Celebratio Mathematica

Saunders Mac Lane

Mathematics at Göttingen under the Nazis

by Saunders Mac Lane

The Math­em­at­ic­al In­sti­tute in Göttin­gen in 1931 had an out­stand­ing tra­di­tion: Gauss, Riemann, Di­rich­let, Fe­lix Klein, Minkowski and Hil­bert. It was loc­ated in a new and ample build­ing (thanks to the Rock­e­feller Found­a­tion, which had also provided such a build­ing for math­em­at­ics at Par­is). The lib­rary was ample, and in­cluded a fam­ous thes­is filling a trunk and giv­ing an ex­pli­cit con­struc­tion “by ruler and com­pass”. The fac­ulty was small (by present stand­ards) but su­perb, with a large rep­res­ent­a­tion of young people.

Be­fore my time, many Amer­ic­an math­em­aticians (most re­cently H. B. Curry) had stud­ied in Göttin­gen. Here I will sum­mar­ize my own ex­per­i­ences there, quot­ing at some length from a few let­ters which I wrote at the time (1933), since they re­cord my re­ac­tions on the spot. In 1931, after gradu­at­ing from Yale and spend­ing a vaguely dis­ap­point­ing year of gradu­ate study at Chica­go, I was search­ing for a really first-class math­em­at­ics de­part­ment which would also in­clude math­em­at­ic­al lo­gic. I found both in Göttin­gen.

Hil­bert had re­tired from his pro­fess­or­ship, but still lec­tured once a week on “In­tro­duc­tion to Philo­sophy on the Basis of Mod­ern Sci­ence”. His suc­cessor, Her­mann Weyl, lec­tured widely on dif­fer­en­tial geo­metry, al­geb­ra­ic to­po­logy and on the philo­sophy of math­em­at­ics (on which I wrote up lec­ture notes). From his sem­in­ar on group rep­res­ent­a­tions, I learned much (e.g., on the use of lin­ear trans­form­a­tions), but I failed to listen to his ur­ging that al­geb­ra­ists should study the struc­ture of Lie al­geb­ras. I also was not con­vinced by his as­ser­tion that set the­ory in­volved too much “sand”. Ed­mund Land­au (pro­fess­or since 1909) lec­tured to large audi­ences with his ac­cus­tomed pol­ished clar­ity — and with as­sist­ants to wash off used (rolling) black­boards. Richard Cour­ant, ad­min­is­trat­ive head of the In­sti­tute, lec­tured and man­aged the many as­sist­ants work­ing on the manuscript of the Cour­ant-Hil­bert book. Gust­av Her­glotz de­livered elo­quently his in­sight­ful lec­tures on a wide vari­ety of top­ics: Lie groups, mech­an­ics, geo­met­ric­al op­tics, func­tions with a pos­it­ive real part. Fe­lix Bern­stein taught stat­ist­ics, but left in Decem­ber 1932 be­fore the de­luge struck. These were then the or­dent­liche pro­fess­ors in Göttin­gen.

The aus­ser­or­dent­liche Pro­fess­oren (with much less prestige) in­cluded Paul Bernays, Paul Hertz and Emmy No­eth­er. Hertz lec­tured on caus­al­ity and phys­ics (the fam­ous Phys­ic­al In­sti­tutes, with Max Born, Richard Pohl and James Franck were right next door). Paul Bernays worked with Hil­bert in lo­gic and on the pre­par­a­tion of the pro­spect­ive Hil­bert-Bernays book Grundla­gen der Math­em­atik. He also taught (with less en­thu­si­asm) the fam­ous Fe­lix Klein course Ele­ment­ary Math­em­at­ics from the High­er Stand­point (in­ten­ded chiefly for fu­ture gym­nas­i­um teach­ers). Emmy No­eth­er (whom Weyl re­garded as his equal) taught en­thu­si­ast­ic but ob­scure courses on her cur­rent re­search in­terests (e.g., on group rep­res­ent­a­tions and on al­geb­ras). Her in­spired stu­dents in­cluded Ernst Witt and Os­wald Teichmüller.

There were many young Privat­dozen­ten and As­sist­en­ten, in­clud­ing Hans Lewy, from whom I learned about P.D.E., Otto Neuge­bauer (his­tory of math­em­at­ics) and Arnold Schmidt (lo­gic), as well as Her­bert Buse­mann, Wern­er Fenchel, Franz Rel­lich and Wil­helm Mag­nus. Of­ten we went to the fine res­taur­ant at the nearby rail­road sta­tion for good food and dis­cus­sion. There were many eager stu­dents, in­clud­ing Ger­hard Gentzen (lo­gic), Fritz John, Peter Scherk, Olga Taussky, and Ernst Witt.

The so­cial life in­cluded a one-time dan­cing party at Pro­fess­or Weyl’s apart­ment. If on a Sunday you called at the pala­tial home of Ed­mund Land­au to leave your card, that ac­tion would en­sure an in­vit­a­tion to a sub­sequent Land­au party, com­plete with com­pet­it­ive games. At one point, Land­au had in­vited G. H. Hardy for a vis­it, so Land­au went to the train to meet him. Hardy, in a trench coat and dark glasses, stepped down from his car. Land­au pounced on him and asked for the latest res­ults on the “minor arcs” used in ana­lyt­ic num­ber the­ory; Hardy re­spon­ded, to Land­au’s dis­may, that he had lost all in­terest in the sub­ject. It turned out that the dark glasses hid not Hardy, but a Land­au stu­dent anxious to play a trick.

There were many oth­er vis­it­ors. Paul Al­ex­an­droff came to present the latest for­mu­la­tions of al­geb­ra­ic to­po­logy (as in his slim volume Ein­fach­ste Grundbe­griffe). Emil Artin came from Ham­burg to ex­pound the ob­scure beau­ties of the class field the­ory. Os­wald Veblen lec­tured (at one meet­ing of the weekly col­loqui­um) on pro­ject­ive re­lativ­ity the­ory. As al­ways, the col­loqui­um was pre­ceded by tea and a dis­play of the latest is­sues of journ­als. Richard von Mises was then a pro­fess­or at Ber­lin (the long-time rival of Göttin­gen math­em­at­ics). He gave an even­ing lec­ture on his (some­what am­bigu­ous) found­a­tion of prob­ab­il­ity the­ory on his no­tion of a Kollekt­iv. The whole Göttin­gen es­tab­lish­ment listened, and then (Hil­bert, Bernays, Bern­stein, and oth­ers) de­nounced his ap­proach. In brief, new ideas were force­fully presen­ted and dis­cussed. There was plenty of per­son­al con­tact; for ex­ample, for a peri­od I lived in Cour­ant’s house in or­der to teach him the use of Eng­lish in pre­par­a­tion for his planned vis­it to the U.S.A.

Thus the Math­em­at­ic­al In­sti­tute at Göttin­gen in 1931–1932 was a dy­nam­ic and suc­cess­ful mod­el of a top math­em­at­ic­al cen­ter.

“The pleasant hills near Göttingen made excursions possible and attractive. One day, at her lecture, Professor Noether observed with distaste that the Mathematical Institute would be closed at her next lecture, in honor of some holiday. To save mathematical research from this sorry interruption, she proposed an excursion to the coffee house of Kerstlingeroden Feld, up in the hills. So on that day we all met at the doors of the Institute — Noether, Paul Bernays, Ernst Witt, etc. After a good hike we consumed coffee, talked algebra, and hiked back, to our general profit. There were other such excursions, as on the occasion of the visit by Oswald Veblen. The picture above (courtesy of Martin Kneser), with some uncertain identifications (was I really there?) may now testify to this.” — Saunders Mac Lane

Standing: Paul Bernays, Hans Lewy(?), O. F. G. Schilling, Schwertfager(?). Woman facing right may be Olga Taussky, then Erna Barrow, Emmy Noether (almost hidden), Paul Alexandroff(?), (?). Seated, front row: Ernst Witt, (?), Mac Lane(?), (?), (?).

In 1931, Ger­many faced massive eco­nom­ic and polit­ic­al prob­lems. The Great De­pres­sion had caused much un­em­ploy­ment in Ger­many, and many Ger­mans still re­called clearly the pain­ful post­war in­fla­tion. The Ger­man chan­cel­lor (Brun­ing) did not have a se­cure ma­jor­ity in the Reich­stag, so he ruled by emer­gency de­crees. The people I knew were con­cerned by these is­sues and of­ten had lib­er­al or left-lean­ing sym­path­ies, but I re­call no one who cor­rectly foresaw the fu­ture. I ar­rived in Ger­many first in Ber­lin to learn Ger­man and to ab­sorb the cul­ture (e.g., Ber­to­ld Brecht and the Drei Groschen Op­era). There com­mun­ists and so­cial demo­crats com­peted with Nazi storm troop­ers (the SA). I care­fully stud­ied a pamph­let The Twenty-sev­en Polit­ic­al Parties of Ger­many; the Wei­mar re­pub­lic had man­aged to get polit­ics badly frag­men­ted. Once I settled in Göttin­gen, I could note every Sunday the young stu­dents with band­aged faces — they came from prac­tice duels of the “col­or” (corps) fra­tern­it­ies; per­haps they an­ti­cip­ated gen­er­al ad­mir­a­tion for pro­fess­ors of law who spor­ted im­press­ive du­el­ing scars. Once in the winter, I de­fen­ded a street urchin who had un­wisely lobbed a snow­ball at a corps stu­dent. The stu­dent thereupon chal­lenged me (“Your card, please”). I had no call­ing card on me, so de­clined the chal­lenge. The stu­dent re­spon­ded, “Mit sol­chen Leu­ten verkehren wir nicht” — “We do not as­so­ci­ate with such people” — and in­deed he did not, passing me of­ten on the street with word­less dis­dain. Per­haps I was lucky. Mar­tin Kneser told me that in 1912 George Polya was in Göttin­gen, was chal­lenged by a stu­dent, de­clined — whereupon the rect­or ad­vised him to leave the uni­versity. I man­aged to stay, to my great profit.

In 1932, Ger­man polit­ics was tur­bu­lent with street battles in Ber­lin and else­where between Nazi storm troop­ers and com­mun­ist groups. Then in Janu­ary 1933, there was an elec­tion in which the Nazis made com­mon cause with the Ger­man Na­tion­al Party (led by von Pa­pen); these Na­tion­al­ists prob­ably thought that they could con­trol Hitler; the com­bined vote was suf­fi­cient to make Hitler Reich­schan­cel­lor. His speeches and his pic­ture ap­peared every­where.

On Feb­ru­ary 12, 1933, I took a study break to vis­it Wei­mar. On ar­rival, I went to the Op­era House, but tick­ets for the next day were all sold out (it was the 50th an­niversary of the death of :Wag­n­er). For­tu­nately, by stand­ing out­side the Op­era House the next morn­ing, I man­aged to get a tick­et; the first half of the op­era (Wag­n­er, of course) was splen­did. In the in­ter­mis­sion, I walked out to the lobby. There, twenty-five feet away, stood Hitler and :Göring (easy to re­cog­nize from their news­pa­per pic­tures). At that time (as I did some months later), I did not fully real­ize the pro­spects of evil. In later years, I vividly re­called the sight of Hitler, but thought that it took place later, in May 1933. It thus later seemed to me to be the one oc­ca­sion where (had I car­ried a weapon) I might have per­son­ally changed his­tory.

On March 5, 1933, the gov­ern­ment co­ali­tion held a second elec­tion, pre­ceded by a vast pro­pa­ganda ef­fort. It pro­duced a much lar­ger vote for the gov­ern­ment. The res­ult­ing situ­ation is de­scribed in two let­ters which I wrote my moth­er — one dated March 10, 1933, and the oth­er un­dated. (The au­thor will provide cop­ies of these let­ters on re­quest.)

The first let­ter (10.III.33) is a tongue-in-cheek praise of pro­pa­ganda. I had nev­er be­fore seen what of­fi­cial pro­pa­ganda could do to al­ter opin­ion. By the time I left Ger­many in Au­gust, I felt so misled by con­tin­ued pro­pa­ganda that I did not know what was really go­ing on in the world.

In the second un­dated let­ter (“ad­dress omit­ted”), I seem to be wor­ried that my mail might be cen­sored. I now think that this worry was ground­less. But I was a bit con­cerned about my copy of Das Kapit­al; I re­call that I care­fully hid it in a draw­er un­der some shirts. Ac­tu­ally, there was a book-burn­ing in Göttin­gen on May 10, 1933. At about that time the cop­ies of the Lit­er­ary Di­gest which my moth­er sent me were no longer al­lowed to come.

After writ­ing those let­ters, I went on a stu­dent-or­gan­ized two-week ski­ing trip to Ober­stdorf in the Tyr­ol. We re­turned (on a group tick­et) by train, stop­ping for three hours in Nuren­berg. This was the day for which Hitler had de­creed a peace­ful boy­cott of all Jew­ish stores. Leav­ing my skis and bag­gage on the train, I went to ex­plore the town. There, at a big shoe store, I saw a seedy-look­ing man peer­ing in­to the dis­play win­dow. The store was closed, but nev­er­the­less the po­lice spot­ted the man and at once hustled him off. Since I had sup­posed the boy­cott to be peace­ful, I was curi­ous and fol­lowed along. Soon I too was ar­res­ted. The earn­est po­lice­man as­sumed that I was one of the Anglo-Sax­on re­port­ers who were col­lect­ing lies about the Reich; he up­braided me. I tried to as­sure him that I was not a re­port­er, but only a stu­dent. He thereupon ob­served that if he were vis­it­ing the U.S.A., he 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 catch it. I re­turned to Göttin­gen to my lodgings at 28 Lötze Strasse (not far from the Math­em­at­ic­al In­sti­tute). There my land­lady reg­u­larly provided me with even­ing tea and talk; I rap­idly dis­covered that two weeks of pro­pa­ganda had con­ver­ted her from mild con­ser­vat­ive views to ar­dent Nazi dis­ciple­ship.

In Ger­many, pro­fess­ors, Privat­dozen­ten and as­sist­ants are all gov­ern­ment of­fi­cials. On April 7, 1933, a new law about such of­fi­cials sum­mar­ily dis­missed all those who were Jew­ish, ex­cept for those ap­poin­ted be­fore 1914 and those who served as sol­diers in the First World War. In ad­di­tion, dis­missal awaited “all those of­fi­cials who are not at every time com­pletely com­mit­ted to the Na­tion­al So­cial­ist State”.

The ef­fect on the Math­em­at­ic­al In­sti­tute was drastic. Cour­ant, No­eth­er, and Bern­stein were im­me­di­ately dis­missed (on April 25). In Cour­ant’s case, his ser­vice in the First World War did not spare him; evid­ently his earli­er polit­ic­al views and his wide math­em­at­ic­al in­flu­ence (in­her­ited from Fe­lix Klein) made him dis­liked. With his de­par­ture, Neuge­bauer was made act­ing head of the In­sti­tute, but he las­ted only one day, when he too was dis­missed, ap­par­ently be­cause of his polit­ic­al sym­path­ies, but per­haps be­cause he failed to mow his lawn! On April 27, Bernays, Hertz and Lewy were dis­missed. Land­au was ad­vised not to lec­ture in the com­ing sum­mer semester; he fol­lowed the ad­vice. As a res­ult of this, my let­ter of May 3 to my moth­er read (in part):

So many pro­fess­ors and in­struct­ors have been fired or have left that the math­em­at­ics de­part­ment is pretty thor­oughly emas­cu­lated. It is rather hard on math­em­at­ics, and we have but the cold com­fort that it is the best thing for the Volk.

For that sum­mer semester, things struggled along some­how. All the stu­dents who could do so hur­ried to fin­ish up de­gree re­quire­ments. I had lost my thes­is ad­visor (Paul Bernays); :Her­mann Weyl took his place, and sub­sequently gave me a tough or­al ex­am­in­a­tion. I man­aged, but in the defin­i­tion of a Haus­dorff space, I for­got the sep­ar­a­tion ax­iom but did not dare men­tion the fact that Weyl had once for­got­ten it in print. For an­oth­er or­al ex­am, I took a course on the philo­sophy of math­em­at­ics with Pro­fess­or Mor­itz Gei­ger. Though Jew­ish, he had served in the First World War, so was still left in of­fice. However, in every lec­ture I could no­tice his nervous anxi­ety about the fu­ture — a jus­ti­fied anxi­ety.

On Ju­ly 14, I wrote my moth­er:

Just re­cently it has been pro­claimed that the Ger­man re­volu­tion is now at an end; now things must pro­ceed in evol­u­tion in a strictly leg­al fash­ion. That some­how gives the im­pres­sion that up to the present everything has not pro­ceeded in a strictly leg­al fash­ion, or at least that the SA (the Sturm Ab­teilung) has on oc­ca­sion taken un­to it­self the rights and priv­ileges of the po­lice. How far that has happened I can­not very well tell.

My fiancée, Dorothy Jones, had come to Göttin­gen from New York to help me fin­ish my thes­is. She learned much about the polit­ic­al situ­ation. When she and I went to the Standes­amt to 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 pro­hib­it 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 uni­versit­ies. It turned out to be a most sens­ible speech. The speak­er (a prom­in­ent Nazi pro­fess­or in Ber­lin) did not de­mand that Wis­senschaft be com­pletely bound down by polit­ics. He said that Wis­senschaft should be in­de­pend­ent but not autonom­ous…. After the meet­ing, we went down­town and drank cof­fee with my friend Gebhardt (whom we had met at the meet­ing). There again we dis­cussed polit­ics, the in­flu­ence of Cath­oli­cism (blind obed­i­ence) upon Hitler­ism, and so on far in­to the night. I have re­cently be­come im­pressed with the great vari­ety of opin­ions with­in the Nazi move­ment. All Nazis do not think alike, even though it may ex­tern­ally seem as if they did!

(Note, 1995: I no longer re­call the dis­cus­sion of Cath­oli­cism; I was then largely ig­nor­ant of Ger­man Cath­oli­cism and a great ad­mirer of my grand­fath­er’s power­ful ser­mon fa­vor­ing tol­er­ance.)

My or­al ex­am still threatened — one on geo­met­ric func­tion the­ory with that re­doubt­able pro­fess­or Gust­av Her­glotz. I con­sul­ted my ex­per­i­enced friends: what to do? They re­minded me that he loved to lec­ture. This I bore in mind dur­ing the ex­am:

Her­glotz: What is the Er­langer Pro­gram?

SM: Everything de­pends on the group.

Her­glotz: What is the group for com­plex ana­lys­is?

SM: The con­form­al group.

That suf­ficed to start Her­glotz on a splen­did lec­ture on geo­met­ric func­tion the­ory in terms of the con­form­al group.

My thes­is was done, and I was through.

But for the In­sti­tute, there were ad­ded losses. Her­mann Weyl was not Jew­ish, but his wife was; this meant then that their two sons were so coun­ted. So at the end of the sum­mer semester 1933, Weyl left for a pro­fess­or­ship at the In­sti­tute for Ad­vanced Study in Prin­ceton. All told, in 1933 eight­een math­em­aticians left or were driv­en out from the fac­ulty at the Math­em­at­ic­al In­sti­tute in Göttin­gen. This in­cluded Land­au; he was not of­fi­cially dis­missed, but when he again star­ted to lec­ture in the winter semester of 1933, the stu­dents or­gan­ized a com­plete boy­cott of his lec­ture. He thereupon resigned and re­tired to Ber­lin.

Math­em­at­ics at the Uni­versity of Ber­lin was also ser­i­ously dis­rup­ted; there twenty-three fac­ulty mem­bers (in­clud­ing Richard Brauer, Max Dehn, Hans Freudent­al, B. H. Neu­mann, Hanna Neu­mann, and Richard von Mises) left. The spe­cif­ic (and of­ten less ex­tens­ive) ef­fects at oth­er Ger­man uni­versit­ies have been care­fully tab­u­lated by Max­imili­an Pinl in four art­icles. De­tailed ana­lys­is of the situ­ation at Göttin­gen has been presen­ted by Schap­pach­er as part of a book on Göttin­gen un­der the Nazis.

One ob­serv­er has sum­mar­ized the ef­fect on math­em­at­ics in the fol­low­ing words:

With­in a few weeks this ac­tion would scat­ter to the winds everything that had been cre­ated over so many dec­ades. One of the greatest tra­gedies ex­per­i­enced by hu­man cul­ture since the time of the Renais­sance was tak­ing place — a tragedy which a few years be­fore would have seemed an im­possib­il­ity un­der twen­ti­eth cen­tury con­di­tions.

There were at­tempts to re­build math­em­at­ics at Göttin­gen. The em­in­ent al­geb­ra­ist Helmut Hasse be­came pro­fess­or and dir­ect­or of the In­sti­tute; for a peri­od he had dif­fi­cult deal­ings with sev­er­al math­em­aticians with Nazi en­thu­si­asm: Os­wald Teichmüller, Wern­er Weber, Ed­ward Torni­er. Torni­er was briefly co-dir­ect­or of the In­sti­tute; at one point he hoped to get Hasse re­moved from the dir­ect­or­ship. Torni­er favored the party; for ex­ample, he later wrote in the then new journ­al Deutsche Math­em­atik, 1936, vol. 1, page 2 (my trans­la­tion):

Pure math­em­at­ics too has real ob­jects — who­ever wishes to deny this is a rep­res­ent­at­ive of Jew­ish-lib­er­al thought, like philo­soph­ic­al soph­ist­ic­ates…. Every the­ory of pure math­em­at­ics has the right to ex­ist if it is really in a po­s­i­tion to an­swer con­crete ques­tions which con­cern real ob­jects like whole num­bers or geo­met­ric fig­ures — or if at least it serves for the con­struc­tion of things which hap­pen there. Oth­er­wise it is in­com­plete, or else a doc­u­ment of Jew­ish-lib­er­al con­fu­sion, born from the brains of root­less artists who by jug­gling with ob­ject-less defin­i­tions mis­lead them­selves and their thought­less pub­lic…. In the fu­ture, we will have Ger­man math­em­at­ics.

Even­tu­ally, the four pro­fess­or­ships at Göttin­gen were again oc­cu­pied (Hasse, Her­glotz, Kaluza, Siegel), but even with Karl Lud­wig Siegel the former glory was not re­stored. At one point, Hasse hoped to in­crease his in­flu­ence with the au­thor­it­ies. So, ac­cord­ing to his son-in-law, Mar­tin Kneser, he ap­plied for mem­ber­ship in the Nazi Party, but it turned out that one of his grand­moth­ers might have been a Jew; his ap­plic­a­tion was put on hold till after the war. After the war, Hasse was dis­missed as part of the de-nazi­fic­a­tion. Since then, the Göttin­gen Math­em­at­ic­al In­sti­tute has been gradu­ally re­con­sti­t­uted as one of sev­er­al such in­sti­tutes at oth­er Ger­man uni­versit­ies. But it has not suc­ceeded in re­claim­ing its ori­gin­al bril­liant dom­in­ance.

As Dorothy and I left in Au­gust of 1933, I car­ried with me, as a treas­ure, something of the vis­ion of the earli­er Göttin­gen as the unique mod­el of a great math­em­at­ics de­part­ment. I mourned the loss, but not only for the sake of sci­ence. I did not fore­see the holo­caust, but I was aware of the power of state pro­pa­ganda and I was act­ively fear­ful of the pro­spects for a world war, al­though pre­ven­tion seemed bey­ond my powers. Now in ret­ro­spect, the whole de­vel­op­ment is a de­cis­ive demon­stra­tion of the dam­age done to aca­dem­ic and math­em­at­ic­al life by any sub­or­din­a­tion to pop­u­lism, polit­ic­al pres­sure and pro­posed polit­ic­al prin­ciples.