# 2008 Frederic Esser Nemmers Mathematics Prize Recipient

###### Congratulations to the 2008 Nemmers Mathematics Prize winner

**Simon Donaldson, ***Imperial College, London*

*Imperial College, London*

### 2008 Nemmers Prize in Mathematics Recipient

#### Simon Donaldson

##### For groundbreaking work in four-dimensional topology, symplectic geometry and gauge theory, and for his remarkable use of ideas from physics to advance pure mathematics

Simon Donaldson is the Royal Society Research Professor at Imperial College, London. The selection committee for the mathematics prize recognized Donaldson for his "groundbreaking work in four-dimensional topology, symplectic geometry and gauge theory, and for his remarkable use of ideas from physics to advance pure mathematics."

"Donaldson's breakthrough work developed new techniques in the geometry of four-manifolds and the study of their smooth structures," said John Franks, professor and chair of mathematics at Northwestern. "His methods," Franks continued, "have been described as extremely subtle, using difficult nonlinear partial differential equations. Using instantons, solutions to the equations of Yang-Mills gauge theory, he gained important insight into the structure of closed four-manifolds. Gauge theory techniques also enabled him to show the existence of four-manifolds with no smooth structure and others with infinitely many. His work has provided the seminal steps for the work of others in study of four-manifolds."

More recently, Donaldson has made fundamental contributions to the understanding of symplectic manifolds, the phase-spaces of classical mechanics, and he shows that a surprisingly large part of the theory of algebraic geometry extends to them.

His two books and more than 60 published papers are widely recognized for their originality as well as their elegance and clarity.

Donaldson received his B.A at Cambridge University and his D.Phil. from Oxford University. In 1986, only three years after completion of his doctorate, he was elected a fellow of the Royal Society. That same year he received the Fields Medal, widely recognized as the most prestigious honor for a mathematician under the age of 40. He was awarded the Royal Medal of the Royal Society in 1992, the Crafoord Prize in 1994, and the King Faisal Prize in 2006. In 2000 he was elected a foreign associate of the National Academy of Sciences.