Two young British academics have won the equivalent of the Nobel prize in mathematics.
Richard Borcherds and Tim Gowers, both of whom are at the University of Cambridge, were awarded the Fields medal at the International Congress of Mathematicians in Berlin this week.
"Two Fields medals at once is a tremendous tribute to the vitality of British mathematics," said Sir Michael Atiyah, a former president of the Royal Society who was awarded the Fields medal in 1966.
"This continues the strong British track record at the highest international level," he said.
The Fields medals, which are awarded every four years, aim not only to recognise work already done but to encourage more achievement. They are by tradition awarded only to mathematicians under the age of 40.
Professor Borcherds won the prize "for initiating a new field of study in algebra, called vertex algebras". In the everyday world of three-dimensional space, a cube can be rotated in 24 ways and still fit into the same space. Professor Borcherds went a few steps further to study "the Monster", a symmetrical snowflake that lives in 196,883-dimensional space.
His work is closely connected to "string theory", an attempt by theoretical physicists to gain a unified understanding of all of the basic forces and fundamental particles of nature.
For Professor Gowers, 196,883-dimensional space is not roomy enough. He won the Fields medal for his work in Banach spaces, the generalisation of finite-dimensional space to infinite dimensions. Professor Gowers solved several of the problems with Banach space that have existed since the Polish mathematician Stefan Banach introduced the concept in the 1920s.
The congress of mathematicians also presented the British mathematician Andrew Wiles with a special award for proving Fermat's last theorem. Professor Wiles, who is now at Princeton University in the United States, was ineligible for the Fields medal because he is more than 40 years old.