(left,Thompson)Schmid/Oberwolfach Photo Collection/(right, Tits)Jean-François Dars/CNRS Images

Multidimensional talent.
Thompson (left) and Tits have won the 2008 Abel Prize for their work in group theory.

Achievements in Group Theory Win Abel Prize

Two scientists who improved our understanding of the mathematics that describes symmetry have been awarded the 2008 Abel Prize in mathematics. John Griggs Thompson, 75, a professor at the University of Florida, Gainesville, and Jacques Tits, 77, a professor emeritus at the Collège de France in Paris, will share the $1.2 million award, the Norwegian Academy of Science and Letters announced this morning in Oslo. The prize, bestowed for the first time in 2003, is considered the Nobel of mathematics.

Both winners helped to advance a branch of mathematics called group theory, which allows mathematicians to describe different kinds of symmetry--including that which governs a Rubik's cube. Just as molecules can be broken down into atoms, mathematicians have developed a periodic table of symmetry that describes geometric objects in many dimensions. (One of the pioneers in the field was Norwegian mathematician Niels Henrik Able, for whom the prize is named.) In 1963, Thompson, with the late Walter Feit, published a proof of the theorem that "every finite group of odd order is soluble," a mathematical way of saying that objects with an odd number of symmetries can be broken down into simpler shapes. For example, a 15-sided polygon can be described as the combination of a pentagon and a triangle. The proof was not only noteworthy for its influence on group theory; at 255 pages, it was "possibly the longest proof that had ever been published," says Marcus du Sautoy of the University of Oxford in the U.K., who explained the winners' work at a press conference.

Tits, a Belgian citizen, is recognized for research that "created a new and highly influential vision of groups as geometric objects," the Abel Committee said in its citation. He borrowed from the vocabulary of architects, describing mathematical "buildings," "apartments," and "galleries" that allowed mathematicians to work with particularly difficult algebraic concepts.

Both men made contributions to the study of the Monster, a group with more symmetries than the number of atoms in the sun. Building on the work of Thompson and Tits, mathematicians were able to complete the "Atlas of Finite Groups," the equivalent of the Periodic Table for group theory mathematicians, which du Sautoy called "perhaps one of the greatest achievements of the 20th century."

The call announcing the prize "was a very nice way to start the day," Thompson says. He was tipped off to the possibility of receiving the prize when his department chair "said I should hang out close to home" on 27 March. The prize ensures that "one stays alive" through the recognition of his work, Tits told the press conference by telephone. "At my age, it is really unexpected." The two will receive the award from Norwegian King Harald V at a 20 May ceremony in Oslo.

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