Major international award for world’s leading group theorist

John Griggs Thompson, Emeritus Rouse-Ball Professor of Mathematics, was awarded the Abel Prize by the Norwegian Academy of Science and Letters, in recognition of his body of work. The prize comes with an award of 6 million Kroner (about £590,000).

Professor Thompson’s research has been fundamental in shaping group theory, the field which involves understanding the relation the different symmetries (such as rotations and reflections) which an object may have.

A group is essentially a set of abstract symmetries, which can be composed and reversed. Apart from their applications in modelling the symmetries of shapes, groups have many important uses in physics, chemistry, cryptography, and other branches of mathematics.

In 1963, Professor Thompson published a paper with the late Walter Feit, which proved that objects and structures with an odd number of symmetries could be ‘built’ out of the properties of symmetrical shapes with a prime number of sides. For example, a 15-sided shape could be ‘built’ in this way from a triangle and a pentagon.

Their proof was perhaps the longest and most complicated completed at the time, taking up a full volume of the Pacific Journal of Mathematics and running to 255 pages.

Later work of Professor Thompson was instrumental in one of the greatest mathematical endeavours ever, an international project known as the Classification of Finite Simple Groups. The project, which took over 30 years to complete, assembled a complete list of the basic ‘building-block’ groups.

His work has also been used to predict the existence of the sporadic groups, certain finite simple groups which do not follow the systematic pattern of the other ‘building-block’ groups, one of which is named after him.

The search for these groups culminated in the discovery of the group known as ‘the Monster’, the 26th and final sporadic group, which is the group of symmetries of a 196,883-dimensional object, and contains more symmetries than there are atoms in the sun.

The prize is the latest in a long list of honours for Professor Thompson, who has also been recipient of the Royal Society’s Sylvester Medal, the United States National Medal of Science and the Fields Medal, widely viewed as the most prestigious award a mathematician can receive.

Professor Thompson remains an active member of the Algebra group at the University’s Department of Pure Mathematics and Mathematical Statistics, having been Rouse-Ball Professor for 23 years, and is currently also a Graduate Research Professor at the University of Florida.