Pembroke College obituary of Michael Atiyah

The following is from Pembroke College, Cambridge Society, Annual Gazette 93 (September 2019).

Michael Francis Atiyah

22 April 1929 - 11 January 2019

Michael Atiyah was one of the greatest British mathematicians since Sir Isaac Newton, making fundamental contributions to our understanding of algebraic geometry and topology. He won the Fields Medal - the mathematical equivalent of a Nobel Prize in 1966, and shared the 2004 Abel Prize with Isadore Singer. He became Master of Trinity College, Cambridge in 1990, as well as President of the Royal Society. He was knighted in 1983, and made a member of the Order of Merit in 1992.

This stunning career began in Lebanon, where Michael was born. In 1940, war had broken out between Vichy France and Britain in Lebanon and Michael's parents sent him to boarding school at Victoria College in Cairo. He developed an interest in chemistry there but decided that 'making sulphuric acid and all that stuff' was not for him, and instead conceived a passion for mathematics that would last the rest of his life. At the age of 16, in 1947, he was sent to Manchester Grammar School with a view to going to Cambridge to study mathematics. He took the entrance exam for Trinity College - along with John Frank Adams, a future and formidable name in mathematics, and John Polkinghorne, who would become a physicist and future Templeton Prize winner for his explorations of the relationships between religion and science - and won a major award to come to Trinity. (Legend has it that the entrance exam contained a major omission which made it impossible for the students taking the exam to prove the theorem they were being asked to prove. However, the first two answer papers answered the question perfectly, as did a third further on down the pile: the three perfect answers belonged to Adams, Atiyah and Polkinghorne.) But first came National Service: Michael joined the Royal Electrical and Mechanical Engineers, serving as a clerk.

The Army was persuaded by Michael's Cambridge Tutor to release him early from National Service and came to Cambridge in 1949. In his second year at Cambridge, he developed the interest in geometry - thinking about mathematics visually while expressing it in abstract symbols - on which he founded his mathematical career. After graduating in 1952, he went on to do a PhD under the supervision of Sir William Hodge. He was then, in 1958, elected a Fellow of Pembroke College where he would stay three years until moving on to a Professorial Fellowship at St Catherine's College Oxford, then becoming Savilian Professor of Geometry at New College, Oxford in 1963. Six years later, America came calling and Michael became Professor of Mathematics at the Institute of Advanced Study, Princeton. He would stay at Princeton for three years before returning to, and settling down in, Oxford, but those three years would be crucial to Michael's development. It was there that he met the men with whom he would collaborate on his key contributions to mathematics: Raoul Bott, Isadore Singer, and Friedrich Hirzebruch.

With Raoul Bott, Michael developed the Atiyah-Bott fixed point theorem. With Isadore Singer, Michael would develop the index theorem, described by many mathematicians as the 'theorem of the century' and by Michael himself as 'a bit of black magic' which revealed a highly significant link between a topological index and the solutions of a differential equation that can, in certain circumstances, prove that a solution to a differential equation must exist, with applications in many different areas of physics. With Friedrich Hirzebruch, Michael developed K-theory, studying the vector bundles associated with topological spaces to reveal when such spaces can or cannot be deformed into each other. Michael's citation for the 1966 Fields Medal mentioned all three of these areas of work as the basis for his award. Michael returned to Oxford in 1972 as a Royal Society Research Professor, which afforded him more freedom to think and write, while mentoring a new generation of mathematicians. Under the influence of Princeton's Edward Witten and Cambridge's Roger Penrose, Michael's attention turned more and more to the applications of his mathematical work to physics, and in particular, quantum field theory. This led Michael to his fourth great achievement in mathematics - his work on gauge theory, formalising certain symmetries of quantum fields and particles. Such symmetries are hugely important in quantum mechanics, and Atiyah was able to make major contributions to the mathematical side of quantum mechanics, using index theory to study instantons (particles that come in and go out of existence instantaneously) and magnetic monopoles. The collaborations that led to these great achievements were typical of Michael: dialogue was essential to his way of developing ideas, and his students would sometimes find themselves named as co-authors on Michael's papers on the basis that 'Well, I had all the ideas while talking to you.'

In 1990, Michael returned to Cambridge as Master of Trinity College, also becoming Director of the Isaac Newton Institute for Mathematical Sciences. He would retain both positions until retirement in 1997. Michael and his wife Lily (whom he married in 1955) then moved back to Lily's home town, Edinburgh. However, Michael remained active as a researcher and speaker, and served as President of the Royal Society of Edinburgh from 2005-2008. Lily died in 2018 (as did Michael's brother Patrick, the distinguished legal thinker). Michael is survived by their sons, David and Robin. Another son, John, died in a climbing accident in 2002.

JOC/EFR January 2020