When Einstein published general relativity, the math carried a devastating flaw: it seemed to violate the conservation of energy, the bedrock of physics. The two most prominent mathematicians alive, Hilbert and Klein, could not crack it, so they handed the problem to a woman their own university refused to hire. Emmy Noether solved it while fighting for the right to teach at all and mourning her mother's sudden death, and the result, Noether's theorem, proved that every continuous symmetry in nature corresponds to a conservation law. Physicists still call it one of the most beautiful ideas in science. She was not allowed to present it herself; a male colleague read her paper to the society in 1918.

Her whole career ran on that pattern of brilliance against barricade: begging professors one by one for permission to audit lectures in a Bavari ...