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Emmy Noether
1918· Person
ProvenTested many times; part of working physics.
German mathematician (1882–1935), a founder of modern abstract algebra, who proved the deep link between symmetry and conservation laws.
See it on the Science map →How it works
Noether was barred from regular university posts because she was a woman; at Göttingen she first lectured under David Hilbert's name. In 1915 Hilbert and Felix Klein invited her to help with puzzles in Einstein's new general relativity, and she proved her theorem, published in 1918. She then reshaped algebra by studying abstract structures rather than calculations. Dismissed by the Nazis in 1933, she taught at Bryn Mawr College until her death.
Why it matters
Her theorem is a pillar of modern physics, and her algebra transformed mathematics. Einstein's 1935 tribute called her a creative mathematical genius.
How the work held up
Her theorem is a mathematical proof, applied and confirmed across every branch of physics. Modern algebra textbooks still follow her approach.
Connections (2)
▸Emmy Noether proved Noether's theorem: symmetry means conservationProven
The relationship
Hilbert and Klein were stuck on how energy conservation works in Einstein's new general relativity. Noether attacked the general question: what do the symmetries of a theory imply? She proved that each smooth symmetry yields a conserved quantity, and explained why general relativity behaves differently from older theories.
How the link was found
Felix Klein presented her paper 'Invariant Variation Problems' to the Göttingen scientific society in July 1918, since she was not a member.
Why it's proven
It is a rigorous proof, re-derived countless times and checked in every field of physics that uses it.
Open questions and mysteries
Its full importance went largely unappreciated until the 1950s–1970s, when particle physicists began building theories around symmetry.
▸Emmy Noether revealed the power of Symmetry and group theoryProven
The relationship
Before Noether, symmetry was mainly a topic in geometry and algebra. Her theorem showed it is the source of physics' conservation laws, and her abstract algebra gave mathematicians cleaner tools for studying symmetry structures. Physicists later adopted symmetry as their main method for finding new laws.
How the link was found
Noether's 1918 theorem, and her algebra work at Göttingen in the 1920s.
Why it's proven
Her theorem is proven, and symmetry-based theories such as the Standard Model have been confirmed repeatedly.
Open questions and mysteries
Why the deepest laws appear to be dictated by symmetry at all is not understood.