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Villani, a mathematician at the University of Lyon in France, won a Fields Medal—akin to a Nobel Prize—in 2010 for a new theorem describ-ing a phenomenon known as Landau damping that occurs in plasmas (the most energetic state of matter). By sharing conversations with colleagues, e-mail chains with his main collaborator, and anecdotes of insights that arrived via dreams and stray thoughts in airport waiting lounges, he illustrates the day-to-day process of devising a theorem, a task that took him two grueling and exhilarating years to complete. Rather than glossing over the mathematical intricacies, Villani includes many of the details and even the equations that went into a proof of his theorem, giving readers a vivid sense of the problems he ran into and the solutions he found, even if the subtleties are beyond many nonmathematicians.
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