it is used to derive a sim- encountered the classification of the interviewed three faculty from each simple groups, having never numeri- ple version of Heisenberg’s uncer- department at Rochester. The arti- cally verified an analytical result, and tainty principle. And my students cle erred in saying that only two fac- having never encountered fixed point have been successful in obtaining po- ulty from the Mathematics Depart- theorems, spinors, the simplex sitions in both industry and academia, ment were interviewed; three method, the traveling salesman prob- primarily because they were willing to mathematics faculty members were lem, graph colorings, Hilbert’s tenth work very hard on very hard ideas in fact interviewed. After the three in- problem, the Riemann zeta function, when those ideas seemed modern and terviews took place, the chair of the knots, etcetera, etcetera. relevant to the world around them. Mathematics Department asked the “Students must learn the old stuff As I mentioned earlier, I sense a administration to interview a fourth first,” we say. “Such ideas are too ad- strong urge in the mathematical com- vanced for them.” Thus we continue munity to return to the status quo. We member of the department, and al- to produce nineteenth-century math- seem to be asking ourselves,“If we though the administration agreed to ematicians who are completely un- just do things the way we have al- do so, this fourth interview never prepared for the twentieth century. ways done them—with a few new took place. And thus we ourselves continue to be wrinkles, of course—then are we re- little more than nineteenth-century ally failing our students?” In a soci- mathematicians with a twentieth-cen- ety that cannot engage in a meaning- tury specialty. In contrast, John ful discussion of its economic health, Winthrop of Harvard began teaching in a time when most of our students the works of Newton less than fifty will never encounter the letters FFT, years after the publication of the Prin- in an age when the technology we rely cipia. Our second president, John on is based on mathematics our grad- Adams, testified that “Mathematicks uate students will never see, and in an and natural Phylosophy attracted the international climate where mathe- most of my Attention” while in college, maticians and scientists rarely con- and many of our other founding fa- tribute to international opinion, I be- thers have made similar statements. lieve the answer is an undeniable “Yes, Like Winthrop, we must also find we are failing our students.” ways to teach mathematics from a In fact, I cannot help but think of modern perspective, and that means the Librarians of Alexandria, who, ac- we must regard teaching as more than cording to H. G. Wells, were within two the ability to plod through a book sec- hundred years of the Library’s incep- tion by section. It means more than tion “…shy, eccentric, unpractical, in- adding a course or two or modifying capable of essentials, strangely fierce a syllabus here or there. As some of upon trivialities of literary detail, … us have discovered, mixing the new For him no method of copying was and the old leads only to compromise, sufficiently tedious and no rare book superficiality, and a great deal of frus- sufficiently inaccessible….For many tration. precious generations the new-lit fires Instead, we must learn to teach all of the human intelligence were to be of our courses from a twentieth-cen- seriously banked down by this by- tury perspective. Measure theory is product.” If we are indeed becoming the proper setting for defining inte- the new Librarians of Alexandria, cre- grals, so we should drop Riemann’s ating a vast wealth of knowledge that definition altogether. He certainly will to the society we live in is increasingly not mind if it means including more strange and meaningless, then his- of his geometry or number theory. My tory tells us it will be our ruin. own experience has been that both my popularity and effectiveness as a Jeff Knisley teacher have increased in direct pro- East Tennessee State University portion to my efforts to reach a mod- (Received January 10, 1996)

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