A Russian-born mathematician whose work has influenced fields from physics to biology has won this year's Abel Prize, the math field's counterpart to the Nobel. The $950,000 prize, first awarded in 2003 by the Norwegian Academy of Science and Letters, goes to Mikhail Gromov of the Institut des Hautes Études Scientifiques (IHES) in Bures-sur-Yvette, France.
Gromov, 65, won the award "for his revolutionary contributions to geometry," says Abel Committee Chair Kristian Seip. The mathematician, who also holds a position at the Courant Institute of Mathematical Sciences in New York City, is credited with making advances in the fields of symplectic and Riemannian geometry, which are closely tied to areas of mathematical physics such as general relativity and string theory. He is also credited with founding the modern study of "geometric group theory," which injects notions of distance and curvature into the study of finite algebraic structures. Gromov's work "has had a tremendous impact on geometry and has reached from there into major applications in analysis and algebra," says George Andrews, president of the American Mathematical Society in Providence. "One cannot imagine a more worthy recipient."
In the 1980s, Gromov showed how to treat the collection of all Riemannian geometries as a geometric space in its own right: Each point in the meta-space is a Riemannian metric, with the distance between two metrics determined by how similar or different the corresponding Riemannian spaces are. The entire subject of metric spaces grows out of a simple observation in classical geometry called the triangle inequality, which states that the length of any one side of a triangle is always shorter than the sum of the lengths of the other two sides (in other words, the shortest distance between two points lies along a straight line). In group theory, Gromov's work on metrics led to the study of "hyperbolic" groups, which have properties closely connected with non-Euclidean hyperbolic geometry. An admiring Dennis Sullivan at the City University of New York once enthused, "It is incredible what Mikhail Gromov can do just with the triangle inequality."
IHES Bures-sur-Yvette Director Jean-Pierre Bourguignon says Gromov's "driving force" has also been instrumental in making unconventional connections at the institute between mathematics and biology. In a 2001 paper co-authored with Alessandra Carbone, now at the Université Pierre et Marie Curie in Paris, for example, Gromov proved a theorem on the virtual certainty of unicellular life in pond water: Within a mathematical framework that stipulates what it takes for a random arrangement of chemicals to be considered living, they found, the "live" states vastly outnumber the "dead" ones. "Misha is often radical in his judgments, but it certainly takes nonconventional minds to make significant steps in this very challenging field," Bourguignon says.