Simon Donaldson conducts research in geometry and topology. As a research student he proved what is known as the diagonalizability theorem, going on to open up a whole new area in four-dimensional geometry. His work has helped physicists to better understand theories of space–time and how matter behaves at sub-nuclear levels.

Simon’s research is marked by deep insights developed from ideas found in theoretical physics, such as his use of instantons — rooted in the Yang–Mills equations of quantum field theory — when proving the diagonalizability theorem. His work continues to have implications across the interface with physics, particularly for supersymmetry and ‘theories of everything’.

Among Simon’s many awards are the Fields Medal (1986), the Crafoord Prize in Mathematics (1994), and the King Faisal International Prize (2006). He was knighted in 2012. In 2014, he was awarded a US$3 million Breakthrough Prize in Mathematics. The prize celebrates scientists and promotes science as an exciting career, and Simon now serves on the selection committee.