Theorem linking continuous symmetries to conservation laws (1918 (proved 1915))
Time symmetry gives conservation of energy; spatial symmetry gives conservation of momentum
Science · Maths, astronomy, medicine & more
Emmy Noether
1882–1935 · German
Mathematics — abstract algebra
Emmy Noether was a German mathematician who transformed abstract algebra and proved one of the most important theorems of theoretical physics. Invited to Göttingen by David Hilbert and Felix Klein, she showed that every continuous symmetry of a physical system corresponds to a conservation law, and her work on rings and ideals founded modern algebra. Dismissed by the Nazis in 1933 because she was Jewish, she moved to Bryn Mawr College in the United States, where she died in 1935; Einstein praised her as a creative mathematical genius.
How to spot them
- ▸Noether's theorem: symmetries give conservation laws
- ▸Noetherian rings; the ascending chain condition; ideal theory
- ▸Göttingen with Hilbert and Klein; 'we are a university, not a bathing establishment'
- ▸Erlangen; Bryn Mawr; the 'Noether boys'
Key discoveries & works
Idealtheorie in Ringbereichen (Ideal Theory in Rings) (1921)
Founded the theory of what are now called Noetherian rings, using the ascending chain condition
Doctoral thesis on invariants of ternary biquadratic forms under Paul Gordan (1907)
A massive computational thesis at Erlangen that she later dismissed as 'rubbish'
Invariante Variationsprobleme (1918)
The paper containing her two theorems on symmetry, presented to the Göttingen Society by Felix Klein
Key ideas
- Noether's theorem underlies modern physics from classical mechanics to the Standard Model
- Conceptual, axiomatic approach to algebra: studying structures such as rings, ideals and modules rather than explicit calculations
- Her school shaped van der Waerden's Moderne Algebra, the textbook that spread the new abstract algebra
Quick-fire facts
- •Born in Erlangen, Bavaria; her father Max Noether was a mathematics professor there
- •Women could audit but not fully enrol at Erlangen when she began; she was one of the first women to earn a mathematics doctorate in Germany (1907)
- •Hilbert and Klein invited her to Göttingen in 1915 to help with general relativity; faculty objected to a woman lecturing
- •Hilbert reportedly retorted that the senate was 'not a bathhouse' (a university, not a bathing establishment)
- •Her students and followers at Göttingen were known as the 'Noether boys'
- •Gave a plenary address at the International Congress of Mathematicians in Zurich in 1932
- •Expelled from Göttingen by the Nazis in 1933; moved to Bryn Mawr College, Pennsylvania, and lectured at the Institute for Advanced Study, Princeton
- •Died in 1935 after surgery to remove a tumour
- •Einstein's letter to the New York Times called her the most significant creative mathematical genius since higher education of women began
Drill it — 7 cards
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Sources
- MacTutor History of Mathematics, University of St Andrews — Amalie Emmy Noether
- Dwight E. Neuenschwander — Emmy Noether's Wonderful Theorem