Amalie (Emmy) Noether (1882 - 1935)
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Amalie (Emmy) Noether (1882 - 1935) Mairi Sakellariadou King’s College London Emmy Noether was born in Erlangen, Germany on March 23, 1882 She was named Amalie, but always called "Emmy" 2 Emmy Noether 10th February 2016 Zakopane Mairi Sakellariadou 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 1865. He moved to the University of Erlagen in 1888. 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 Emmy Noether 10th February 2016 Zakopane Mairi Sakellariadou 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 Emmy Noether 10th February 2016 Zakopane Mairi Sakellariadou The family . Emmy 1882 – 1935 Professor of Mathematics in Erlagen, Gottingen, and Bryn Mawr (USA) . Alfred 1883 – 1918 Chemist . Fritz 1884 – 1937 Professor of Mathematics in Breslavia (Germany) and in Tomsk (Russia) . Gustav Robert 1889 -- 1928 5 Emmy Noether 10th February 2016 Zakopane Mairi Sakellariadou The family a bit before the first world war 6 Emmy Noether 10th February 2016 Zakopane Mairi Sakellariadou The Erlagen period (1882 – 1915) 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 Emmy Noether 10th February 2016 Zakopane Mairi Sakellariadou The Erlagen period (1882 – 1915) 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 Emmy Noether 10th February 2016 Zakopane Mairi Sakellariadou The Erlagen period (1882 – 1915) 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. After one semester at Göttingen, Emmy returned to Erlangen. Klein Hilbert 9 Emmy Noether 10th February 2016 Zakopane Mairi Sakellariadou The Erlagen period (1882 – 1915) 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 Emmy Noether 10th February 2016 Zakopane Mairi Sakellariadou The Erlagen period (1882 – 1915) Research and teaching at Erlagen University (1908-1915) 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 1911. 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 Emmy Noether 10th February 2016 Zakopane Mairi Sakellariadou Research and teaching at Erlagen University (1908-1915) 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 Emmy Noether 10th February 2016 Zakopane Mairi Sakellariadou The Göttingen period (1915 –1933) 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 1849 – 1925 David Hilbert: 1862 – 1943 13 Emmy Noether 10th February 2016 Zakopane Mairi Sakellariadou The Göttingen period (1915 –1933) 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 Emmy Noether 10th February 2016 Zakopane Mairi Sakellariadou The Göttingen period (1915 –1933) Soon after arriving at Göttingen, Noether proved her two theorems in 1915, published in 1918, under the title Invariante Variationsprobleme 15 Emmy Noether 10th February 2016 Zakopane Mairi Sakellariadou The Göttingen period (1915 –1933) 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. 235-257. 16 Emmy Noether 10th February 2016 Zakopane Mairi Sakellariadou The Göttingen period (1915 –1933) 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. 235-257. 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 Emmy Noether 10th February 2016 Zakopane Mairi Sakellariadou Emmy submitted the “invariant Variationsprobleme” for her Habilitation, finally obtained in 1919. She never referred to her article in her subsequent publications. In Göttingen, Emmy had only one immediate follower, Erich Bessel-Hagen (1898-1946), 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 Emmy Noether 10th February 2016 Zakopane Mairi Sakellariadou The Göttingen period (1915 –1933) 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: 1879-1955 David Hilbert: 1862 – 1943 19 Emmy Noether 10th February 2016 Zakopane Mairi Sakellariadou 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 Emmy Noether 10th February 2016 Zakopane Mairi Sakellariadou The Göttingen period (1922 –1933) Assistant professor in 1922 During her time at the University of Gottingen, she accumulated a small following of students known as Noether's boys.