Jacques Tits of the Collège de France and the American John Griggs Thompson have been jointly awarded the 2008 Abel Prize, one of the most prestigious prizes in mathematics, ‘for their
profound achievements in algebra and in particular for shaping modern group theory’.
The NOK 6 million (?750,000) award is handed out annually by the Norwegian Academy of Science and Letters and recognises outstanding work in the field of mathematics. It is named after the
Norwegian mathematician Neils Henrik Abel, who is credited with laying the foundations of group theory in the early 19th century.
Professors Tits and Thompson both work in a field known as ‘group theory’, a complex subject which is normally only taught to maths students in their third year at university. In the late 18th
century, the Abel committee explains, it was realised that ‘the key to understanding even the simplest equations lies in the symmetries of their solutions’. This eventually led to the
development of the notion of a ‘group’ as a powerful way to capture the idea of symmetry.
Group theory can best be summed up as ‘the science of symmetry’, where mathematicians investigate the mirror and rotational images of an object and even combine symmetries to produce new
symmetries to create new symmetries. Mathematicians use these tools to solve complex equations, as well as to provide solutions to tricky problems like the Rubik’s cube!
Professor Tits’ contribution to group theory is a new and highly influential vision of groups as geometric objects. Borrowing terms from architecture, he created a system where purely algebraic
structures could be given geometrical descriptions, to make the solving of difficult algebraic questions more intuitive. This so-called ‘Tits-architecture’ has had a wide range of applications
in fields as diverse as theoretical physics and computer science.
‘The theory of buildings is a central unifying principle with an amazing range of applications,’ the Abel committee writes in its citation. Born in Brussels, Belgium, in 1930, Jacques Tits’
skill in mathematics was evident at an early age. After his father died when Jacques was just 13, the budding mathematician tutored students older than himself to help support his family. He
received his doctorate from the Free University of Brussels at the age of 20, and became a professor there in 1962 before moving to Bonn, Germany, two years later. He moved to the
Collège de France in Paris in 1973 to take up the position of Chair of Group Theory, a position he held until his retirement in 2000.
Meanwhile Professor Thompson, who is based at the University of Florida in the US, is credited with revolutionising the theory of finite groups by providing theorems which lay the foundation
for the complete classification of finite simple groups.
‘The achievements of John Thompson and Jacques Tits are of extraordinary depth and influence,’ the Abel Committee states in its citation. ‘They complement each other and together form the
backbone of modern group theory.’
The two mathematicians will receive the award from King Harald of Norway at a ceremony in Oslo on 20 May.
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