Affiliation when awarded Breakthrough Prize: Stony Brook University and Imperial College London.
Citation: For the new revolutionary invariants of 4-dimensional manifolds and for the study of the relation between stability in algebraic geometry and in global differential geometry, both for bundles and for Fano varieties.
Acceptance Remarks: It has been my great good fortune that my career has spanned a period of exceptionally exciting developments in my field. Ideas and techniques from different areas—topology, physics, differential equations, geometry—have become interwoven in ways that no one would have predicted half a century ago. It is a privilege to have been able to witness this and take some part in it. Mathematics has a long timescale. One of the pleasantest things is, looking back in time, to contemplate how the developments we see in our lifetimes fit into the longer term. And, looking forward in time, we have confidence that the problems that seem to us intractable will yield to future advances, invisible to us now. I owe enormous thanks to my advisors, Michael Atiyah, and Nigel Hitchin, and to all the mathematicians who made Oxford in the 1980s such a special place. What I learnt then has underpinned my whole career. Looking forward, rather than back, it has been my great good fortune to have been able to watch the development of many extraordinary research students. I would like to thank my wife Nora, my parents and all my family for their support.