“The mathematician patiently answered all questions from the audience after his lecture. Those questions came furiously. "But that solution will blow up in finite time," came a voice from the middle of the room. "It doesn't matter," replied Perelman; "we can cut it out and restart the flow." Silence, then a couple of nods. The listeners were cautious, weighing what they heard. They would have to ponder his words for months to come, but this sounded promising.

Much of the mathematics Perelman called upon would have been inconceivable three decades previously. The technical tools that he used were at the very edge of what was possible and depended critically on the work of a number of persons in the audience. The atmosphere was tense. Everyone knew how delicate and how subtle the speaker's arguments were, and how easy it was to go astray. Everyone wanted them to hold. […]

The Poincare conjecture and Perelman's proof of it is one of the greatest achievements of our age; it tells us much about the possible nature and shape of our universe. The Ricci-flow equation Perelman wrote, a type of heat equation, is a distant relative of the Black-Scholes equation that bond traders around the world use to price stock and bond options. But curvature is more complicated than temperature or money. As subsequent chapters will explain, curvature is a geometric object that requires more than one number to describe it, and the Ricci-flow equation that Perelman uses is shorthand for six linked equations, a triumph of elegance, simple to behold and concealing dazzling riches. Its closest analogue is the Einstein equation of general relativity that expresses the curvature of space-time.” -Donal O'Shea, The Poincare Conjecture-In Search of the Shape of the Universe (2007).
Grigory Perelman
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