Amalie Emmy Noether (23 March 1882 – 14 April 1935) was a German mathematician who made many important contributions to abstract algebra and mathematical physics. As one of the leading mathematicians of her time, she developed theories of rings, fields, and algebras. She also proved Noether's first and second theorems, which play a fundamental role in mathematical physics, by explaining the connection between symmetry and conservation laws.
Education
Noether showed early proficiency in French and English. In 1900, she took the examination for teachers of these languages and received an overall score of sehr gut (very good). Her performance qualified her to teach languages at schools reserved for girls, but she chose instead to continue her studies at the University of Erlangen–Nuremberg, where her father was a professor.
This was an unconventional decision; two years earlier, the Academic Senate of the university had declared that allowing mixed-sex education would "overthrow all academic order". One of just two women in a university of 986 students, Noether was allowed only to audit classes rather than participate fully, and she required the permission of individual professors whose lectures she wished to attend. Despite these obstacles, on 14 July 1903 she passed the graduation exam at a Realgymnasium in Nuremberg.
During the 1903–04 winter semester, Noether studied at the University of Göttingen, attending lectures given by astronomer Karl Schwarzschild and mathematicians Hermann Minkowski, Otto Blumenthal, Felix Klein, and David Hilbert.
Habilitation and Noether's theorem
In early 1915, Noether was invited to return to the University of Göttingen by Hilbert and Felix Klein. Their effort to recruit her was initially blocked by the philologists and historians among the philosophical faculty, who insisted that women should not become privatdozenten. In a joint department meeting on the matter, 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, who believed Noether's qualifications were the only important issue and that gender was irrelevant, objected with indignation and scolded those protesting her habilitation. His exact words have not been preserved, but his objection is often said to have included the remark that the university was "not a bathhouse".
Pavel Alexandrov recalled that faculty members' opposition to Noether was based not just in sexism, but also in their objections to her social-democratic political beliefs and Jewish ancestry.
Physics
For illustration, if a physical system behaves the same, regardless of how it is oriented in space, the physical laws that govern it are rotationally symmetric; from this symmetry, Noether's theorem shows the angular momentum of the system must be conserved. The physical system itself need not be symmetric; a jagged asteroid tumbling in space conserves angular momentum despite its asymmetry. Rather, the symmetry of the physical laws governing the system is responsible for the conservation law. As another example, if a physical experiment works the same way at any place and at any time, then its laws are symmetric under continuous translations in space and time; by Noether's theorem, these symmetries account for the conservation laws of linear momentum and energy within this system, respectively.
At the time, physicists were not familiar with Sophus Lie's theory of continuous groups, on which Noether had built. Many physicists first learned of Noether's theorem from an article by Edward Lee Hill that presented only a special case of it. Consequently, the full scope of her result was not immediately appreciated. During the latter half of the 20th century, Noether's theorem became a fundamental tool of modern theoretical physics, because of the insight it gives into conservation laws, and also as a practical calculation tool. Her theorem allows researchers to determine the conserved quantities from the observed symmetries of a physical system. Conversely, it facilitates the description of a physical system based on classes of hypothetical physical laws.