Emmy Noether (1882-1935)
Born Amalie but always called "Emmy," she was born in Erlangen, Germany. At the age of 18, she decided to take classes in math at the University of Erlangen, where her father was a professor in mathematics. The university refused to let her take classes, because she was a woman. She was, however, able to audit classes, and then took the exam that permitted her to be a doctoral student in mathematics. She passed the test and then was able to study for five more years, eventually receiving a degree in mathematics. She was the second woman to have done so at the university.
She is known for her profound theorems in ring theory, but she most notably changed the way mathematicians think about math. Her colleague P.S. Alexandroff said about her, "She taught us to think in simple, and thus general, terms... homomorphic image, the group or ring with operators, the ideal... and not in complicated algebraic calculations." She cleared a path toward the discovery of new algebraic patterns. Her work is typically split into 3 epochs: 1907-1919, in which she devoted her time to algebraic invariant theory, Galois Theory, and physics. One of her theorems, known as "Noether's Theorem," is one of the most significant contributions in the development of modern physics. In her second epoch from 1920-1926, she concentrated on the theory of mathematical rings. She developed the abstract and conceptual approach to algebra, resulting in principles unifying topology, logic, geometry, algebra, and linear algebra. In her third epoch, from 1927-1935, she focused primarily on non-commutative algebras, representation theory, hyper-complex numbers, and linear transformations. She was awarded the Ackermann-Teubner Memorial Prize in Mathematics in 1932.
Check out this entertaining and informative video explaining Noether's Theorem.