Professor Timothy Gowers was awarded the 1998 Fields Medal for his solutions of several problems related to Banach spaces, which are mathematical sets with members that are not numbers but complicated mathematical objects such as functions or operators. These objects can be manipulated in the spaces for different applications, including in quantum physics.

The International Mathematical Union (IMU), which confers the medal, noted in its citation that he had combined two mathematics fields, namely functional analysis and combinatorics, that appeared to have little in common. It continued: “A key question for mathematicians and physicists concerns the inner structure of Banach spaces, and what symmetry they show. Professor Gowers was able to construct a Banach space which has almost no symmetry.”

This has served as a suitable counter-example for many conjectures in functional analysis, and opened the way to the solution of one of the most famous problems in functional analysis, the ‘homogenous space problem’. Professor Gowers also delivered a new proof of a theorem of the mathematician Endre Szemerédi that gave, for the first time, reasonable quantitative bounds. “Such a feat requires extremely deep mathematical understanding,” the IMU said.

Professor Gowers has also written a book, titled Mathematics: A Very Short Introduction, and edited another book, called The Princeton Companion to Mathematics, for which he won the 2011 Euler Book Prize. More recently, he started two free mathematics journals, Discrete Analysis and Advances in Combinatorics.

The Polymath Project, in which mathematicians collaborate to solve important and difficult mathematical problems, was his brainchild. This inspired the CrowdMath Project, which gives high school and college students the opportunity to work together on a large mathematical research project with top-tier mentors.

For his work, Professor Gowers has also received the European Mathematical Society Prize, Sylvester Medal and De Morgan Medal, and was knighted in Britain in 2012. He is also a fellow of the Royal Society. He is currently Professor of Combinatorics at the Collège de France.

Timothy Gowers

Fields Medal

1998