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’.