Barry Mazur

A mathematician whose work sits at the foundation of modern number theory: Mazur's torsion theorem settled a long-standing question about elliptic curves, and his techniques became a critical building block in Andrew Wiles's eventual proof of Fermat's Last Theorem, one of the most famous problems in the field's history. He has also left his name on constructions in geometric and differential topology — the Mazur swindle and the Mazur manifold — and has spent his career as a professor at Harvard.