For those who don't know, Alexander[1] Grothendieck revolutionized algebraic geometry, which is (in a very rough sense) the study of solutions of systems of polynomial equations as both algebraic and geometric objects. Grothendieck gave a totally new foundation for the subject via category theory, and one could argue that he is a primary reason why categories are so central in modern mathematics.

[1]: He spelled his own name different from the French spelling, apparently.