Amalie (Emmy) Noether ( ) Mairi Sakellariadou King s College London

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1 Amalie (Emmy) Noether ( ) Mairi Sakellariadou King s College London

2 Emmy Noether was born in Erlangen, Germany on March 23, 1882 She was named Amalie, but always called "Emmy" 2

3 The family The father: Max Noether (1844 Mannheim 1921 Erlangen) From a Jewish family of wealthy wholesale hardware dealers. At 14, Max contracted polio and was afflicted by its effects for the rest of his life. Through self-study, he learned advanced mathematics and entered the University of Heidelberg in He moved to the University of Erlagen in While there, he helped to found the field of algebraic geometry. In 1880 he married Ida Amalia Kaufmann, the daughter of another wealthy Jewish merchant family. Two years later they had their first child, named Amalia ( Emmy ) after her mother. 3

4 The family The mother: Ida Amalia Kaufmann (1852 Koln 1951 Erlagen) From a wealthy Jewish merchant family. Ida had a brother who was a professor at the University of Berlin. In 1880 she married Max Noether ; they had four children. Ida was a skilled pianist. 4

5 The family Emmy Professor of Mathematics in Erlagen, Gottingen, and Bryn Mawr (USA) Alfred Chemist Fritz Professor of Mathematics in Breslavia (Germany) and in Tomsk (Russia) Gustav Robert

6 The family a bit before the first world war 6

7 The Erlagen period ( ) Emmy's childhood was unexceptional, going to school, learning domestic skills, and taking piano lessons. Her passion was dancing. Since girls were not eligible to enroll in the gymnasium, she attended the Municipal School for Higher Education of Daughters in Erlangen, where she studied arithmetic and languages. Emmy also loved mathematics, but she knew that the rules of the time meant she would not be allowed to follow in her father s footsteps to become a University academic. At age18, she was qualified to teach English and French in girls schools. 7

8 The Erlagen period ( ) Although a career in teaching offered her financial security, her love of mathematics proved to be too strong. Emmy decided to abandon teaching and apply to the University of Erlangen to observe mathematics lectures. She could only observe lectures, because women were not permitted to enroll officially at the University. Emmy was one of the two female students sitting in on courses at Erlangen. Between 1900 and 1902 Emmy studied mathematics at Erlangen. In July 1903 she went to Nürnberg and passed the matriculation examination allowing her to study mathematics (but not officially enroll) at any German University. 8

9 The Erlagen period ( ) Emmy chose to go for a semester to the University of Göttingen. She attended lectures given by: Schwarzschild Minkowski Blumenthal Again she was not allowed to be a properly matriculated student but was only allowed to sit in on lectures. Klein Hilbert After one semester at Göttingen, Emmy returned to Erlangen. 9

10 The Erlagen period ( ) At this point the rules were changed and women students were allowed to matriculate on an equal basis to the men. On 24 October 1904 Emmy matriculated at Erlangen and in 1907, at the age of 25, she was granted a doctorate after working under Paul Gordan,. Her thesis was entitled On the construction of the system of forms of a ternary biquadratic form (the search for the invariants of a homogeneous polynomial of degree 4 in 3 variables). Emmy was the only student Gordan ever accepted as a Ph.D. candidate... her dissertation with Gordan pursued a huge calculation that had stumped Gordan forty years before and which Noether could not complete either. So far as I know no one has ever completed it or even checked it as far as she went. Colin McLarty (2011) 10

11 The Erlagen period ( ) Research and teaching at Erlagen University ( ) Having completed her doctorate the normal progression to an academic post would have been the habilitation. However this route was not open to women so Emmy remained at Erlangen, helping her father who, particularly because of his own disabilities, was grateful for his daughter's help. Emmy also worked on her own research; she was influenced by Ernst Fischer who had succeeded Gordan to the chair of mathematics when he retired in Emmy wrote about Fischer's influence: Above all I am indebted to Mr E Fischer from whom I received the decisive impulse to study abstract algebra from an arithmetical viewpoint, and this remained the governing idea for all my later work. 11

12 Research and teaching at Erlagen University ( ) Dr. Noether, Mathematics Lecturer In 1908 Emmy was appointed to the position of mathematics lecturer at Erlangen. Unfortunately, it was an unpaid position. Emmy s parents supported her as much as they could through this time. Nevertheless, her life was a struggle financially. While working as a lecturer, Emmy became fascinated by work Hilbert had done in Göttingen. 1908: member of the Mathematical Circle of Palermo 1909: member of the Mathematical German Society 12

13 The Göttingen period ( ) Hilbert was working on physics, in particular on ideas on the theory of relativity close to those of Albert Einstein. He decided that he needed the help of an expert on invariant theory and, after discussions with Klein, they issued the invitation. Felix Klein David Hilbert:

14 The Göttingen period ( ) In 1915 Hilbert invited her to become a lecturer in Göttingen. This provoked a storm of protest from philologists and historians among the faculty. One faculty member protested: What will our soldiers think when they return to the university and find that they are required to learn at the feet of a woman? Hilbert responded with indignation, stating, I do not see that the sex of the candidate is an argument against her admission... After all, we are a university, not a bath house. Emmy was so eager to join Hilbert s department in Göttingen that, to overcome Hilbert s opponents, she agreed not to be formally appointed as a lecturer and to receive no pay. Her father continued supporting her financially (her mother died in 1915) and the lectures she gave were advertised as lectures by Professor Hilbert, with assistance from Dr. E. Noether. 14

15 The Göttingen period ( ) Soon after arriving at Göttingen, Noether proved her two theorems in 1915, published in 1918, under the title Invariante Variationsprobleme 15

16 The Göttingen period ( ) Soon after arriving at Göttingen, Noether proved her two theorems in 1915, published in 1918, under the title Invariante Variationsprobleme in Nachrichten von der Koniglichen Gesellschaft der Wissenschaften zu Gottingen, Mathematisch-physikalische Klasse, 1918, pp

17 The Göttingen period ( ) Soon after arriving at Göttingen, Noether proved her two theorems in 1915, published in 1918, under the title Invariante Variationsprobleme in Nachrichten von der Koniglichen Gesellschaft der Wissenschaften zu Gottingen, Mathematisch-physikalische Klasse, 1918, pp Emmy s theorems relate symmetry groups of a variational integral to properties of its associated Euler-Lagrange equations. Every differentiable symmetry of the action of a physical system has a corresponding conservation law. Among the most important mathematical theorems ever proved in guiding the development of modern physics. 17

18 Emmy submitted the invariant Variationsprobleme for her Habilitation, finally obtained in She never referred to her article in her subsequent publications. In Göttingen, Emmy had only one immediate follower, Erich Bessel-Hagen ( ), who was Klein s student. He formulated the two Noether theorems slightly more general than they had been formulated in her article, and added I owe these to an oral communication by Miss Emmy Noether herself. 18

19 The Göttingen period ( ) November 1915 Albert Einstein publishes his theory of General Relativity. David Hilbert states the Variational Principle. The contribution of Emmy s work was fundamental. Albert Einstein: David Hilbert:

20 Although Noether's theorem had a profound effect upon physics, among mathematicians she is best remembered for her seminal contributions to Abstract Algebra. In 1924 B. L. van der Waerden, arrived at the University of Göttingen. van der Waerden later said that her originality was absolute beyond comparison. In 1931 van der Waerden published Modern Algebra, a central text in the field; its second volume borrowed heavily from Emmy's work.... The development of abstract algebra, which is one of the most distinctive innovations of twentieth century mathematics, is largely due to her in published papers, in lectures, and in personal influence on her contemporaries..." Nathan Jacobson in his introduction to Nother s collected papers 20

21 The Göttingen period ( ) Assistant professor in 1922 During her time at the University of Gottingen, she accumulated a small following of students known as Noether's boys. Completely unegotistical and free of vanity, she never claimed anything for herself, but promoted the works of her students above all. Emmy as Assistant. Professor was teaching Group Theory and Hypercomplex Numbers Hypercomplex Quantities and Representation Theory Noncommutative Algebra Noncommutative Arithmetic Algebra of Hypercomplex Quantities but during the first few years she was not receiving a salary. van der Waerden She was living in a student pension, until she was thrown out after student leaders complained of living with "a Marxist-leaning Jewess". She was taking her meals in a canteen for poor people. 21

22 The Göttingen period ( ) In the twenties, Göttingen gathered the best mathematicians. Apart Hilbert and Klein, there were also Hermann Weyl, Richard Courant, Constantin Caathéodory, and many more. Many visitors were also spending long periods, like for instance André Weil, Solomon Lefschetz, and Claude Chevalley. Emmy was playing a protagonist role in this golden period of mathematics. 22

23 The Göttingen period ( ) In the winter of Emmy accepted an invitation to Moscow State University, where she continued working with P. S. Alexandrov. In addition to carrying on with her research, she taught classes in Abstract Algebra and Algebraic Geometry. She worked with the topologists, Lev Pontryagin and Nikolai Chebotaryov, who later praised her contributions to the development of Galois theory. 23

24 The Göttingen period ( ) Recognition In 1932 Emmy Noether and Emil Artin received the Ackermann Teubner Memorial Award for their contributions to mathematics. In November 1932 Emmy delivered a plenary address on "Hyper-complex systems in their relations to commutative algebra and to number theory" at the International Congress of Mathematicians in Zürich. The congress was attended by 800 people. But she was not elected to the Göttingen Academy of Sciences and was never promoted to the position of Full Professor. For her fiftieth birthday (1932) Helmut Hasse dedicated an article to her in the Mathematische Annalen, wherein he confirmed her suspicion that some aspects of noncommutative algebra are simpler than those of commutative algebra by proving a noncommutative reciprocity law. 24

25 In January 1933 Adolf Hitler becomes the German Reichskanzle At the University of Göttingen the German Student Association led the attack on the "un-german spirit" attributed to Jews and was aided by a Werner Weber, a former Emmy s student. In April 1933 Emmy received a notice from the Prussian Ministry for Sciences, Art, and Public Education which read: "On the basis of paragraph 3 of the Civil Service Code of 7 April 1933, I hereby withdraw from you the right to teach at the University of Göttingen. Emmy accepted the decision calmly, providing support for others during this difficult time. She remained focused on mathematics, gathering students in her apartment to discuss class field theory. When one of her students appeared in the uniform of the Nazi, she showed no sign of agitation. 25

26 Bryn Mawr: Albert Einstein and Hermann Weyl were appointed by the Institute for Advanced Study in Princeton, while others worked to find a sponsor required for legal immigration. Emmy was contacted by representatives of two educational institutions, the Bryn Mawr College for female students in Philadephia (USA) and the Somerville College at the University of Oxford in England. After a series of negotiations with the Rockefeller Foundation, a grant to Bryn Mawr was approved for Emmy and she took a position there, starting in late

27 Bryn Mawr: At Bryn Mawr, Emmy worked with Anna Wheeler, who had studied at Göttingen just before Emmy arrived there. Another source of support was the Bryn Mawr president, Marion Edwards Park, who enthusiastically invited mathematicians in the area to "see Dr. Noether in action!. Emmy and a small team of students worked through van der Waerden's book Modern Algebra I and parts of Erich Hecke's Theory of algebraic numbers. In 1934, Emmy began lecturing at the Institute for Advanced Study in Princeton.. However, she remarked about Princeton University that she was not welcome at the "men's University, where nothing female is admitted. 27

28 Bryn Mawr: 1935 In April 1935 doctors discovered that she had a tumour. Two days later they operated, finding further tumours which they believed to be benign and did not remove. The operation seemed a success and for three days her condition improved. However, on the fourth day, 14 th April 1935, Emmy suddenly collapsed and developed a very high temperature. She died later that day. Her body was cremated and the ashes interred under the walkway around the cloisters of the M. Carey Thomas Library at Bryn Mawr. 28

29 In the judgment of the most competent living mathematicians, Fräulein Noether was the most significant creative mathematical genius thus far produced since the higher education of women began. In the realm of algebra, in which the most gifted mathematicians have been busy for centuries, she discovered methods which have proved of enormous importance in the development of the present-day younger generation of mathematicians... " Albert Einstein New York Times (1935) 29

30 E. Noether s famous 1918 paper, Invariant variational problems crystallised essential mathematical relationships among symmetries, conservation laws, and identities for the variational or `action principles of physics... Thus, Noether s abstract analysis continues to be relevant to contemporary physics, as well as to applied mathematics. Gregg Zuckerman (1987) 30

31 Emmy Noether: