Emmy Noether: breathtaking mathematics
By the mid 1920s, Emmy Noether had made fundamental contributions to commutative algebra and to the theory of invariants. Her crowning achievement from this period was "Noether's Theorem," establishing deep connections between conserved quantities in physics and mathematical invariants. She then tackled noncommutative algebra and demonstrated its significance for many fields of mathematics, including number theory, representation theory, and even commutative theory. The relationship between the non-commutative and the commutative was the overarching theme of her plenary lecture at the International Congress of Mathematicians in 1932, a high point of her remarkable career. Her mathematical legacy is still very much in evidence in the numerous concepts and results that can be traced back to her work, many of which bear her name.