British and American mathematicians have won the second Abel Prize in mathematics. Michael Atiyah and Isadore Singer are to share the $875,000 award for their proof of a theorem that links two very different areas of mathematics--topology and differential equations.
Topology is the study of abstract objects such as 12-dimensional hyperspheres; differential equations is a discipline related to how mathematical functions vary in space and time and are extremely useful to physicists and engineers. The two disciplines each have their own theorems, their own discoveries, and their own intractable problems.
In the 1960s, Atiyah, currently at the University of Edinburgh, and Singer, now at the Massachusetts Institute of Technology, together forged a link between the two seemingly different fields. The so-called Atiyah-Singer index theorem is a tool "for using topological methods for proving powerful theorems in differential equations," says John Milnor, a mathematician at the University of Stony Brook in New York. "It was one of the major developments in 20th century mathematics."
Atiyah won the Fields Medal in 1966 and was knighted for this and other mathematical discoveries, whereas Singer received less high-profile adulation, although he is a member of the National Academy of Sciences. Nevertheless, says Milnor, both are worthy of the prize: "I think these are good people who deserve it."