Sir Michael Atiyah

Sir Michael Atiyah
Name	Michael Francis Atiyah
Honorifics	Sir, OM, FRS
Birth date	22 April 1929
Birth place	London, England
Death date	11 January 2019
Death place	Edinburgh, Scotland
Fields	Mathematics
Alma mater	Trinity College, Cambridge, Magdalen College, Oxford
Known for	Atiyah–Singer index theorem, K-theory, gauge theory, topological quantum field theory
Awards	Fields Medal, Abel Prize, Copley Medal

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Sir Michael Atiyah Sir Michael Francis Atiyah was a British mathematician whose work established deep links between algebraic topology, differential geometry, and mathematical physics. He made foundational contributions through the development of K-theory and the proof of the Atiyah–Singer index theorem with Isadore Singer, influencing research in quantum field theory, string theory, and representation theory. Atiyah served in leadership roles at institutions such as the University of Oxford and the University of Cambridge, and he received many of the highest honours in mathematics.

Early life and education

Atiyah was born in Paddington and raised in a family with links to Sri Lanka and England. He attended Bishop's Stortford College before reading mathematics at Magdalen College, Oxford and then completing doctoral studies at Trinity College, Cambridge under supervision associated with William V. D. Hodge and influence from Harold Davenport and G. H. Hardy's legacy at Cambridge. His early academic formation intersected with the postwar British mathematical milieu that included figures such as John von Neumann's influence on operator theory and contemporaries like Roger Penrose and Alan Turing in nearby faculties.

Atiyah's research forged bridges between topology, analysis, and geometry and engaged with concepts from theory of characteristic classes, index theory, and vector bundles. In collaboration with Isadore Singer, he proved the Atiyah–Singer index theorem, connecting the analytical index of elliptic operators with topological invariants derived from K-theory and Chern classes. He introduced and developed topological K-theory alongside Friedrich Hirzebruch, producing tools employed across algebraic geometry, symplectic geometry, and homotopy theory. Atiyah's work on the Bott periodicity theorem and on the Atiyah–Hirzebruch spectral sequence impacted computations in cobordism and stable homotopy groups.

Atiyah applied these structural ideas to problems in mathematical physics, collaborating with figures such as Edward Witten, Michael Berry, and Simon Donaldson to relate index-theoretic techniques to Yang–Mills theory, instantons, and monopoles. His investigations of equivariant cohomology and the formulation of the Atiyah–Bott fixed-point theorem (with Raoul Bott) influenced studies in moduli spaces of holomorphic bundles and intersected with developments in mirror symmetry and topological quantum field theory associated with Graeme Segal and Maxim Kontsevich. Later work considered twistor theory in dialogue with Roger Penrose's program and explored the mathematical structure underlying supersymmetry and string theory.

Atiyah received many prestigious awards: the Fields Medal (1966), the Abel Prize (2004), and the Copley Medal (2008). He was knighted as part of the Order of the British Empire and appointed to the Order of Merit. He was elected a Fellow of the Royal Society and served as President of the Royal Society during a period marked by interactions with the Wellcome Trust and the Royal Institution. Other honours included the Sylvester Medal, the Royal Medal, and honorary degrees from institutions such as Harvard University, University of Paris (Sorbonne), and University of Cambridge affiliates, and memberships in academies including the National Academy of Sciences and the Academia Europaea.

Atiyah held professorial chairs at University of Oxford (Savilian Chair), University of Cambridge (Lowndean Professor of Astronomy and Geometry), and was a Fellow of Trinity College, Cambridge and Magdalen College, Oxford during his career. He served as Master of Trinity College, Cambridge and as Director of the Isaac Newton Institute for Mathematical Sciences, fostering links with institutes such as the Institute for Advanced Study and the Mathematical Sciences Research Institute (MSRI). Atiyah supervised and influenced many students and collaborators, including Michael Hopkins, Simon Donaldson, Raoul Bott (collaborator), Graeme Segal (colleague), and Isadore Singer (collaborator), shaping generations of mathematicians working on gauge theory, index theory, and topology.

Atiyah engaged publicly through lectures at venues such as the Royal Institution, keynote addresses at the International Congress of Mathematicians, and participation in advisory roles for bodies like the Royal Society and the European Research Council. He took part in interdisciplinary conferences with physicists from CERN and mathematicians from the Fields Institute and contributed to debates on research funding and the role of mathematics in society alongside figures from the Wellcome Trust and Nesta. In later years he proposed conjectures that attracted attention from communities around number theory, prime numbers, and Riemann hypothesis discussions, leading to publicized exchanges with researchers at institutions including Princeton University and University of Cambridge.

Atiyah's personal life intersected with academic circles in Cambridge and Oxford; he had family connections to Sri Lanka and maintained friendships with mathematicians such as Raoul Bott, Michael Freedman, and Freeman Dyson. He died in Edinburgh in 2019. Atiyah's legacy endures through the Atiyah–Singer index theorem, the body of work in K-theory, and through the many students and institutions shaped by his leadership; his ideas continue to influence research at centers such as Princeton University, MIT, Harvard University, University of California, Berkeley, and École Normale Supérieure.

Category:British mathematicians Category:Recipients of the Abel Prize