## The entropy formula for the Ricci flow and its geometric applications

Grigori Perelman is one of the greatest mathematicians of our time, a Russian genius who solved the Poincaré Conjecture, which plagued the brightest minds for a century. At the height of his fame, he refused a million-dollar award for his work. Then he disappeared. Our writer hunts him down on the streets of St. Petersburg. […]

Word was that someone had solved an unsolvable math problem. The Poincaré conjecture concerns three-dimensional spheres, and it has broad implications for spatial relations and quantum physics, even helping to explain the shape of the universe. For nearly 100 years the conjecture had confused the sharpest minds in math, many of whom claimed to have proven it, only to have their work discarded upon scrutiny. The problem had broken spirits, wasted lives. By the time Perelman defeated the conjecture, after many years of concentrated exertion, the Poincaré had affected him so profoundly that he appeared broken too.

Perelman, now 46, had a certain flair. When he completed his proof, over a number of months in 2002 and 2003, he did not publish his findings in a peer-reviewed journal, as protocol would suggest. Nor did he vet his conclusions with the mathematicians he knew in Russia, Europe and the U.S. He simply posted his solution online in three parts—the first was named “The Entropy Formula for the Ricci Flow and Its Geometric Applications”—and then e-mailed an abstract to several former associates, many of whom he had not contacted in nearly a decade.