Einstein called her a “creative mathematical genius.” She's one of the most important people in the history of physics. She worked without pay because she was a woman. InternationalWomensDay
But Hilbert and Klein stumbled on a puzzle. Attempts to use the framework of general relativity to write an equation for conservation of energy resulted in a tautology: Like writing “0 equals 0,” the equation had no physical significance. This situation was a surprise to the pair; no previously accepted theories had energy conservation laws like this. The duo wanted to understand why general relativity had this peculiar feature.
This is what Noether did best: fitting specific concepts into their broader mathematical context. “She was just able to see what’s right at the heart of what’s going on and to generalize it,” says philosopher of science Katherine Brading of Duke University, who has studied Noether’s theorems. As a woman, Noether struggled to find a paid academic position, even after being recruited to the University of Göttingen. Her supporters there argued that her sex was irrelevant. “After all, we are a university and not a bathing establishment,” Hilbert reportedly quipped. But that wasn’t enough to get her a salary.
She made a habit of taking long walks in the countryside with her students and colleagues, holding lengthy, math-fueled debates. When legs began to ache, Noether and company would plop down in a meadow and continue chatting.
Gauge symmetry appears in the definition of electric voltage. A voltage — between two ends of a battery, for example — is the result of a difference in electric potential. The actual value of the electric potential itself doesn’t matter, only the difference.
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