Celebratio Mathematica

Emmy Noether

Memorial address: Emmy Noether

by Hermann Weyl

With deep dis­may Emmy No­eth­er’s friends liv­ing in Amer­ica learned about her sud­den passing away on Sunday, April 14. She seemed to have got well over an op­er­a­tion for tu­mor; we thought her to be on the way to con­vales­cence when an un­ex­pec­ted com­plic­a­tion led her sud­denly on down­ward the path to her death with­in a few hours. She was such a par­agon of vi­tal­ity, she stood on the earth so firm and healthy with a cer­tain sturdy hu­mor and cour­age for life, that nobody was pre­pared for this even­tu­al­ity. She was at the sum­mit of her math­em­at­ic­al cre­at­ive power; her far-reach­ing ima­gin­a­tion and her tech­nic­al abil­it­ies ac­cu­mu­lated by con­tin­ued ex­per­i­ence, had come to a per­fect bal­ance; she had eagerly set to work on new prob­lems. And now sud­denly — the end, her voice si­lenced, her work ab­ruptly broken off.

Down, down, down in­to the dark­ness of the grave
Gently they go, the beau­ti­ful, the tender, the kind;
Quietly they go, the in­tel­li­gent, the witty, the brave.
I know. But I do not ap­prove. And I am not resigned.

A mood of de­fi­ance sim­il­ar to that ex­pressed in this “Dirge without mu­sic” by Edna St. Vin­cent Mil­lay, mingles with our mourn­ing in the present hour when we are gathered to com­mem­or­ate our friend, her life and work and per­son­al­ity.

I am not able to tell much about the out­ward story of her life; far from her home and those places where she lived and worked in the con­tinu­ity of dec­ades, the ne­ces­sary in­form­a­tion could not be se­cured. She was born the 23rd of March, 1882, in the small South Ger­man uni­versity town of Er­lan­gen. Her fath­er was Max No­eth­er, him­self a great math­em­atician who played an im­port­ant rôle in the de­vel­op­ment of the the­ory of al­geb­ra­ic func­tions as the chief rep­res­ent­at­ive of the al­geb­ra­ic-geo­met­ric school. He had come to the Uni­versity of Er­lan­gen as a pro­fess­or of math­em­at­ics in 1875, and stayed there un­til his death in 1921. Be­sides Emmy there grew up in the house her broth­er Fritz, young­er by two and a half years. He turned to ap­plied math­em­at­ics in later years, was un­til re­cently pro­fess­or at the Tech­nis­che Hoch­schule in Bre­slau, and by the same fate that ended Emmy’s ca­reer in Göt­tin­gen is now driv­en off to the Re­search In­sti­tute for Math­em­at­ics and Mech­an­ics and in Tomsk, Siber­ia. The No­eth­er fam­ily is a strik­ing ex­ample of the hered­it­ary nature of the math­em­at­ic­al tal­ent, the most shin­ing il­lus­tra­tion of which is the Basle Huguenot dyn­asty of the Bernoullis.

Side by side with No­eth­er in Er­lan­gen was his close and in­tim­ate friend Gordan, also a math­em­atician, who had come to Er­lan­gen shortly be­fore, in 1874, and he, too, re­mained as­so­ci­ated with that uni­versity un­til his death in 1912. Emmy wrote her doc­tor’s thes­is un­der him in 1907. Be­sides her fath­er, Gordan must have been well-nigh one of the most fa­mil­i­ar fig­ures in Emmy’s early life, first as a friend of the house, later as a math­em­atician also; she kept a pro­found rev­er­ence for him though her own math­em­at­ic­al taste soon de­veloped in quite a dif­fer­ent dir­ec­tion. I re­mem­ber that his pic­ture dec­or­ated the wall of her study in Göt­tin­gen. These two men, the fath­er and Gordan, de­term­ined the at­mo­sphere in which she grew up. The fath­er was — such as the im­pres­sion I gath­er from his pa­pers and even more from the many ob­it­u­ary bio­graph­ies he wrote for the Math­em­at­ische An­nalen — a very in­tel­li­gent, warm-hearted, har­mo­ni­ous man of many-sided in­terests and ster­ling edu­ca­tion. This sci­entif­ic kin­ship of fath­er and daugh­ter — who be­came in a cer­tain sense his suc­cessor in al­gebra, but stands be­side him in­de­pend­ent in her fun­da­ment­al at­ti­tude and in her prob­lems — is something ex­tremely beau­ti­ful and grat­i­fy­ing.

It is queer that a form­al­ist like Gordan was the math­em­atician from whom her math­em­at­ic­al or­bit set out; a great­er con­trast is hardly ima­gin­able than between her first pa­per, the dis­ser­ta­tion, and her works of ma­tur­ity; for the former is an ex­treme ex­ample of form­al com­pu­ta­tions and the lat­ter con­sti­tute an ex­treme and gran­di­ose ex­ample of con­cep­tu­al ax­io­mat­ic think­ing in math­em­at­ics that ab­horred all cal­cu­la­tion and op­er­ated in a much thin­ner air of ab­strac­tion than Hil­bert, the young li­on, ever dared.

It is not quite easy to evoke be­fore an Amer­ic­an audi­ence a true pic­ture of that state of Ger­man life in which Emmy No­eth­er grew up in Er­lan­gen; maybe the present gen­er­a­tion in Ger­many is still more re­mote from it. The great sta­bil­ity of burgh­er life was in her case ac­cen­tu­ated by the fact that No­eth­er (and Gordan too) were settled at one uni­versity for so long as un­in­ter­rup­ted peri­od. One may dare to add that the time of the primary prop­er im­pulses of their pro­duc­tion was gone, though they un­doubtedly con­tin­ued to be pro­duct­ive math­em­aticians; in this re­gard, too, the at­mo­sphere around her was cer­tainly tinged by a quiet uni­form­ity. Moreover, there be­longs to the pic­ture the high stand­ing, and the great solid­ity in the re­cog­ni­tion of spir­itu­al val­ues; based on a sol­id edu­ca­tion, a deep and genu­ine act­ive in­terest in the high­er achieve­ments of in­tel­lec­tu­al cul­ture, and on a well-de­veloped fac­ulty of en­joy­ing them. There must have pre­vailed in the No­eth­er home a par­tic­u­larly warm and com­pan­ion­able fam­ily life. Emmy No­eth­er her­self was, if I may say so, warm like a loaf of bread. There ir­ra­di­ated from her a broad, com­fort­ing, vi­tal warmth. Our gen­er­a­tion ac­cuses that time of lack­ing all mor­al sin­cer­ity, of hid­ing be­hind its com­fort and bour­geois peace­ful­ness, and of ig­nor­ing the pro­found cre­at­ive and ter­rible forces that really shape man’s des­tiny; moreover of shut­ting its eyes to the con­trast between the spir­it of true Chris­tian­ity which was con­fessed, and the private and pub­lic life as it was ac­tu­ally lived. Ni­et­z­sche arose in Ger­many as a great awaken­er. It is hardly pos­sible to ex­ag­ger­ate the sig­ni­fic­ance which Ni­et­z­sche (whom by the way No­eth­er once met in the En­gad­in) had in Ger­many for the thor­ough change in the mor­al and men­tal at­mo­sphere. I think he was fun­da­ment­ally right — and yet one should not deny that in wide circles in Ger­many, as with the No­eth­ers, the es­teem in which the spir­itu­al goods were held, the in­tel­lec­tu­al cul­ture, good-hearted­ness, and hu­man warmth were thor­oughly genu­ine — not­with­stand­ing their sen­ti­ment­al­ity, their Wag­n­eri­an­ism, and their plush so­fas.

Emmy No­eth­er, as a young girl, took part in the house­work, dus­ted and cooked and went to dances, and it seems her life would have been that of an or­din­ary wo­man had it not happened that just about that time it be­came pos­sible in Ger­many for a girl to enter on a sci­entif­ic ca­reer without meet­ing any too marked res­ist­ance. There was noth­ing re­bel­li­ous in her nature; she was will­ing to ac­cept con­di­tions as they were. But now she be­came a math­em­atician. Her de­pend­ence on Gordan did not last long; he was im­port­ant as a start­ing point, but was not of last­ing sci­entif­ic in­flu­ence upon her. Nev­er­the­less the Er­lan­gen math­em­at­ic­al air may have been re­spons­ible for mak­ing her in­to an al­geb­ra­ist. Gordan re­tired in 1910; he was fol­lowed first by Er­hard Schmidt, and the next year by Ernst Fisc­her. Fisc­her’s field was al­gebra again, in par­tic­u­lar the the­ory of elim­in­a­tion and of in­vari­ants. He ex­er­ted upon Emmy No­eth­er, I be­lieve, a more pen­et­rat­ing in­flu­ence than Gordan did. Un­der his dir­ec­tion the trans­ition from Gordan’s form­al stand­point to the Hil­bert meth­od of ap­proach was ac­com­plished. She refers in her pa­pers at this time again and again to con­ver­sa­tions with Fisc­her. This epoch ex­tends un­til about 1919.

Already in Er­lan­gen about 1913 Emmy lec­tured oc­ca­sion­ally, sub­sti­tut­ing for her fath­er when he was taken ill. She must have been to Göt­tin­gen about that time, too, but I sup­pose only on a vis­it with her broth­er Fritz. At least I re­mem­ber him much bet­ter than her from my time as a Göt­tinger Privat­dozent, 1910–1913. Dur­ing the war, in 1916, Emmy came to Göt­tin­gen for good; it was due to Hil­bert’s and Klein’s dir­ect in­flu­ence that she stayed. Hil­bert at that time was over head and ears in the gen­er­al the­ory of re­lativ­ity, and for Klein, too, the the­ory of re­lativ­ity and its con­nec­tion with his old ideas of the Er­lan­gen pro­gram brought the last flareup of his math­em­at­ic­al in­terests and math­em­at­ic­al pro­duc­tion. The second volume of his his­tory of math­em­at­ics in the nine­teenth cen­tury bears wit­ness there­of. To both Hil­bert and Klein Emmy was wel­come as she was able to help them with her in­vari­ant the­or­et­ic know­ledge. For two of the most sig­ni­fic­ant sides of the gen­er­al re­lativ­ity the­ory she gave at that time the genu­ine and uni­ver­sal math­em­at­ic­al for­mu­la­tion.

Still dur­ing the war, Hil­bert tried to push through Emmy No­eth­er’s “Ha­bil­it­a­tion” in the Philo­soph­ic­al Fac­ulty in Göt­tin­gen. He failed due to the res­ist­ance of the philo­lo­gists and his­tor­i­ans. It is a well-known an­ec­dote that Hil­bert sup­por­ted her ap­plic­a­tion by de­clar­ing at the fac­ulty meet­ing, “I do not see that the sex of the can­did­ate is an ar­gu­ment against her ad­mis­sion as Privat­dozent. After all, we are a uni­versity and not a bathing es­tab­lish­ment.” Prob­ably he pro­voked the ad­versar­ies even more by that re­mark. Nev­er­the­less, she was able to give lec­tures in Göt­tin­gen, that were an­nounced un­der Hil­bert’s name. But in 1919, after the end of the War and the pro­clam­a­tion of the Ger­man Re­pub­lic had changed the con­di­tions, her Ha­bil­it­a­tion be­came pos­sible. In 1922 there fol­lowed her nom­in­a­tion as a “nicht-beamteter aus­ser­or­dent­lich­er Pro­fess­or”; this was a mere title car­ry­ing no ob­lig­a­tions and no salary. She was, however, en­trus­ted with a “Lehrauftrag” for al­gebra, which car­ried a mod­est re­mu­ner­a­tion. Dur­ing the wild times after the Re­volu­tion of 1918, she did not keep aloof from the polit­ic­al ex­cite­ment, she sided more or less with the So­cial Demo­crats; without be­ing ac­tu­ally in party life she par­ti­cip­ated in­tensely in the dis­cus­sion of the polit­ic­al and so­cial prob­lems of the day. One of her first pu­pils, Grete Her­mann, be­longed to Nel­son’s philo­soph­ic-polit­ic­al circle in Göt­tin­gen. It is hardly ima­gin­able nowadays how will­ing the young gen­er­a­tion in Ger­many was at that time for a fresh start, to try to build up Ger­many, Europe so­ci­ety in gen­er­al, on the found­a­tions of reas­on, hu­mane­ness and justice. But alas! the mood among the aca­dem­ic youth soon enough veered around; in the struggles that shook Ger­many dur­ing the fol­low­ing years and which took on the form of civil war here and there, we find them mostly on the side of the re­ac­tion­ary and na­tion­al­ist­ic forces. In later years Emmy No­eth­er took no part in mat­ters polit­ic­al. She al­ways re­mained, however, a con­vinced pa­ci­fist, a stand which she held very im­port­ant and ser­i­ous.

In the mod­est po­s­i­tion of a “nicht-beamteter aus­ser­or­dent­lich­er Pro­fess­or” she worked in Göt­tin­gen un­til 1933, dur­ing the last years in the beau­ti­ful new Math­em­at­ic­al In­sti­tute that had ris­en in Göt­tin­gen chiefly by Cour­ant’s en­ergy and the gen­er­ous fin­an­cial help of the Rock­e­feller Found­a­tion. I have a vivid re­col­lec­tion of her when I was in Göt­tin­gen as vis­it­ing pro­fess­or in the winter semester of 1926–1927, and lec­tured on rep­res­ent­a­tions of con­tinu­ous groups. She was in the audi­ence; for just at that time the hy­per­com­plex num­ber sys­tems and their rep­res­ent­a­tions had caught her in­terest and I re­mem­ber many dis­cus­sions when I walked home after the lec­tures, with her and von Neu­mann, who was in Göt­tin­gen as a Rock­e­feller Fel­low, through the cold, dirty, rain-wet streets of Göt­tin­gen. When I was called per­man­ently to Göt­tin­gen in 1930, I earn­estly tried to ob­tain from the Min­is­teri­um a bet­ter po­s­i­tion for her be­cause I was ashamed to oc­cupy such a pre­ferred po­s­i­tion be­side her whom I knew to be my su­per­i­or as math­em­atician in many re­spects. I did not suc­ceed, nor did an at­tempt to push through her elec­tion as a mem­ber of the Göt­tinger Gesell­schaft der Wis­senschaften. Tra­di­tion, pre­ju­dice, ex­tern­al con­sid­er­a­tions, weighted the bal­ance against her sci­entif­ic mer­its and sci­entif­ic great­ness, by that time denied by no one. In my Göt­tin­gen years, 1930–1933, she was without doubt the strongest cen­ter of math­em­at­ic­al activ­ity there, con­sid­er­ing both the fer­til­ity of her sci­entif­ic re­search pro­gram and her in­flu­ence upon a large circle of pu­pils.

Her de­vel­op­ment in­to that great in­de­pend­ent mas­ter whom we ad­mire today was re­l­at­ively slow. Such a later matur­ing is a rare phe­nomen­on in math­em­at­ics; in most cases the great cre­at­ive im­pulses lie in early youth. Sophus Lie, like Emmy No­eth­er, is one of the few great ex­cep­tions. Not un­til 1920, thir­teen years after her pro­mo­tion, ap­peared in the Math­em­at­ische Zeits­chrift that pa­per of her writ­ten with Schmeidler, “Über Mod­uln in nicht-kom­mut­at­iven Bereichen, ins­beson­dere aus Dif­fer­en­tial-und Dif­fer­en­zen-Aus­drüken,” [e1] which seems to mark the de­cis­ive turn­ing point. It is here for the first time that Emmy No­eth­er ap­pears whom we all know, and who changed the face of al­gebra by her work.

Not less char­ac­ter­ist­ic for Emmy was her col­lab­or­a­tion with an­oth­er, in this case with Schmeidler. I sup­pose that Schmeidler gave as much as he re­ceived in this coöper­a­tion. In later years, however, Emmy No­eth­er fre­quently ac­ted as the true ori­gin­at­or; she was most gen­er­ous in shar­ing her ideas with oth­ers. She had many pu­pils, and one of the chief meth­ods of her re­search was to ex­pound her ideas in a still un­fin­ished state in lec­tures, and then dis­cuss them with her pu­pils. Some­times she lec­tured on the same sub­ject one semester after an­oth­er, the whole sub­ject tak­ing on a bet­ter ordered and more uni­fied shape every time, and gain­ing of course in the sub­stance of res­ults. It is ob­vi­ous that this meth­od some­times put enorm­ous de­mands upon her audi­ence. In gen­er­al, her lec­tur­ing was cer­tainly not good in tech­nic­al re­spects. For that she was too er­rat­ic and she cared too little for a nice and well ar­ranged form. And yet she was an in­spired teach­er; he who was cap­able of ad­just­ing him­self en­tirely to her, could learn very much from her. Her sig­ni­fic­ance for al­gebra can­not be read en­tirely from her own pa­pers; she had great stim­u­lat­ing power and many of her sug­ges­tions took fi­nal shape only in the works of her pu­pils or co-work­ers. And one can­not read the scope of her ac­com­plish­ments from the in­di­vidu­al res­ults of her pa­pers alone: she ori­gin­ated above all a new and epoch-mak­ing style of think­ing in al­gebra.

She lived in close com­mu­nion with her pu­pils; she loved them, and took in­terest in their per­son­al af­fairs. They formed a some­what noisy and stormy fam­ily, “the No­eth­er boys” as we called them in Göt­tin­gen.

In the spring of 1933 the storm of the Na­tion­al Re­volu­tion broke over Ger­many. The Göt­tinger Math­em­at­isch-Natur­wis­senschaft­liche Fak­ultät, for the build­ing up and con­sol­id­a­tion of which Klein and Hil­bert had worked for dec­ades, was struck at its roots. After an in­ter­regnum of one day by Neuge­bauer, I had to take over the dir­ec­tion of the Math­em­at­ic­al In­sti­tute. But Emmy No­eth­er, as well as many oth­ers, was pro­hib­ited from par­ti­cip­a­tion in all aca­dem­ic activ­it­ies, and fi­nally her ve­nia le­gendi, as well as her “Lehrauftrag” and the salary go­ing with it, were with­drawn. A stormy time of struggle like this one we spent in Göt­tin­gen in the sum­mer of 1933 draws people closer to­geth­er; thus I have got a par­tic­u­larly vivid re­col­lec­tion of these months. Emmy No­eth­er, her cour­age, her frank­ness, her un­con­cern about her own fate, her con­cili­at­ory spir­it, were, in the midst of all the hatred and mean­ness, des­pair and sor­row sur­round­ing us, a mor­al solace. It was at­temp­ted, of course, to in­flu­ence the Min­is­teri­um and oth­er re­spons­ible and ir­re­spons­ible but power­ful bod­ies so that her po­s­i­tion might be saved. I sup­pose there could hardly have been in any oth­er case such a pile of en­thu­si­ast­ic testi­mo­ni­als filed with the Min­is­teri­um as was sent in on her be­half. At that time we really fought; there was still hope left that the worst could be war­ded off. It was in vain. Franck, Born, Cour­ant, Land­au, Emmy No­eth­er, Neuge­bauer, Bernays and oth­ers — schol­ars the uni­versity had be­fore been proud of — had to go be­cause the pos­sib­il­ity of work­ing was taken away from them. Göt­tin­gen scattered in­to the four winds! This fate brought Emmy No­eth­er to Bryn Mawr, and the short time she taught here and as guest at our In­sti­tute for Ad­vanced Study in Prin­ceton is still too fresh in our memory to need to be spoken of. She har­bored no grudge against Göt­tin­gen and her fath­er­land for what they had done to her. She broke no friend­ship on ac­count of polit­ic­al dis­sen­sion. Even last sum­mer she re­turned to Göt­tin­gen, and lived and worked there as though all things were as be­fore. She was sin­cerely glad that Hasse was en­deavor­ing with suc­cess to re­build the old, hon­or­able and proud math­em­at­ic­al tra­di­tion of Göt­tin­gen even in the changed polit­ic­al cir­cum­stances. But she had ad­jus­ted her­self with per­fect ease to her new Amer­ic­an sur­round­ings, and her girl stu­dents here were as near to her heart as the No­eth­er boys had been in Göt­tin­gen. She was happy at Bryn Mawr; and in­deed per­haps nev­er be­fore in her life had she re­ceived so many signs of re­spect, sym­pathy, friend­ship, as were be­stowed upon her dur­ing her last one and a half years at Bryn Mawr. Now we stand at her grave.

It shall not be for­got­ten what Amer­ica did dur­ing these last two stress­ful years for Emmy No­eth­er and for Ger­man sci­ence in gen­er­al.

If this sketch of her life is to be fol­lowed by a short syn­op­sis of her work and her hu­man and sci­entif­ic per­son­al­ity, I must at­tempt to draw in a few strokes the scene of her work: the world of al­gebra.

Emmy No­eth­er’s sci­entif­ic pro­duc­tion seems to me to fall in­to three clearly dis­tinct epochs: (1) the peri­od of re­l­at­ive de­pend­ence, 1907–1919; (2) the in­vest­ig­a­tions grouped around the gen­er­al the­ory of ideals, 1920–26; (3) the study of the non-com­mut­at­ive al­geb­ras, their rep­res­ent­a­tions by lin­ear trans­form­a­tions, and their ap­plic­a­tion to the study of com­mut­at­ive num­ber fields and their arith­met­ics, from 1927 on. The first epoch was de­scribed in the sketch of her life. I should now like to say a few words about the second epoch, the epoch of the gen­er­al the­ory of ideals.

I must fore­go giv­ing a pic­ture of the con­tent of these pro­found in­vest­ig­a­tions. In­stead, I had bet­ter try to close with a short gen­er­al es­tim­ate of Emmy No­eth­er as a math­em­atician and as a per­son­al­ity.

Her strength lay in her abil­ity to op­er­ate ab­stractly with con­cepts. It was not ne­ces­sary for her to al­low her­self to be led to new res­ults on the lead­ing strings of known con­crete ex­amples. This had the dis­ad­vant­age, however, that she was some­times but in­com­pletely cog­niz­ant of the spe­cif­ic de­tails of the more in­ter­est­ing ap­plic­a­tions of her gen­er­al the­or­ies. She pos­sessed a most vivid ima­gin­a­tion, with the aid of which she could visu­al­ize re­mote con­nec­tions; she con­stantly strove to­ward uni­fic­a­tion. In this she sought out the es­sen­tials in the known facts, brought them in­to or­der by means of ap­pro­pri­ate gen­er­al con­cepts, es­pied the vant­age point from which the whole could best be sur­veyed, cleansed the ob­ject un­der con­sid­er­a­tion of su­per­flu­ous dross, and thereby won through to so simple and dis­tinct a form that the ven­ture in­to new ter­rit­ory could be un­der­taken with the greatest pro­spect of suc­cess.

Emmy No­eth­er was a zeal­ous col­lab­or­at­or in the edit­ing of the Math­em­at­ische An­nalen. That this work was nev­er ex­pli­citly re­cog­nized may have caused her some pain.

It was only too easy for those who met her for the first time, or had no feel­ing for her cre­at­ive power, to con­sider her queer and to make fun at her ex­pense. She was heavy of build and loud of voice, and it was of­ten not easy for one to get the floor in com­pet­i­tion with her. She preached migh­tily, and not as the scribes. She was a rough and simple soul, but her heart was in the right place. Her frank­ness was nev­er of­fens­ive in the least de­gree. In every­day life she was most un­as­sum­ing and ut­terly un­selfish; she had a kind and friendly nature. Nev­er­the­less she en­joyed the re­cog­ni­tion paid her; she could an­swer with a bash­ful smile like a young girl to whom one had whispered a com­pli­ment. No one could con­tend that the Graces had stood by her cradle; but if we in Göt­tin­gen of­ten chaff­ingly re­ferred to her as “der No­eth­er” (with the mas­cu­line art­icle), it was also done with a re­spect­ful re­cog­ni­tion of her power as a cre­at­ive thinker who seemed to have broken through the bar­ri­er of sex. She pos­sessed a rare hu­mor and sense of so­ci­ab­il­ity; a tea in her apart­ments could be most pleas­ur­able. But she was a one-sided who was thrown out of bal­ance by the over­weight of her math­em­at­ic­al tal­ent. Es­sen­tial as­pects of hu­man life re­mained un­developed in her, among them, I sup­pose, the erot­ic, which, if we are to be­lieve the po­ets, is for many of us the strongest source of emo­tions, rap­tures, de­sires, and sor­rows, and con­flicts. Thus she some­times gave the im­pres­sion of an un­wieldy child, but she was a kind-hearted and cour­ageous be­ing, ready to help, and cap­able of the deep­est loy­alty and af­fec­tion. And of all I have known, she was cer­tainly one of the hap­pi­est.

Com­par­is­on with the oth­er wo­man math­em­atician of world renown, Sonya Ko­va­levskaya, sug­gests it­self. Sonya had cer­tainly the more com­plete per­son­al­ity, but was also of a much less happy nature. In or­der to pur­sue her stud­ies Sonya had to defy the op­pos­i­tion of her par­ents, and entered in­to a mar­riage in name only, al­though it did not quite re­main so. Emmy No­eth­er had, as I have already in­dic­ated, neither a re­bel­li­ous nature nor Bo­hemi­an lean­ings. Sonya pos­sessed fem­in­ine charm, in­stincts and van­ity; so­cial suc­cesses were by no means im­ma­ter­i­al to her. She was a creature of ten­sion and whimsy; math­em­at­ics made her un­happy, where­as Emmy found the greatest pleas­ure in her work. […] But Emmy No­eth­er without doubt pos­sessed by far the great­er power, the great­er sci­entif­ic tal­ent.

In­deed, two traits de­term­ined above all her nature: First, the nat­ive pro­duct­ive power of her math­em­at­ic­al geni­us. She was not clay-pressed by the artist­ic hands of God in­to a har­mo­ni­ous form, but rather a chunk of hu­man primary rock in­to which He had blown His cre­at­ive breath of life. Second, her heart knew no malice; she did not be­lieve in evil — in­deed it nev­er entered her mind that it could play a rôle among men. This was nev­er more force­fully ap­par­ent to me than in the last stormy sum­mer, that of 1933, which we spent to­geth­er in Göt­tin­gen. The memory of her work in sci­ence and of her per­son­al­ity among her fel­lows will not soon pass away. She was a great math­em­atician, the greatest, I firmly be­lieve, that her sex has ever pro­duced and a great wo­man.