Google has honoured Emmy Noether's birthday. Few people know who she is but, amongst other contributions to mathematics, she proved a theorem, known as Noether's theorem, that underpins all of physics because it deals with symmetry and conservation laws of energy and momentum.
The mathematics is well over my head, but I appreciate its ramifications. Basically, it deals with the mathematical relationships between symmetry in space and conservation of momentum, symmetry in time and conservation of energy and symmetry of rotation and conservation of angular momentum. This applies in particular to quantum mechanics, though conservation laws are equally relevant in relativity theory.
Symmetry, in this context, is about translation: translations in space, translations in time and translations in rotation. Richard Feynman gives a good exposition in Six Not-So-Easy Pieces, where I came across it for the first time, and he describes it thus: ...a most profound and beautiful thing, is that, in quantum mechanics, for each of the rules of symmetry there is a corresponding conservation law; there is a definite connection between the laws of conservation and the symmetry of physical laws.
You can read about it in some detail in Wikipedia, though I confess it's a bit esoteric.
Noether died relatively young in America at age 53, 2 years after escaping Nazi Germany, and Einstein wrote a moving tribute to her in the New York Times (1935). Physicists, Leon M. Lederman and Christopher T. Hill, in Symmetry and the Beautiful Universe, give the following accolade: “..certainly one of the most important mathematical theorems ever proved in guiding the development of modern physics…”
The sad part about her story is that she is virtually unknown and was not given due recognition in her own time, simply because she was a woman.
Addendum: It's also 100 years since Noether developed her seminal theorem - the same year that Einstein developed his General Theory of Relativity, incorporating gravity.
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