Emmy Noether
Why are conserved quantities conserved?
That time, that place
Göttingen would not appoint her to a professorship. When Hilbert pushed, the faculty objected — must soldiers returning from the war learn at the feet of a woman?
Hilbert replied that the university is not a bathhouse.
She was still not appointed. In the end the lectures were listed under Hilbert's name and Noether taught them. For years, unpaid.
Why this question
In general relativity, energy conservation behaved strangely. Hilbert and Klein brought her in to sort it out.
What she proved was not that one problem. It was something far more general.
What was found
Wherever a physical law has a symmetry, a corresponding conserved quantity must exist.
If the law is the same whenever you run the experiment, energy is conserved. If it is the same wherever you run it, momentum is conserved. If it is the same however you rotate the apparatus, angular momentum is conserved.
This matters because until then conservation laws were facts established by experiment. No one could say why energy is conserved.
Noether's theorem answers that. What is conserved follows from the form of the law itself. Where nature is indifferent to something, that indifference preserves something.
Conservation laws were merely facts found by experiment
A mathematical proof deriving conserved quantities from symmetries
When the Nazis came to power she was dismissed as a Jew and left for America. She died two years later of surgical complications, and Einstein published a tribute in the New York Times