On April 14 of this year, in the small town of Bryn Mawr (Pennsylvania, U.S.A.), Emmy Noether, former professor at Göttingen University and one of the foremost mathematicians of modern times, died at the age of 53 following an operation.
The death of Emmy Noether is not only a great loss for mathematical science, it is a tragedy in the full sense of the word. The greatest woman mathematician who ever lived died at the very height of her creative powers; she died, driven from her homeland and torn from the scientific school which she had created over the years and which had become one of the most brilliant schools of mathematics in Europe; she died, torn from her family, which had been scattered to different countries because of the same political barbarism that caused Emmy Noether herself to emigrate from Germany.
We of the Moscow Mathematical Society pay our respects today to the memory of one of our leading members, who for more than ten years maintained continual and close ties, constant scientific interaction, and sincere good will and friendship with the Society, with the Moscow mathematical community, with the mathematicians of the Soviet Union… Permit me in the name of the Society to express our deepest condolences to the brother of the deceased,, formerly of the Technische Hochschule in Breslau and currently of the Tomsk Mathematical Institute, who is with us today.
The biography of Emmy Noether is simple. She was born on March 23, 1882 in Erlangen to the family of the famous mathematician Max Noether. Her mathematical talent developed slowly. A student of Gordan in Erlangen, she defended her dissertation in 1907; her work was on Gordan’s formal computational invariant theory. She often alluded to this dissertation afterwards, and always referred to it with disdainful epithets, such as “Formelngestriipp” [jungle of formalism] and “Rechnerei” [routine computations]. Despite all of this it should be noted that Emmy Noether, the ardent foe of computation and algorithms in mathematics, herself was fully capable of mastering such methods — this is proved not only by her first dissertation, which in actual fact was not a major work, but also by her subsequent papers on differential invariants (1918), which have become classics. But in these papers we already see the fundamental characteristic of her mathematical talent: the striving for general formulations of mathematical problems and the ability to find the formulation which reveals the essential logical nature of the question, stripped of any incidental peculiarities which complicate matters and obscure the fundamental point.
She wrote the papers on differential invariants when she was still in Göttingen, where she had moved in 1916. Her work of this period was heavily influenced by. It is often forgotten that in this period Emmy Noether obtained excellent results concerning the concrete algebraic problems of Hilbert. These results and her work on differential invariants would have been enough by themselves to earn her the reputation of a first class mathematician and are hardly less of a contribution to mathematics than the famous research of . But when we think of Emmy Noether as a mathematician, we have in mind not these early works, important though they were in their concrete results, but rather the main period of her research, beginning in about 1920, when she became the creator of a new direction in algebra and the leading, the most consistent and prominent representative of a certain general mathematical doctrine — all that which is characterized by the words “begriffliche Mathematik” [abstract mathematics].
Emmy Noether herself is partly responsible for the fact that her work of the early period is rarely given the attention that it would naturally deserve. With the singlemindedness that was part of her nature, she herself was ready to forget what she had done in the early years of her scientific life, since she considered those results to have been a diversion from the main path of her research, which was the creation of a general, abstract algebra.
It is not my task to analyze and illuminate everything that Emmy Noether did in mathematics. In the first place, not being an algebraist, I do not consider myself qualified to perform such a task. In the second place, to the extent appropriate for an obituary, this task was performed in an excellent and completely competent manner by(in an address delivered at a commemorative meeting in honor of Emmy Noether on April 26, 1935 at Bryn Mawr, Pennsylvania, U.S.A., and published in Scripta Mathematica, v. III, no. 3, June 1935) and by (Mathematische Annalen, v. III, 1935, p. 469). My purpose today is somewhat different: I would like to evoke for you as accurate an image as possible of the deceased, as a mathematician, as the head of a large scientific school, as a brilliant, original, and fascinating personality.
Emmy Noether embarked on her own completely original mathematical path in the years 1919/1920. She herself dated the beginning of this fundamental period in her work with the famous joint work with(Mathematische Zeitschrift, v. 8, 1920). In a sense this paper serves as a prologue to her general theory of ideals, which she revealed in 1921 in the classic memoir “Idealtheorie in Ringbereichen.” I believe that, of everything that Emmy Noether did, it is the foundations of general ideal theory and everything connected with this that has had, is continuing to have, and will have in the future the greatest impact on mathematics as a whole. Not only have these ideas already led to many specific fundamental applications — for example, in van der Waerden’s work on algebraic geometry — moreover, they have had an essential influence on algebraic thinking itself, and in certain respects on general mathematical thinking, in our times. If the development of mathematics today is moving forward under the sign of algebraization, the penetration of algebraic ideas and methods into the most diverse mathematical theories, then this only became possible after the work of Emmy Noether. It was she who taught us to think in terms of simple and general algebraic concepts — homeomorphic mappings, groups and rings with operators, ideals — and not in terms of cumbersome algebraic computations; and thereby opened up the path to finding algebraic principles in places where such principles had been obscured by some complicated special situation which was not at all suited for the accustomed approach of the classical algebraists. Theorems such as the “homeomorphism and isomorphism theorem”, concepts such as the ascending and descending chain conditions for subgroups and ideals, or the notion of groups with operators, were first introduced by Emmy Noether and have entered into the daily practice of a wide range of mathematical disciplines as a powerful and constantly applicable tool, even though these disciplines may concern subjects which have no relation to the work of Emmy Noether herself. We need only glance at Pontryagin’s work on the theory of continuous groups, the recent work of on the combinatorial topology of locally bicompact spaces, the work of on the theory of continuous mappings, to say nothing of van der Waerden’s work on algebraic geometry, in order to sense the influence of Emmy Noether’s ideas. This influence is also keenly felt in H. Weyl’s book Gruppentheorie und Quantenmechanik.
I have purposely indicated areas of mathematics which are different from the direct subject of Emmy Noether’s research; if one speaks of algebra itself (including group theory), then we see that she created a major new direction in which a large number of very talented mathematicians work, continuing the research of Emmy Noether in many concrete areas. In particular, general elimination theory and the theory of algebraic varieties are among the most significant achievements that have arisen on the groundwork of Emmy Noether’s general ideal theory. In connection with what I have just said, I would like to recall that, among the major works of algebra that we have produced here in Moscow over the last decade, the famous work ofon unique direct product decomposition of groups, and also the work of , were heavily influenced by Emmy Noether.
Despite all of the concrete and constructive explicit results of Emmy Noether that came out of the various creative periods in her life, there can be no doubt that the fundamental strength and the fundamental dynamism of her talent went in the direction of general mathematical conceptions having a marked axiomatic coloration. The present moment is especially opportune for subjecting this side of her creativity to detailed analysis — not only because the question of the general and the special, the abstract and the concrete, the axiomatic and the constructive is now one of the sharpest questions in our mathematical life. Interest in this entire problem is especially pertinent because, on the one hand, the mathematical journals have undoubtedly become over-burdened with a great number of articles which generalize, axiomatize and so on, often without any concrete mathematical content; on the other hand, from time to time one hears proclamations to the effect that the only true mathematics is that which is “classical.” This slogan sweeps aside important mathematical problems only because they contradict one or another habit of thought, because they make use of concepts which were not in use a few decades ago, such as, for example, the concepts of general algebraic rings and fields, of topological and function spaces, and many others. In the obituary cited above, H. Weyl also poses this question. His words on this subject so penetrate to the heart of the matter that I cannot refrain from citing them in their entirety:
In a conference on topology and abstract algebra as two ways of mathematical understanding, in 1931, I said this:
Nevertheless I should not pass over in silence the fact that today the feeling among mathematicians is beginning to spread that the fertility of these abstracting methods is approaching exhaustion. The case is this: that all these nice general notions do not fall into our laps by themselves. But definite concrete problems were first conquered in their undivided complexity, singlehanded by brute force, so to speak. Only afterwards the axiomaticians came along and stated: Instead of breaking in the door with all your might and bruising your hands, you should have constructed such and such a key of skill, and by it you would have been able to open the door quite smoothly. But they can construct the key only because they are able, after the breaking in was successful, to study the lock from within and without. Before you can generalize, formalize and axiomatize, there must be a mathematical substance. I think that the mathematical substance in the formalizing of which we have trained ourselves during the last decades, becomes gradually exhausted. And so I foresee that the generation now rising will have a hard time in mathematics.
“Emmy Noether,” continues Weyl “protested against that: and indeed she could point to the fact that just during the last years the axiomatic method had disclosed in her hands new, concrete, profound problems… and had shown the way to their solution.”
Much in this quotation deserves our attention. In the first place, one cannot, of course, dispute the point of view that every axiomatic presentation of a mathematical theory must be preceded by a concrete, one might say a naive mastery of it; that, moreover, axiomatics is only interesting when it relates to tangible mathematical knowledge (what Weyl calls “mathematical substance”), and is not tilting at windmills, so to speak. All of this is indisputable, and, of course, it was not against this that Emmy Noether protested. What she protested against was the pessimism that shows through the last words of the quotation from Weyl’s speech of 1931; the substance of human knowledge, including mathematical knowledge, is inexhaustible, at least for the foreseeable future — this is what Emmy Noether firmly believed. The “substance of the last decades” may be exhausted, but not mathematical substance in general, which is connected by thousands of intricate threads with the reality of the external world and human existence. Emmy Noether deeply felt this connection between all great mathematics, even the most abstract, and the real world; even if she did not think this through philosophically, she intuited it with all of her being as a great scientist and as a lively person who was not at all imprisoned in abstract schemes. For Emmy Noether mathematics was always knowledge of reality, and not a game of symbols; she protested fervently whenever the representatives of those areas of mathematics which are directly connected with applications wanted to appropriate for themselves the claim to tangible knowledge. In mathematics, as in knowledge of the world, both aspects are equally valuable: the accumulation of facts and concrete constructions and the establishment of general principles which overcome the isolation of each fact and bring the factual knowledge to a new stage of axiomatic understanding.
A profound feeling for reality lay at the foundation of Emmy Noether’s mathematical creativity; her entire scientific personality opposed the tendency (which is widespread in many mathematical circles) to transform mathematics into a game, into some sort of peculiar mental sport. In the numerous conversations I had with her about the nature of mathematical knowledge and creativity, most of which were naive discussions in the sense that we did not enter into a truly philosophical statement of the question, I often — with her evident sympathy — recalled my favorite quotation from: “Si l’homme s’était borné à recueillir des faits, la science ne serait qu’une nomenclature stérile et jamais il n’eut connu les grandes lois de la nature.” [If man had limited himself to the accumulation of facts, then science would have been merely a fruitless nomenclature, and he would never have learned the great laws of nature.] These words, spoken by one of the most prominent representatives of physical knowledge, by a scientist who had both feet firmly on the ground, contain an entire program of interrelations between the concrete and the abstract in human thought in general, and in mathematics in particular. And it seems to me that Emmy Noether brought this program to realization in her work.
In 1924–1925 Emmy Noether’s school made one of its most brilliant discoveries: the student van der Waerden from Amsterdam. He was then 22 years old, and was one of the brightest young mathematical talents of Europe. Van der Waerden quickly mastered Emmy Noether’s theories, added significant new results, and, more than anyone else, helped to make her ideas widely known. The course on general ideal theory which van der Waerden gave in Göttingen in 1927 was tremendously successful. In van der Waerden’s brilliant presentation, the ideas of Emmy Noether overwhelmed the mathematical public, first in Göttingen and then in the other major mathematical centers of Europe. It is not surprising that Emmy Noether needed a popularizer for her ideas: her lectures were aimed at a small circle of students working in the area of her research and listening to her constantly. They were not at all suitable for a broad mathematical audience. To an outsider Emmy Noether seemed to lecture poorly, in a rapid and confusing manner; but her lectures contained a tremendous force of mathematical thought and an extraordinary warmth and enthusiasm. The same is true of her reports at meetings and congresses. Her lectures conveyed very much to a mathematician who already understood her ideas and was interested in her work; but a mathematician who was far from her research normally would have great difficulty understanding her exposition.
From 1927 on, as the influence of Emmy Noether’s ideas on modern mathematics constantly increased, the scholarly renown of the author of those ideas was similarly increasing. Meanwhile, the direction of her own work was changing, moving more and more toward the areas of noncommutative algebra, representation theory and the general arithmetic of hypercomplex systems. The two most fundamental works of her later period show this trend: “Hyperkomplexe Grossen und Darstellungstheorie” (1929) and “Nichtkommutative Algebra” (1933), both published in Mathematische Zeitschrift (vol. 30 and 37). These and related papers immediately produced numerous reverberations in the work of algebraic number theorists, especially. Her best known student of this period was , who published a book “Algebren” in Ergebnisse der Mathematik, where he gave a survey of Emmy Noether’s work on hypercomplex systems. In addition, her school included many young mathematicians who were starting their careers, such as Witt, Fitting, and others.
Emmy Noether lived to see the full recognition of her ideas. If in 1923–1925 she was striving to prove the importance of the theories she was developing, in 1932, at the International Congress of Mathematicians in Zurich, her accomplishments were lauded on all sides. The major survey talk that she gave at the Congress was a true triumph for the direction of research she represented. At that point she could look back upon the mathematical path she had traveled not only with an inner satisfaction, but with an awareness of her complete and unconditional recognition in the mathematical community. The Congress in Zurich marked the high point of her international scientific position. A few months later, German culture and, in particular, Göttingen University, which had nurtured that culture for centuries, were struck by the catastrophe of the fascist takeover, which in a matter of weeks scattered to the winds everything that had been painstakingly created over the years. What occurred was one of the greatest tragedies that had befallen human culture since the time of the Renaissance, a tragedy which only a few years ago had seemed impossible in twentieth-century Europe. One of its many victims was Emmy Noether’s Göttingen school of algebraists. The leader of the school was driven from the halls of the university; having lost the right to teach, Emmy Noether was forced to emigrate from Germany. She accepted an invitation from the women’s college in Bryn Mawr (1933), where she lived for the last year and a half of her life.
Emmy Noether’s career was full of paradoxes, and will always stand as an example of shocking stagnancy and inability to overcome prejudice on the part of the Prussian academic and civil service bureaucracies. Her appointment as Privatdozent in 1919 was only possible because of the persistence of Hilbert and, who overcame some extreme opposition from reactionary university circles. The basic formal objection was the sex of the candidate: “How can we allow a woman to become a Privatdozent: after all, once she is a Privatdozent, she may become a Professor and member of the University Senate; is it permissible for a woman to enter the Senate?” This provoked Hilbert’s famous reply: “Meine Herren, der Senat ist ja keine Badenanstalt, warum darf eine Frau nicht dorthin!” [Gentlemen, the Senate is not a bathhouse, so I do not see why a woman cannot enter it!] In actual fact, the opposition of influential representatives of reactionary academic circles was caused not only and not even primarily because Emmy Noether was a woman, but by her well-known and very radical political beliefs, along with the aggravating circumstance in their eyes of her Jewish nationality. But I shall return to this later.
Eventually she received the appointment as Privatdozent, and later as honorary Professor; as a result of Courant’s efforts she received a so-called Lehrauftrag, i.e., a small salary (200–400 marks per month) for her lectures, which required reconfirmation every year by the Ministry. It was in this position, without even a guaranteed salary, that she lived until the moment she was dismissed from the university and forced to leave Germany. She was not a member of a single academy, including the academy of the city whose university was the setting for all of her research. Here is what H. Weyl writes about this in his obituary:
When I was called permanently to Göttingen in 1930,1
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 a 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.2
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.
Emmy Noether had close ties to Moscow. Her connection with Moscow began in 1923, whenwho has now also passed away, and I first went to Göttingen and immediately found ourselves in the mathematical circle led by Emmy Noether. The basic features of the Noether school struck us right away: the intellectual enthusiasm of its leader, which was transmitted to all of her students, her deep conviction in the importance and mathematical fertility of her ideas (a conviction which far from everyone shared at that time, even in Göttingen), and the extraordinary simplicity and warmth of the relations between the head of the school and her pupils. At that time the school consisted almost entirely of young Göttingen students; the period when it became international in its composition and was recognized as the most important center of algebraic thought in terms of its international impact, was still in the future.
The mathematical interests of Emmy Noether (who was then at the height of her work on general ideal theory) and the mathematical interests of Uryson and myself, which were then centered around problems in so-called abstract topology, had many points of contact with one another, and soon brought us together in constant, almost daily mathematical discussions. Emmy Noether was not, however, only interested in our topological work; she was interested in everything mathematical (and not only mathematical!) that was being done in Soviet Russia. She did not hide her sympathy toward our country and its social and governmental structure, despite the fact that such expressions of sympathy were considered shocking and improper by most representatives of Western European academic circles. It went so far that Emmy Noether was literally expelled from one of the Göttingen boarding-houses (where she lived and dined) at the insistence of the student boarders, who did not want to live under the same roof as a “pro-Marxist Jew” — an excellent prologue to the drama that came at the end of her life in Germany.
And Emmy Noether was sincerely glad of the scientific and mathematical successes of the Soviet Union, since she saw in this a decisive refutation of all of the prattle about how “the Bolsheviks are destroying culture,” and she felt the approaching blossoming of a great new culture. Though the representative of one of the most abstract areas of mathematics, she distinguished herself with an amazing sensitivity in understanding the great historic transformations of our times; she always had a lively interest in politics, with all of her being she hated war and chauvinism in all of its manifestations, in this area she never wavered. Her sympathies were always steadfastly with the Soviet Union, where she saw the beginning of a new era in the history of mankind and a firm support for everything progressive in human thought. This feature was such a shining aspect of Emmy Noether’s character, it left such a deep imprint on her entire personality, that to be silent about it would signify a tendentious distortion of Emmy Noether’s nature as a scientist and as a person.
The scientific and personal friendship between Emmy Noether and me which started in 1923, continued until her death. Referring to this friendship, Weyl says in his obituary: “She held a rather close friendship with Alexandrov in Moscow. I believe that her mode of thinking has not been without influence upon Alexandrov’s topological investigations.” I am happy to take this opportunity to confirm the accuracy of Weyl’s supposition. Emmy Noether’s influence on my own and on other topological research in Moscow was very great and affected the very essence of our work. In particular, my theory of continuous partitions of topological spaces arose to a large extent under the influence of conversations with her in December to January of 1925–1926, when we were both in Holland. On the other hand, this was also the time when Emmy Noether’s first ideas on the set theoretic foundations of group theory arose, serving as the subject for her course of lectures in the summer of 1926. In their original form these ideas were not developed further, but later she returned to them several times. The reason for this delay is probably the difficulty involved in axiomatizing the notion of a group starting from its partition into cosets as the fundamental concept. But the idea of a set-theoretic analysis of the concept of a group itself turned out to be fruitful, as shown by the recent work of Ore, Kurosh, and others.
Subsequent years saw a strengthening and deepening of Emmy Noether’s topological interests. In the summers of 1926 and 1927 she went to the courses on topology which Hopf and I gave at Göttingen. She rapidly became oriented in a field that was completely new for her, and she continually made observations, which were often deep and subtle. When in the course of our lectures she first became acquainted with a systematic construction of combinatorial topology, she immediately observed that it would be worthwhile to study directly the groups of algebraic complexes and cycles of a given polyhedron and the subgroup of the cycle group consisting of cycles homologous to zero; instead of the usual definition of Betti numbers and torsion coefficients, she suggested immediately defining the Betti group as the complementary (quotient) group of the group of all cycles by the subgroup of cycles homologous to zero. This observation now seems self-evident. But in those years (1925–1928) this was a completely new point of view, which did not immediately encounter a sympathetic response on the part of many very authoritative topologists. Hopf and I immediately adopted Emmy Noether’s point of view in this matter, but for some time we were among a small number of mathematicians who shared this viewpoint. These days it would never occur to anyone to construct combinatorial topology in any way other than through the theory of abelian groups; it is thus all the more fitting to note that it was Emmy Noether who first had the idea of such a construction. At the same time she noticed how simple and transparent the proof of the Euler–Poincare formula becomes if one makes systematic use of the concept of a Betti group. Her remarks in this connection inspired Hopf completely to rework his original proof of the well-known fixed point formula, discovered byin the case of manifolds and generalized by Hopf to the case of arbitrary polyhedra. Hopf’s work “Eine Verallgemeinerung der Euler–Poincaréschen Formel,” published in Gattinger Nachrichten in 1928, bears the imprint of these remarks of Emmy Noether.
Emmy Noether spent the winter of 1928–1929 in Moscow. She gave a course on abstract algebra at Moscow University and led a seminar on algebraic geometry in the Communist Academy. She quickly established contact with the majority of Moscow mathematicians, in particular, withand O. Yu. Schmidt. It is not hard to follow the influence of Emmy Noether on the developing mathematical talent of Pontryagin; the strong algebraic flavor in Pontryagin’s work undoubtedly profited greatly from his association with Emmy Noether. In Moscow Emmy Noether readily familiarized herself with our life, both scientific and day-to-day. She lived in a modest room in the KSU dormitory near the Krymskii Bridge, and usually walked to the University. She was very interested in the life of our country, especially the life of Soviet youth and the students.
That winter of 1928–1929 I made frequent trips to Smolensk, where I gave lectures on algebra at the Pedagogical Institute. Inspired by continual conversations with Emmy Noether, that year I gave my lectures in her field. Among my listeners A. G. Kurosh immediately stood out; the theories I was presenting, which were imbued with the ideas of Emmy Noether, appealed to his spirit. In this way, through my teaching, Emmy Noether acquired another student, who has since, as we all know, grown into an independent scientist, whose work is still largely concerned with the circle of ideas created by Emmy Noether.
In the spring of 1929 she left Moscow for Göttingen with the firm intention of paying us a return visit within the next few years. Several times she came close to realizing this intention, especially in the last year of her life. After her exile from Germany, she seriously considered finally settling in Moscow, and I had a correspondence with her on this question. She clearly understood that nowhere else were there such possibilities of creating a brilliant new mathematical school to replace the one that was taken from her in Göttingen. And I had already been negotiating with Narkompros about appointing her to a chair in algebra at Moscow University. But, as it happens, Narkompros delayed in making the decision and did not give me a final answer. Meanwhile time was passing, and Emmy Noether, deprived even of the modest salary which she had had in Göttingen, could not wait, and had to accept the invitation from the women’s college in the American town of Bryn Mawr.
With the death of Emmy Noether I lost the acquaintance of one of the most captivating human beings I have ever known. Her extraordinary kindness of heart, alien to any affectation or insincerity; her cheerfulness and simplicity; her ability to ignore everything that was unimportant in life — created around her an atmosphere of warmth, peace and good will which could never be forgotten by those who associated with her. But her kindness and gentleness never made her weak or unable to resist evil. She had her opinions and was able to advance them with great force and persistence. Though mild and forgiving, her nature was also passionate, temperamental, and strong-willed; she always stated her opinions forthrightly, and did not fear objections. It was moving to see her love for her students, who comprised the basic milieu in which she lived and replaced the family she did not have. Her concern for her students’ needs, both scientific and worldly, her sensitivity and responsiveness, were rare qualities. Her great sense of humor, which made both her public appearances and informal association with her especially pleasant, enabled her to deal lightly and without ill will with all of the injustices and absurdities which befell her in her academic career. Instead of taking offense in these situations, she laughed. But she took extreme offense and sharply protested whenever the least injustice was done to one of her students. The entire reservoir of her maternal feelings went to them!
Sociable, good-willed and simple in relations with others, she was able to combine expansiveness with a certain calmness and the absence of any vanity. Glory-seeking and the pursuit of worldly success were alien to her. But she knew her worth, and fought for scientific influence.
In her house — more precisely, in the mansard-roofed apartment she occupied in Göttingen (Friedlanderweg 57) — a large group would get together eagerly and often. People of diverse scholarly reputations and positions — from Hilbert,, and Weyl to the youngest students — would gather at her home and feel relaxed and unconstrained, as in few other scientific salons in Europe. These “festive evenings” in her apartment were arranged on any possible occasion; for example, in the summer of 1927 it was the frequent visits of her student van der Waerden from Holland. The evenings at Emmy Noether’s, and the walks with her outside town, were a shining and unforgettable feature of the mathematical life of Göttingen for an entire decade (1923–1932). Many lively mathematical conversations were held during these evenings, but there was also much gaiety and laughter, good Rhine wine would sometimes be on the table and many sweets would be consumed…
Such was Emmy Noether, the greatest of women mathematicians, a leading scientist, wonderful teacher and unforgettable person. She did not have the characteristics of the so-called “woman scholar” or “blue stocking.” To be sure, Weyl said in his obituary, “No one could contend that the Graces had stood by her cradle,” and he is right, if we have in mind her well-known heavy build. But at this point Weyl is speaking of her not only as a major scientist, but as a major woman! And this she was — her feminine psyche came through in the gentle and delicate lyricism that lay at the foundation of the wide-ranging but never superficial relationships connecting her with people, with her avocation, with the interests of all mankind. She loved people, science, life with all the warmth, all the joy, all the selflessness and all the tenderness of which a deeply feeling heart — and a woman’s heart — was capable.