Sir Michael Atiyah: Obituaries

Sir Michael Ariyah: One of the greatest British mathematicians since Isaac Newton, by Ian Stewart; The Guardian, 15 January 2019.

Sir Michael Atiya (1929 – 2019), by Nigel Hitchin; IMU-Net 93: January 2019, A Bimonthly Email Newsletter from the International Mathematical Union.

Sir Michael Atiyah died in Edinburgh, aged 89, on January 11th 2019. He was one of the giants of mathematics whose work influenced an enormous range of subjects. His most notable achievement, with Isadore Singer, is the Index Theorem which occupied him for over 20 years, generating results in topology, geometry and number theory using the analysis of elliptic differential operators. Then, in mid-life, he learned that theoretical physicists also needed the theorem and this opened the door to an interaction between the two disciplines which he pursued energetically till the end of his life. It led him not only to mathematical results on the Yang-Mills equations that the physicists needed but also to encouraging the importation of concepts from quantum field theory into pure mathematics.

Born of a Lebanese father and a Scottish mother, his early years were spent in English schools in the Middle East. He then followed the natural course for a budding mathematician in that environment by going to Cambridge where he ended up writing his thesis under William Hodge and becoming a Fellow at Trinity College where he started to pursue his research. But, attending the ICM in Amsterdam in 1954, his eyes were opened to the exciting work that was going on in the outside world and the opportunity then arose to spend a year at the Institute for Advanced Study in Princeton where he met his future collaborators and close friends Raoul Bott, Fritz Hirzebruch and Singer. The benefits of international collaboration which he valued so highly were made concrete when in 1957 Hirzebruch established in Bonn the annual Arbeitstagung where Michael was always the first speaker. In those years he and Hirzebruch developed topological K-theory, which subsequently became the natural vehicle for the index theorem.

A visit by Singer to Oxford in 1962 (where Atiyah had recently moved) began the actual work on the Index Theorem, which ultimately led to a Fields Medal in 1966 and, with Singer, the Abel Prize in 2004. Another visit in 1977 brought mathematical questions concerning gauge theory. Using quite sophisticated algebraic geometry and the novel work of Roger Penrose this yielded a precise
answer to the physicists’ questions: the so-called ADHM construction of instantons. The fact that mathematicians and physicists had common ground in a completely new context made a huge impression on Michael and he was energetic in the following years in facilitating this cooperation.

With a naturally effervescent personality he possessed, in Singer’s words, “speed, depth, power and energy”. His strong voice could be heard across many a departmental common room explaining some crucial point. Collaborations were all-important, bouncing ideas around, two or three people in front of the blackboard, exploring ideas, erasing them, sudden insights. This also held for his students — he needed continuous feedback and challenges. He had a natural talent for lecturing: leaving the lecture theatre you always had the feeling you had understood things, though trying to reproduce them later was a different matter. Beauty in mathematics was a feature he took seriously. It was in evidence in so many of his ideas and proofs and in his later years he actually instigated a neurological experiment to detect its presence.

Sir Michael received numerous awards and honours. He worked for the mathematical community in many ways. In particular, he was instrumental in founding the Isaac Newton Institute (where he insisted that it should be for the Mathematical Sciences) and the European Mathematical Society. He was also President of the Royal Society of London where he found himself in a situation where he could voice long-held views about science in general. He contributed to the IMU itself in many ways, including two terms on the Executive Committee. He will be greatly missed by all.

Nigel Hitchin (Oxford, UK)

The Polar Star and the Life Endgame (elegy for a departed friend), by Matilde Marcolli.