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Simon Kirwan Donaldson, born in Cambridge in 1957, is an English mathematician famous for his work on the topology of smooth (differentiable) four-dimensional manifolds.

Donaldson gained a BA in mathematics from Pembroke College, Cambridge in 1979, and in 1980 began postgraduate work at Worcester College, Oxford, first under Nigel Hitchin and later under Atiyah's supervision. Still a graduate student, Donaldson soon proved in 1982 a result that would establish his fame. He published the result in a paper Self-dual connections and the topology of smooth 4-manifolds which appeared in 1983. In the words of Atiyah, the paper "stunned the mathematical world".

Whereas Michael Freedman classified topological four-manifolds, Donaldson's work focused on four-manifolds admitting a differentiable structure, using instantons, a particular solution to the equations of Yang-Mills gauge theory which has its origin in quantum field theory. One of Donaldson's first results gave severe restrictions on the intersection form of a smooth four-manifold. As a consequence, a large class of the topological four-manifolds do not admit any smooth structure at all. Donaldson also derived polynomial invariants from gauge theory. These were new topological invariants sensitive to the underlying smooth structure of the four-manifold. They made it possible to deduce the existence of "exotic" smooth structures - certain topological four-manifolds could carry an infinite family of different smooth structures.

After gaining his doctorate from Oxford University in 1983, Donaldson was appointed a Junior Research Fellow at All Souls College, Oxford, he spent the academic year 1983–84 at the Institute for Advanced Study at Princeton, and returned to Oxford as Wallis Professor of Mathematics in 1985. In 1999, he moved to Imperial College London.

Donaldson received the Junior Whitehead Prize from the London Mathematical Society in 1985 and in the following year he was elected a Fellow of the Royal Society and, also in 1986, he received a Fields Medal. Ironically he was turned down for fellowship of the Institute of Mathematics and its Applications on the grounds that he applied too soon after his doctorate. He was awarded the 1994 Crafoord Prize.

Donaldson now lives with his wife and children in England and he still works in Imperial College

• O'Connor, John J., and Edmund F. Robertson. "Simon Donaldson". MacTutor History of Mathematics archive.
• Simon Donaldson at the Mathematics Genealogy Project
• Home page at Imperial College

• Donaldson, S. K. An application of gauge theory to four-dimensional topology. J. Differential Geom., 18, (1983), 279–315.
• Donaldson, S. K. Self-dual connections and the topology of smooth 4-manifolds. Bull. Amer. Math. Soc.. 8, (1983), 81–83.
• Donaldson, S. K. and Kronheimer, P. B. The geometry of four-manifolds. Oxford Mathematical Monographs, Oxford University Press, New York, (1990) ISBN 0-19-853553-8.