**Michael Atiyah** worked in Topology and Geometry and was best known for his work on K-theory and the Atiyah-Singer Index Theorem. He was awarded a Fields Medal in 1966. He retired from the mastership of Trinity College Cambridge to live in Scotland.

- Although he was born in London, Michael grew up in Khartoum.
- Michael's primary school education was at the Diocesan school in Khartoum which he entered in 1934 at the age of five.
- Michael was sent to Victoria College in Cairo.
- This was a boarding school modelled on the English boarding school system and it was a school that Edward Atiyah had attended.
- After the war ended in 1945, Edward Atiyah returned to live permanently in England.
- Michael Atiyah attended Manchester Grammar School, one of the best schools for mathematics in the country.
- Many of his fellow students had decided to postpone their National Service, so Atiyah was one of the older of the students in his year.
- After graduating with his BA in 1952, Atiyah continued to undertake research at Trinity College, Cambridge obtaining his doctorate in 1955 with his thesis Some Applications of Topological Methods in Algebraic Geometry.
- Atiyah published two joint papers with his thesis advisor William Hodge, Formes de seconde espèce sur une variété algébrique Ⓣ(Forms of the second kind on an algebraic variety) (1954) and Integrals of the second kind on an algebraic variety (1955).
- Atiyah was awarded a Commonwealth Fellow to study at the Institute for Advanced Study in Princeton during session 1955-56.
- This was an important year for Atiyah who met, among others, Jean-Pierre Serre, Friedrich Hirzebruch, Kunihiko Kodaira, Donald Spencer, Raoul Bott and Isadore Singer.
- Atiyah was soon to fill the highly prestigious Savilian Chair of Geometry at Oxford from 1963, holding this chair until 1969 when he was appointed professor of mathematics at the Institute for Advanced Study in Princeton.
- After three years in Princeton, Atiyah returned to England, becoming a Royal Society Research Professor at Oxford.
- Oxford was to remain Atiyah's base until 1990 when he became Master of Trinity College, Cambridge and Director of the newly opened Isaac Newton Institute for Mathematical Sciences in Cambridge.
- Atiyah showed how the study of vector bundles on spaces could be regarded as the study of cohomology theory, called K-theory.
- For these early achievements Atiyah was awarded a Fields Medal at the International Congress at Moscow in 1966.
- The K-theory and the index theorem are studied in Atiyah's book K-theory (1967, reprinted 1989) and his joint work with G B Segal, The Index of Elliptic Operators I-V, in the Annals of Mathematics, volumes 88 and 93 (1968, 1971).
- Atiyah also described his work on the index theorem in The index of elliptic operators given as an American Mathematical Society Colloquium Lecture in 1973.
- The ideas which led to Atiyah being awarded a Fields Medal were later seen to be relevant to gauge theories of elementary particles.
- Atiyah initiated much of the early work in this field and his student Simon Donaldson went on to make spectacular use of these ideas in 4-dimensional geometry.
- More recently Atiyah has been influential in stressing the role of topology in quantum field theory and in bringing the work of theoretical physicists, notably E Witten, to the attention of the mathematical community.
- The theories of superspace and supergravity and the string theory of fundamental particles, which involves the theory of Riemann surfaces in novel and unexpected ways, were all areas of theoretical physics which developed using the ideas which Atiyah was introducing.
- Atiyah and John Tate described the Clay Mathematics Institute Millennium Prize Problems in a lecture in Paris on 24 May 2000.
- Atiyah's lecture covered the Poincaré conjecture, the Hodge conjecture, quantum Yang-Mills theory and the Navier-Stokes equation.
- Six volumes of Atiyah's Collected Works have been published.
- Another important aspect of Atiyah's contribution is the remarkable collection of doctoral students he supervised.
- Atiyah has received many honours during his career, in addition to the Fields Medal referred to above, and although we cannot list them all we will give a fairly full account.
- Atiyah was the American Mathematical Society Colloquium Lecturer in 1973.
- Atiyah was knighted in 1983 and made a member of the Order of Merit in 1992.
- Lily Atiyah died on 13 March 2018 at the age of 90.
- Atiyah himself died on 11th January 2019.
- Both Michael and Lily Atiyah are buried in Binning Memorial Wood, Tyninghame, Scotland.

Born 22 April 1929, London, England. Died 11 January 2019, Edinburgh, Scotland.

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Prize Abel, Prize Fields Medal, Origin England, Topology

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive