Simon Kirwan Donaldson, born in Cambridge in 1957, is a mathematician famous for his work on exotic four-dimensional spaces in differential geometry using instantons, and the discovery of new differential invariants.

Donaldson gained a BA in mathematics from Pembroke College, Oxford in 1979, and in 1980 began postgraduate work at Worcester College, Oxford, first under Nigel Hitchen and later under Atiyah's supervision. In 1982, as a second-year graduate student, Donaldson proved a result that stunned the mathematical world. He published the result in a paper Self-dual connections and the topology of smooth 4-manifolds which appeared in 1983.

Donaldson's result, together with work of Michael Freedman implied that there are "exotic" 4-spaces, i.e. 4-dimensional differentiable manifolds which are topologically but not differentiably equivalent to the standard Euclidean 4-space R⁴. In other words, 4-space has more than one differential structure. The result is remarkable as it is only for n = 4 that such exotic n-spaces exist.

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 it he applied too soon after his doctorate! He was awarded the 1994 Crafoord Prize.

External links

• home page at Imperial College London

References

• 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 0198535538.