Raoul Bott, a mathematician who made innovative contributions to differential geometry and topology, has died at the age of 82.

His family said he died of lung cancer on Dec. 20 in Carlsbad, Calif, The New York Times reported.

The Harvard University mathematician collaborated with Michael Atiyah of the University of Edinburgh to find topological ways of investigating solutions to differential equations.

The collaboration yielded the Atiyah-Bott fixed-point theorem, which in part shows that a mathematical map has a fixed point and also provides a means to count the number of fixed points on a given map, the newspaper said.

Bott was also widely known for the Bott periodicity theorem in 1959, the importance of which some mathematicians have compared to the discovery of the periodic table of the elements.

More recently, his research was directed toward developing mathematical tools to aid physicists working to reconcile theories of general and quantum relativity.

In 1990, the American Mathematical Society awarded Bott its Leroy P. Steele Prize for Lifetime Achievement. He received the National Medal of Science in 1987 and won the Wolf Foundation Prize in Mathematics in 2000.

*Copyright 2006 by United Press International*

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