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Glad to see the NY Times with an article today about the life and work of Emmy Noether. Noether was famous for her work on abstract algebra and group theory, but most of all for the theorem which bears her name, probably one of the single most important results in mathematical physics.

Briefly, what the theorem says is that whenever a system has a continuous symmetry – say, a cylinder looks the same whenever you rotate it about its axis, or any arrangement of objects looks the same if you shift the whole thing to the left – then motion in that direction has a corresponding momentum, and that momentum is conserved; and likewise, whenever there is a conserved quantity, there's an associated underlying symmetry. Conservation of momentum is tied to the symmetry of moving things left and right; of energy, to shifting forwards and backwards in time; and conservation of electric charge and mass are tied to the subtler symmetries which underpin quantum field theory and General Relativity. It's no exaggeration to say that this theorem is one of the things which most shaped 20th-century physics. (It also has the unusual property that the quantum-mechanical version is considerably easier to prove than the classical version)

So on the occasion of what would be her 130th birthday last week, I'm glad to see her getting a bit more of the recognition she always deserved.
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