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Fellows Directory

Michael Atiyah

Sir Michael Atiyah OM HonFREng FRS


Elected: 1962


Sir Michael Atiyah is a mathematician who has made outstanding contributions to geometry and topology. He is best known for his co-development of topological K-theory and the Atiyah–Singer index theorem. As well as advancing pure mathematics, Sir Michael’s work has been fruitfully applied and extended to both pillars of theoretical physics — quantum theory and general relativity.

His research involves deep insights relating to mathematical concepts known as vector bundles. The well-known Möbius strip and the Klein bottle can both be mathematically described in terms of vector bundles.

Sir Michael has received very many awards, including the 1966 Fields Medal, the 1968 Royal Medal of the Royal Society, the 1988 Copley Medal of the Royal Society, and the 2004 Abel Prize of the Norwegian Academy of Arts and Sciences. He was knighted in 1983, appointed to the Order of Merit in 1992 and was made a Grand Officer of the Légion d’honneur in 2011.

Professional positions

Honorary Professor, University of Edinburgh, School of Mathematics, University of Edinburgh
Fellow, Trinity College, University of Cambridge

Interests and expertise

Subject groups


Algebraic geometry, Differential geometry, Particle physics, Systems analysis, Topology


  • Abel Prize

    For discovery and proof of the index theorem, bringing together topology, geometry and analysis, and their outstanding role in building new bridges between mathematics and theoretical physics.

  • Bakerian Medal and Lecture

    On 'Global geometry'.

  • Copley Medal

    In recognition of his fundamental contributions to a wide range of topics in geometry, topology, analysis and theoretical physics.

  • Fields Medal

    Did joint work with Hirzebruch in K-theory; proved jointly with Singer the index theorem of elliptic operators on complex manifolds; worked in collaboration with Bott to prove a fixed point theorem related to the "Lefschetz formula.

  • Humphry Davy and Claude Bernard Lectures

    On 'Les developpements nouveaux dans la geometre et la physique theorique'.

  • King Faisal International Prize

    In the field of mathematics.

  • Royal Medals

    In recognition of his distinguished contributions to algebraic geometry and to the study of differential equations by the methods of algebraic topology.