for their many brilliant contributions to geometry in 3 and 4 dimensions.
Geometry and Physics have been closely related from the earliest times and the differential calculus of Newton and Leibniz became the common mathematical tool that connected them. The geometry of 2-dimensional surfaces was fully explored by these techniques in the 19th century. It was closely related to algebraic curves and also to the flow of fluids.
Extending our understanding to 3-dimensional space and 4-dimensional space-time has been fundamental for both geometers and physicists in the 20th and 21st centuries. While the calculus is still employed, the problems are now much deeper and totally new phenomena appear.
Over the past 30 years, geometry in 3 and 4 dimensions has been totally revolutionized by new ideas emerging from theoretical physics. Old problems have been solved but, more importantly, new vistas have been opened up which will keep mathematicians busy for decades to come.
While the initial spark has come from physics (where it was extensively pursued by Edward Witten), the detailed mathematical development has required the full armoury of non-linear analysis, where deep technical arguments have to be carefully guided by geometric insight and topological considerations.
Simon K Donaldson, born 1957 in Cambridge, UK, is currently the Royal Society Research Professor of Pure Mathematics and President of the Institute for Mathematical Sciences at Imperial College, London, UK. He received his BA from Pembroke College, Cambridge in 1979 and his PhD from Oxford University in 1983. In 1986 he was elected as Fellow of the Royal Society.
Clifford H Taubes, born 1954 in Rochester, New York, USA, is currently the William Petschek Professor of Mathematics at Harvard University. He was an undergraduate at Cornell University and received his PhD in Physics from Harvard University in 1980. He is a member of the US National Academy of Sciences.
