Michael Atiyah
1929–2019, London, England, Edinburgh, Scotland
AlgebraGeometryTopologyFields Medal 1966Abel Prize 2004
British mathematician who created K-theory and the Atiyah–Singer index theorem, linking topology, geometry, and analysis.
Michael Atiyah reshaped twentieth-century geometry through K-theory, index theory, and the interaction between topology and differential equations. The Atiyah–Singer index theorem explains how an analytic index equals a topological index, with consequences across geometry, analysis, and mathematical physics. He received the Fields Medal in 1966 and the Abel Prize in 2004.
Workplaces: University of Oxford, University of Cambridge
United Kingdom
Award-winning work
Fields Medal 1966The 1966 Fields Medal honored Atiyah's work at the interface of geometry, topology and analysis. With Hirzebruch he built topological K-theory into a powerful generalized cohomology theory, and with Singer he proved the index theorem, which expresses the analytic index of an elliptic operator on a compact manifold entirely in terms of topological invariants. The Atiyah–Singer index theorem unified and vastly generalized results such as the Riemann–Roch theorem and Hirzebruch's signature theorem. It created a permanent bridge between analysis and topology, with consequences reaching from gauge theory to mathematical physics.