Sir Michael Atiyah OM. 22 April 1929–11 January 2019

Michael Atiyah was the dominant figure in UK mathematics in the latter half of the twentieth century. He made outstanding contributions to geometry, topology, global analysis and, particularly over the last 30 years, to theoretical physics. Not only was he held in high esteem at a worldwide level, winning a Fields Medal in 1966, the Abel Prize in 2004 and innumerable other international awards, but his irrepressible energy and broad interests led him to take on many national roles too, including the presidency of the Royal Society, the mastership of Trinity College, Cambridge, and the founding directorship of the Isaac Newton Institute for Mathematical Sciences. His most notable mathematical 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 that he pursued energetically until the end of his life. It led him not only to mathematical results on the Yang--Mills equations that the physicists were seeking, but also to encouraging the importation of concepts from quantum field theory into pure mathematics.