Alexandre Grothendieck Turns 80 in Self-Imposed Seclusion

June 4, 2008

Living alone in a village in the Pyrenees, Alexandre Grothendieck, a revered figure in the mathematics, turned 80 last March. A master of abstract approaches to mathematics, Grothendieck made major contributions to algebraic geometry, homological algebra, functional analysis, and other areas. He won a Fields Medal in 1966.

Grothendieck "was a master of the power of generalization," Luc Illusie of Paris-Sud University told Science News. Illusie had been one of Grothendieck's students.

He "had an extraordinary sensitivity to the harmony of things," Illusie noted. "It's not just that he introduced new techniques and proved big theorems. He changed the very way we think about many branches of mathematics."

Much of Grothendieck's work was in a branch of mathematics known as "category theory," which seeks to identify properties common to many different mathematical objects. These relationships, Grothiendick had argued, are the key to their structure. Grothendieck, along with Pierre Deligne and others, also proved the Weil conjectures, which are important theorems in algebraic geometry.

In 1990, Groethendieck rid himself of his papers and vanished into the Pyrenees. Later, two mathematicians, Pierre Lochak and Leila Schneps, found him living alone in a tiny village. Now, Schneps said, "he's not in a state to be visited."

But Grothendieck's work lives on. Without his advances, "it would have been impossible to attack any of the great problems in number theory and algebraic geometry that have been solved during the last 30 years," Illusie said. Among the breakthroughs are proofs of Fermat's last theorem and the Mordell conjecture.

"He had this whole thing about being buried, but it's so utterly false," said David Mumford of Brown University. "We would so much like to see him and tell him how much he's still remembered."

Source: Science News, May 9, 2008.