It was a good week for mathematical physics. Three of the four winners of the 2010 Fields Medal, considered the Nobel Prize for mathematics, were honored for studies in the field.
The Fields Medal is not entirely analogous to the Nobel: The award is given once every four years; its recipients must be younger than 40; and Fields medalists win about $14,000, compared to about $1.4 million that come with a Nobel.
(The fact is, there is no Nobel Prize in mathematics and never has been, and so the Fields Medal is the highest honor a mathematician can receive. Maybe mathematicians are just above all that.)
At the award ceremony on Aug. 19 in Hyderabad, India, the International Mathematical Union honored mathematicians Cedric Villani, Stanislav Smirnov and Elon Lindenstrauss, as well as mathematician Ngo Bau Chau.
IMU granted the award to Villani, of the Henri Poincare Institute in Paris, for his achievements in understanding Boltzmann’s kinetic theory of gases. This theory explains entropy, but instead of "tracking the individual motion of billions of individual atoms, it studies the evolution of the probability that a particle occupies a certain position and has a certain velocity,” according to the International Congress of Mathematicians website. Villani’s work also dealt with plasma physics.
Smirnov, of the University of Geneva, investigated what happens to probability in lattice models -- grids used in statistical physics -- when the blocks in the grid become infinitely small. “The proof is elegant, and it is based on extremely insightful combinatorial arguments,” the website said. “Smirnov’s work gave the solid foundation for important methods in statistical physics like Cardy’s Formula, and provided an all-important missing step in the theory of Schramm-Loewner Evolution in the scaling limit of various processes.”
IMU awarded the Fields Medal to Lindenstrauss, of the Hebrew University of Jerusalem, for studies of ergodic theory, which had implications for other theories, including quantum theory.
According to his profile, Lindenstrauss and his collaborators "have found many other unexpected applications of these ergodic theoretic techniques in problems in classical number theory. His work is exceptionally deep.”
