⚡ Emmy Noether Research Paper

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Emmy Noether Research Paper



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The most significant genius: Emmy Noether

Again she was not allowed to be a properly matriculated student but was only allowed to sit in on lectures. At this point the rules were changed and women students were allowed to matriculate on an equal basis to the men. On 24 October Noether matriculated at Erlangen where she now studied only mathematics. In she was granted a doctorate after working under Paul Gordan. The oral examination took place on Friday 13 December and she was awarded the degree 'summa cum laude'. Hilbert 's basis theorem of had given an existence result for finiteness of invariants in n n n variables. Gordan , however, took a constructive approach and looked at constructive methods to arrive at the same results.

Noether's doctoral thesis followed this constructive approach of Gordan and listed systems of covariant forms. Colin McLarty writes that [ 39 ] So far as I know no one has ever completed it or even checked it as far as she went. It was old-fashioned at the time, a witness to the pleasant isolation of Erlangen, and made no use of Gordan 's own work building on Hilbert 's ideas. 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 Noether remained at Erlangen, helping her father who, particularly because of his own disabilities, was grateful for his daughter's help.

Noether also worked on her own research, in particular she was influenced by Ernst Fischer who had succeeded Gordan to the chair of mathematics when he retired in Noether 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. Fischer 's influence took Noether towards Hilbert 's abstract approach to the subject and away from the constructive approach of Gordan. Now this was very important to her development as a mathematician for Gordan , despite his remarkable achievements, had his limitations. Noether's father, Max Noether , said of Gordan see [ 3 ] :- Gordan was never able to do justice to the development of fundamental concepts; even in his lectures he completely avoided all basic definitions of a conceptual nature, even that of the limit.

Noether's reputation grew quickly as her publications appeared. In she was elected to the Circolo Matematico di Palermo , then in she was invited to become a member of the Deutsche Mathematiker-Vereinigung and in the same year she was invited to address the annual meeting of the Society in Salzburg. In she lectured in Vienna, again to a meeting of the Deutsche Mathematiker-Vereinigung. While in Vienna she visited Franz Mertens and discussed mathematics with him. One of Merten's grandsons remembered Noether's visit see [ 5 ] During these years in Erlangen she advised two doctoral students who were both officially supervised by her father. These were Hans Falckenberg doctorate and Fritz Seidelmann doctorate For information on these and Noether's other Ph.

The reason for this was that 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. Van der Waerden writes [ 68 ] :- She came and at once solved two important problems. First: How can one obtain all differential covariants of any vector or tensor field in a Riemannian space? The second problem Emmy investigated was a problem from special relativity. She proved: To every infinitesimal transformation of the Lorentz group there corresponds a Conservation Theorem.

This result in theoretical physics is sometimes referred to as Noether's Theorem, and proves a relationship between symmetries in physics and conservation principles. This basic result in the theory of relativity was praised by Einstein in a letter to Hilbert when he referred to Noether's penetrating mathematical thinking. This was a time of extreme difficulty and she lived in poverty during these years and politically she became a radical socialist. However, they were extraordinarily rich years for her mathematically. Hermann Weyl , in [ 69 ] writes about Noether's political views:- During the wild times after the Revolution of , 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.

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 a long battle with the university authorities to allow Noether to obtain her habilitation there were many setbacks and it was not until that permission was granted and she was given the position of Privatdozent. During this time Hilbert had allowed Noether to lecture by advertising her courses under his own name. For example a course given in the winter semester of - 17 appears in the catalogue as:- Mathematical Physics Seminar: Professor Hilbert , with the assistance of Dr E Noether, Mondays from 4 - 6 , no tuition.

In this paper she gave the decomposition of ideals into intersections of primary ideals in any commutative ring with ascending chain condition. Emanuel Lasker who became the world chess champion had already proved this result for a polynomial ring over a field. In this paper she gave five conditions on a ring which allowed her to deduce that in such commutative rings every ideal is the unique product of prime ideals. The major part of the second volume consists of Noether's work. From onwards Noether collaborated with Helmut Hasse and Richard Brauer in work on non-commutative algebras. In addition to teaching and research, Noether helped edit Mathematische Annalen.

Much of her work appears in papers written by colleagues and students, rather than under her own name. She received no pension or any other form of compensation but, nevertheless, she considered herself more fortunate than others. She wrote to Helmut Hasse on 10 May see for example [ 5 ] :- Many thanks for your dear compassionate letter! Edmunds P. Neumann P. Neumann N. Bingham E. Lance J. McConnell J. Jones J. Rawnsley P. Holgate D. Garling J. Hubbuck R. Archbold P. Dixon A. Pears F.

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