Saunders Mac Lane (August 4, 1909 - April 14, 2005) was an American mathematician who cofounded category theory with Samuel Eilenberg.
Mac Lane earned a BA from Yale University in 1930, and an MA from the University of Chicago in 1931. He attended the University of Göttingen, 1931–1933, studying logic and mathematics under Paul Bernays, Emmy Noether and Hermann Weyl. Göttingen's Mathematisches Institut awarded him the Ph.D. in 1934.
Mac Lane served as vice president of the National Academy of Sciences and the American Philosophical Society, and as president of the American Mathematical Society. While presiding over the Mathematical Association of America in the 1950s, he initiated its activities aimed at improving the teaching of modern mathematics. In 1976, he led a delegation of mathematicians to China to study the conditions affecting mathematics there. Mac Lane was elected to the National Academy of Sciences in 1949, and received the National Medal of Science in 1989.
After a thesis in mathematical logic, his early work was in field theory and valuation theory. He wrote on valuation rings and Witt vectors, and separability in infinite field extensions. He started writing on group extensions in 1942, and began his epochal collaboration with Samuel Eilenberg in 1943, resulting in what are now called Eilenberg–Mac Lane spaces K(G,n), having a single non-trivial homotopy group G in dimension n. This work opened the way to group cohomology in general.