Ferdinand Georg Frobenius

Ferdinand Georg Frobenius approached mathematics with a combinative power that sought unity across fields. His career, spent largely at the University of Berlin, was characterized by deep, structural thinking. While he made early contributions to differential equations and elliptic functions, his most enduring work revolutionized abstract algebra. He virtually founded the theory of group representations, introducing group characters and proving fundamental theorems that connected groups to matrices. His name is attached to the Frobenius endomorphism, a cornerstone in fields from number theory to algebraic geometry. He was also the first to publish a complete proof of the Cayley-Hamilton theorem in algebra. A figure of immense rigor, his work provided the language and tools that would fuel much of twentieth-century mathematics, though he often engaged in fierce priority disputes with contemporaries like Dedekind and Stickelberger.