Mathematical Styles & the Process of Discovery

Five years ago, the mathematician Cédric Villani, the 2010 Fields Medal winner and the author of Théorème vivant, a work that could be called Theory of Life/Life in Theory, met John Nash at Princeton, but, Villani said, he “did not have the courage to talk to him.” Nash was a legend; Villani was well short of forty. But Nash has always worn his legend lightly, when he is not impatiently casting it off, and Villani has since shown the ability to bring mathematical questions of dispersal, order, disorder, and entropy into the realm where people of all sorts live, talk, and think. Nash, who received his Ph.D. at the age of twenty-two, in 1950, worked in geometry, game theory, and, less publically, more experimentally, in cryptography—in Villani’s words, “my mathematical hero . . . in ten years and three theorems revolutionized analysis and geometry.” That is the legend of the scientist devoured by his own genius, as portrayed in in Rebecca Goldstein’s novel The Mind-Body Problem and Sylvia Nasar’s biography A Beautiful Mind and by Russell Crowe in the film of the same name—but it is also beside the point. Nash and Villani may be generations apart; as translators of what may seem to many the emanations of invisible worlds, they speak the same language, and in a manner that allows anyone entry into the conversation.

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John F. Nash, Jr. is Senior Research Mathematician at Princeton University; his current work focuses on, in his words, “logic, game theory, cosmology, and gravitation.” In 1978 he was awarded the John von Neumann Theory Prize; in 1994, with John Harsanyi and Reinhard Selten, he received the Nobel Memorial Prize in Economic Sciences.

Cédric Villani is professor of mathematics at the University of Lyon, and the director of the Institut Henri Poincaré in Paris. His discipline-shuffling Théorème vivant was published in 2012. The English translation Birth of a Theorem: A Mathematical Adventure will be published by Faber & Faber in 2015. Villani was awarded the Fields Medal in 2010.

Antonin Baudry is the Cultural Counselor of the Embassy of France in New York. As Abel Lanzac, with Christophe Blain he is the author of the two-volume graphic novel Quai d’Orsay (2010-2011), published in English in 2014 as Weapons of Mass Diplomacy. In 2013, it was adapted as a film by
Bertrand Tavernier under the alternate title The French Minister.