Whitehead Prize from the London Mathematical Society. In 1994, he was awarded the Crafoord Prize in Mathematics. In February 2006, Donaldson was awarded the King Faisal International Prize for science for his work in pure mathematical theories linked to physics, which have helped in forming an understanding of the laws of matter at a subnuclear level. In April 2008, he was awarded the Nemmers Prize in Mathematics, a mathematics prize awarded by Northwestern University. In 2009, he was awarded the Shaw Prize in Mathematics (jointly with Clifford Taubes) for their contributions to geometry in 3 and 4 dimensions. In 2014, he was awarded the Breakthrough Prize in Mathematics "for the new revolutionary invariants of 4-dimensional manifolds and for the study of the relation between stability in algebraic geometry and in global differential geometry, both for bundles and for Fano varieties." In January 2019, he was awarded the Oswald Veblen Prize in Geometry (jointly with Xiuxiong Chen and Song Sun). In 2020 he received the Wolf Prize in Mathematics (jointly with Yakov Eliashberg). In 1986, he was elected a Fellow of the Royal Society and received a Fields Medal at the International Congress of Mathematicians (ICM) in Berkeley. In 2010, Donaldson was elected a foreign member of the Royal Swedish Academy of Sciences. He was knighted in the 2012 New Year Honours for services to mathematics. In 2012, he became a fellow of the American Mathematical Society. In March 2014, he was awarded the degree "Docteur Honoris Causa" by Université Joseph Fourier, Grenoble. In January 2017, he was awarded the degree "Doctor Honoris Causa" by the Universidad Complutense de Madrid, Spain. Research Donaldson's work is on the application of mathematical analysis (especially the analysis of elliptic partial differential equations) to problems in geometry. The problems mainly concern gauge theory, 4-manifolds, complex differential geometry and symplectic geometry. The following theorems have been mentioned: The diagonalizability theorem : If the intersection form of a smooth, closed, simply connected 4-manifold is positive- or negative-definite then it is diagonalizable over the integers. This result is sometimes called Donaldson's theorem. A smooth h-cobordism between simply connected 4-manifolds need not be trivial . This contrasts with the situation in higher dimensions. A stable holomorphic vector bundle over a non-singular projective algebraic variety admits a Hermitian–Einstein metric , proven using an inductive proof and the theory of determinant bundles and Quillen metrics. A non-singular, projective algebraic surface can