The story
In 1918 the German mathematician Emmy Noether published a result, in a paper titled Invariante Variationsprobleme, showing that for any physical system governed by a variational principle, each continuous symmetry corresponds to a conservation law. If the laws of physics are the same today as tomorrow, energy is conserved. If they are the same here as elsewhere, momentum is conserved. If they do not depend on direction, angular momentum is conserved. Felix Klein presented the work to the Gottingen scientific society in July 1918.
Energy conservation had been formulated in the 1840s, and Newtonian mechanics already used it. Einstein's general relativity of 1915 made the situation puzzling: in curved spacetime, energy conservation seemed to fail or lose its meaning. David Hilbert and Felix Klein at Gottingen asked Noether to help, and she had been invited there in 1915 even though the faculty refused for years to give a woman a regular post. Her work showed exactly how conservation laws follow from symmetries and why energy takes a subtler form in general relativity.
The theorem became a working tool of modern physics. In quantum field theory, conserved electric charge follows from a symmetry in the phase of the wave function, and the Standard Model is built from such symmetries. Noether also transformed abstract algebra, and structures now called Noetherian rings carry her name. She left Nazi Germany in 1933 for Bryn Mawr College in the United States and died in April 1935 after surgery, aged 53. Einstein wrote an appreciation in the New York Times calling her a creative mathematical genius.
Why it mattered
- Symmetry became the main organizing principle of fundamental physics, guiding the search for new laws and particles.
- The Standard Model of particle physics rests on symmetry principles whose conserved charges follow from Noether's theorem.
- Physicists gained a systematic way to derive conservation laws instead of discovering them one at a time.
- Her algebraic work on rings and ideals shaped twentieth century abstract algebra.
Sources
- Colloquium: A Century of Noether's Theorem arXiv
- To the Editor of The New York Times (Einstein on Emmy Noether) MacTutor, University of St Andrews
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