- Person
- Emmy Noether
- Lived
- 1882–1935
- Field
- Mathematics
- From
- German
The story
Emmy Noether was born in 1882 in Erlangen, Bavaria, to a Jewish family; her father Max was a mathematics professor. Women were largely shut out of academic careers, and after her doctorate she worked at Erlangen for years without pay. Her expertise in invariant theory, the study of quantities that stay the same under transformations, was nevertheless recognised. In 1915 David Hilbert and Felix Klein invited her to Göttingen, one of the world's great centres of mathematics, because they wanted her help in understanding Albert Einstein's new general theory of relativity.
Hilbert had noticed a puzzle: conservation of energy seemed to fail in general relativity, because gravitational energy could itself produce gravity. Noether resolved the paradox and in doing so found something far more general. Her paper "Invariante Variationsprobleme" was presented by Felix Klein on 26 July 1918 to the Royal Society of Sciences at Göttingen, presumably because she was not a member. It contained two theorems, the first of which is now called Noether's theorem.
The theorem shows that every continuous symmetry of the laws of physics comes with a quantity that is conserved. If the laws are the same at every moment, energy is conserved; if they are the same everywhere in space, momentum is conserved; if they do not depend on direction, angular momentum is conserved. It is the symmetry of the laws, not of the object, that matters: a jagged asteroid tumbling in space still conserves angular momentum. Einstein wrote to Hilbert praising her paper and remarking that the old guard at Göttingen could learn from her.
At first physicists, unfamiliar with Sophus Lie's theory of continuous groups on which she built, did not grasp the full scope of the result. In the second half of the twentieth century it became a fundamental tool of theoretical physics, both for understanding conservation laws and for testing new theories: any theory with a continuous symmetry must have a conserved quantity that experiments can check. The physicists Leon Lederman and Christopher Hill have called it one of the most important mathematical theorems ever proved in guiding modern physics.
Despite the theorem, the faculty delayed her habilitation until 1919. Noether went on to transform abstract algebra. Dismissed by the Nazi government in 1933 because she was Jewish, she moved to Bryn Mawr College in Pennsylvania and lectured at the Institute for Advanced Study in Princeton until her death in 1935. Einstein then wrote that she was the most significant creative mathematical genius produced since the higher education of women began.
Why it matters
Noether's theorem tied modern physics to the mathematics of symmetry and is a basic tool used throughout theoretical physics today.
About Emmy Noether
Erlangen-born mathematician who linked symmetry to conservation laws and reshaped abstract algebra, despite years of unpaid work as a woman and dismissal by the Nazis as a Jew.
More about Emmy Noether
- Emmy Noether's bound solved a problem in invariant theoryIn 1915 Emmy Noether solved the finite basis problem for finite groups, proving a degree limit now called Noether's bound. A last open case was settled only in 2000 and 2001.
- Emmy Noether helped classify division algebrasWith Richard Brauer and Helmut Hasse, Emmy Noether proved the Brauer–Hasse–Noether theorem, which allows all central division algebras over a number field to be classified.
- Emmy Noether helped create algebraic topologyAttending lectures by Pavel Alexandrov and Heinz Hopf in 1926–27, Emmy Noether suggested the idea of homology groups, helping turn combinatorial topology into algebraic topology.
- Emmy Noether's 1921 paper gave us Noetherian ringsIn her 1921 paper Idealtheorie in Ringbereichen, Emmy Noether turned the theory of ideals into a powerful general tool, and objects with her chain condition are still called Noetherian.
- Emmy Noether built a school of brilliant studentsEmmy Noether's Göttingen circle, the Noether boys, included doctoral students such as Grete Hermann, Ernst Witt, Max Deuring and Jacob Levitzki, who later taught in Jerusalem.
- Emmy Noether unified group representation theoryEmmy Noether gave the first general representation theory of groups and algebras, combining scattered earlier results into a single theory of modules and ideals.
- Emmy Noether worked seven years without payOne of only two women among 986 students at Erlangen, Emmy Noether earned her doctorate in 1907 and then worked at the university's Mathematical Institute for seven years without pay.
- Dismissed by the Nazis, Emmy Noether taught at homeAfter the Nazis barred her from teaching in 1933, Emmy Noether gathered students in her apartment to keep doing mathematics, unruffled even when one arrived in SA uniform.
Sources
- Emmy Noether Wikipedia
- Emmy Noether: creative mathematical genius Plus Magazine, University of Cambridge
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