Sir Michael Francis Atiyah (; 22 April 1929 – 11 January 2019) was a British-Lebanese mathematician specialising in geometry. His contributions include the Atiyah–Singer index theorem and co-founding topological K-theory. He was awarded the Fields Medal in 1966 and the Abel Prize in 2004.
Early life and education
Atiyah was born on 22 April 1929 in Hampstead, London, England, the son of Jean (née Levens) and Edward Atiyah. His mother was Scottish and his father was a Lebanese Orthodox Christian. He had two brothers, Patrick (deceased) and Joe, and a sister, Selma (deceased). Atiyah went to primary school at the Diocesan school in Khartoum, Sudan (1934–1941), and to secondary school at Victoria College in Cairo and Alexandria (1941–1945); the school was also attended by European nobility displaced by the Second World War and some future leaders of Arab nations. He returned to England and Manchester Grammar School for his HSC studies (1945–1947) and did his national service with the Royal Electrical and Mechanical Engineers (1947–1949). His undergraduate and postgraduate studies took place at Trinity College, Cambridge (1949–1955). He was a doctoral student of William V. D. Hodge and was awarded a doctorate in 1955 for a thesis entitled Some Applications of Topological Methods in Algebraic Geometry. During his time at Cambridge, he was president of The Archimedeans.
Career and research
Atiyah spent the academic year 1955–1956 at the Institute for Advanced Study, Princeton, then returned to Cambridge University, where he was a research fellow and assistant lecturer (1957–1958), then a university lecturer and tutorial fellow at Pembroke College, Cambridge (1958–1961). In 1961, he moved to the University of Oxford, where he was a reader and professorial fellow at St Catherine's College (1961–1963). He became Savilian Professor of Geometry and a professorial fellow of New College, Oxford, from 1963 to 1969. He took up a three-year professorship at the Institute for Advanced Study in Princeton after which he returned to Oxford as a Royal Society Research Professor and professorial fellow of St Catherine's College. He was president of the London Mathematical Society from 1974 to 1976.
Atiyah was president of the Pugwash Conferences on Science and World Affairs from 1997 to 2002. He also contributed to the foundation of the InterAcademy Panel on International Issues, the Association of European Academies (ALLEA), and the European Mathematical Society (EMS). Within the United Kingdom, he was involved in the creation of the Isaac Newton Institute for Mathematical Sciences in Cambridge and was its first director (1990–1996). He was President of the Royal Society (1990–1995), Master of Trinity College, Cambridge (1990–1997), Chancellor of the University of Leicester (1995–2005), and president of the Royal Society of Edinburgh (2005–2008). From 1997 until his death in 2019 he was an honorary professor in the University of Edinburgh. He was a Trustee of the James Clerk Maxwell Foundation. Atiyah's mathematical collaborators included Raoul Bott, Friedrich Hirzebruch and Isadore Singer, and his students included Graeme Segal, Nigel Hitchin, Simon Donaldson, and Edward Witten. Together with Hirzebruch, he laid the foundations for topological K-theory, an important tool in algebraic topology, which, informally speaking, describes ways in which spaces can be twisted. His best known result, the Atiyah–Singer index theorem, was proved with Singer in 1963 and is used in counting the number of independent solutions to differential equations. Some of his more recent work was inspired by theoretical physics, in particular instantons and monopoles, which are responsible for some corrections in quantum field theory. He was awarded the Fields Medal in 1966 and the Abel Prize in 2004.
Collaborations
Atiyah collaborated with many mathematicians. His three main collaborations were with Raoul Bott on the Atiyah–Bott fixed-point theorem and many other topics, with Isadore M. Singer on the Atiyah–Singer index theorem, and with Friedrich Hirzebruch on topological K-theory, all of whom he met at the Institute for Advanced Study in Princeton in 1955. His other collaborators included; J. Frank Adams (Hopf invariant problem), Jürgen Berndt (projective planes), Roger Bielawski (Berry–Robbins problem), Howard Donnelly (L-functions), Vladimir G. Drinfeld (instantons), Johan L. Dupont (singularities of vector fields), Lars Gårding (hyperbolic differential equations), Nigel J. Hitchin (monopoles), William V. D. Hodge (Integrals of the second kind), Michael Hopkins (K-theory), Lisa Jeffrey (topological Lagrangians), John D. S. Jones (Yang–Mills theory), Juan Maldacena (M-theory), Yuri I. Manin (instantons), Nick S. Manton (Skyrmions), Vijay K. Patodi (spectral asymmetry), A. N. Pressley (convexity), Elmer Rees (vector bundles), Wilfried Schmid (discrete series representations), Graeme Segal (equivariant K-theory), Alexander Shapiro (Clifford algebras), L. Smith (homotopy groups of spheres), Paul Sutcliffe (polyhedra), David O. Tall (lambda rings), John A. Todd (Stiefel manifolds), Cumrun Vafa (M-theory), Richard S. Ward (instantons) and Edward Witten (M-theory, topological quantum field theories). His later research on gauge field theories, particularly Yang–Mills theory, stimulated important interactions between geometry and physics, most notably in the work of Edward Witten.
Atiyah's students included Peter Braam 1987, Simon Donaldson 1983, K. David Elworthy 1967, Howard Fegan 1977, Eric Grunwald 1977, Nigel Hitchin 1972, Lisa Jeffrey 1991, Frances Kirwan 1984, Peter Kronheimer 1986, Ruth Lawrence 1989, George Lusztig 1971, Jack Morava 1968, Michael Murray 1983, Peter Newstead 1966, Ian R. Porteous 1961, John Roe 1985, Brian Sanderson 1963, Rolph Schwarzenberger 1960, Graeme Segal 1967, David Tall 1966, and Graham White 1982. Other contemporary mathematicians who influenced Atiyah include Roger Penrose, Lars Hörmander, Alain Connes and Jean-Michel Bismut. Atiyah said that the mathematician he most admired was Hermann Weyl, and that his favourite mathematicians from before the 20th century were Bernhard Riemann and William Rowan Hamilton. The seven volumes of Atiyah's collected papers include most of his work, except for his commutative algebra textbook; the first five volumes are divided thematically and the sixth and seventh arranged by date.
Algebraic geometry (1952–1958)
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