Day 75 · Mar 15

Birthday of Emil Artin (1898)

Emil Artin is one of the founders of modern abstract algebra. His reciprocity law generalised Gauss's quadratic reciprocity to all algebraic number fields — a result that had been the goal of number theorists for over a century. He also proved the theory of braids (1925), developed the theory of real closed fields, and made fundamental contributions to class field theory. Forced out of Hamburg by the Nazis in 1937, he emigrated to the United States, where he influenced a generation of mathematicians including Serge Lang, John Tate, and Kolchin.

Gauss's quadratic reciprocity asks: if p is a square mod q, is q a square mod p? How would you even begin to investigate this pattern?

Practice related topics on DuelMath

Challenge someone →