Math Labs

Edward Witten

fl. 1951, Baltimore, Maryland, United States

Mathematical physicsTopologyAnalysisFields Medal 1990Breakthrough Prize in Mathematics 2012Kyoto Prize in Basic Sciences 2014

American theoretical physicist whose quantum-field-theory methods transformed topology and geometry; the only physicist to win the Fields Medal (1990).

Edward Witten was born in Baltimore in 1951, the son of theoretical physicist Louis Witten. He studied history at Brandeis University before switching to physics, taking his PhD at Princeton in 1976 under David Gross. After holding a professorship at Princeton he moved in 1987 to the Institute for Advanced Study, where he has spent his career.

Witten is the central figure in the dialogue between quantum field theory, string theory and pure mathematics. Among the works cited by his 1990 Fields Medal are the supersymmetric reformulation of Morse theory, a path-integral derivation of the Atiyah–Singer index theorem, the interpretation of Donaldson invariants via topological gauge theory, and the discovery that Chern–Simons theory yields knot invariants such as the Jones polynomial. Later he introduced with Nathan Seiberg the Seiberg–Witten invariants (1994), which simplified four-manifold theory and led to a simple proof of the Thom conjecture; he also gave a supersymmetric proof of the positive energy theorem in general relativity and proposed M-theory (1995) unifying the five superstring theories.

His honors include the MacArthur Fellowship (1982), the Fields Medal (1990), the inaugural Fundamental Physics Prize (2012), and the Kyoto Prize (2014). He remains the most influential figure at the interface of mathematics and physics.

Workplaces: Institute for Advanced Study, Princeton

United States

Award-winning work

Fields Medal 1990Witten — a physicist — earned the medal for injecting quantum field theory into the heart of mathematics. His 1982 'supersymmetry and Morse theory' paper recast Morse theory as the quantum mechanics of a supersymmetric particle, giving a physics-proof of the Morse inequalities and inspiring Floer homology. He gave a path-integral proof of the Atiyah–Singer index theorem via supersymmetric localization, reinterpreted Donaldson's four-manifold invariants as correlation functions of a topological Yang–Mills theory, and showed that Chern–Simons theory on a three-manifold produces link invariants — including the Jones polynomial — as expectation values of Wilson loops. These insights created topological quantum field theory as a mathematical subject and remain the paradigm of physics–mathematics interaction.
Breakthrough Prize in Mathematics 2012Inaugural Fundamental Physics Prize for contributions to string theory and quantum field theory.
Kyoto Prize in Basic Sciences 2014Kyoto Prize in Basic Sciences for outstanding contributions to mathematical science through the exploration of superstring theory.

Contributions, linked to the library