Perfect Rigor: A Genius and the Mathematical Breakthrough of the Century

By Masha Gessen

A gripping and tragic story that sheds infrequent mild at the certain burden of genius


In 2006, an eccentric Russian mathematician named Grigori Perelman solved the Poincare Conjecture, an incredibly complicated topological challenge that had eluded the easiest minds for over a century. A prize of 1 million cash was once provided to an individual who may well get to the bottom of it, yet Perelman declined the winnings, and in doing so encouraged journalist Masha Gessen to inform his tale. Drawing on interviews with Perelman’s lecturers, classmates, coaches, teammates, and associates in Russia and the United States—and trained by means of her personal history as a math whiz raised in Russia—Gessen exposed a brain of unequalled computational energy, one who enabled Perelman to pursue mathematical recommendations to their logical (sometimes far away) finish. yet she additionally stumbled on that this very power grew to become out to be Perelman's undoing and the cause of his withdrawal, first from the area of arithmetic after which, more and more, from the area in general.

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Indb one hundred fifty five 8/26/2009 8:50:51 AM 156  /  P E R F E C T R I G O R an offer, and a few colleagues of Tian’s had approached Perelman the former night and tried to persuade him that the assets of MIT could let him to paintings extra productively. Tian requested Perelman for his response. no matter what Perelman acknowledged to him in response, the well mannered, exceptionally soft-­spoken Tian wouldn't repeat to me. “He made a few comments,” Tian allowed. “I ­don’t are looking to say them. ” the matter used to be not only that this time Perelman had little interest in staying on within the usa.

Those that desired to specialize early may well song a lot of the remainder of arithmetic out. Perelman represented the rarest breed of Mathmech scholar: one that sought to be universally proficient in arithmetic. such a lot mathematically formidable scholars had for years identified their specialization was once preordained: they'd one type of mind or the opposite. The algebraists may perhaps then search for the main promising difficulties of algebra whereas the geometers may perhaps solid approximately for the main attention-grabbing geometer with whom to check, yet typically, their instructions have been set.

Perelman controlled to turn out major issues. First, he confirmed that Hamilton didn't have to imagine that the curvature might continually be uniformly sure; within the imaginary area during which the evidence opened up, this easily could continuously be the case. moment, he confirmed that each one the singularities that may improve stemmed from a similar root; they'd seem while the curvature started to “blow up,” to develop unmanageable. on the grounds that all of the singularities had 004671_Gessen_Book_APP. indb 146 8/26/2009 8:50:50 AM T H E P R O B L E M   /  147 an identical nature, a unmarried device will be potent opposed to all of them — and the surgical procedure initially expected through Hamilton might do the activity.

Kleiner’s personal zone of study lay relatively close to Perelman’s, so Perelman’s reticence appeared average to him. yet there has been most likely one more reason for the reticence, one who Perelman articulated in a talk with Cheeger in 1995. As Cheeger recalled, Perelman stopped via his of­fice whereas he used to be in short in long island urban they usually mentioned a few matters relating to Alexandrov areas yet to not the spe­cific points Perelman had studied some time past. This time, even though, Perelman was once very or even spoke of one of many questions because the “holy grail” of the topic.

I learn it and fashionable it much. yet I felt it used to be a little too terse, a bit of now not making the insights as appear as they can be. So I acknowledged this to him and he stated he may contemplate it. yet I ­couldn’t relatively get him to alter. I ­don’t understand. have you ever visible the movie Amadeus? ” The scene Cheeger used to be recalling was once the single during which Mozart offers an opera he has written and the emperor indicates the piece is exceptional yet now not excellent: it has too many 004671_Gessen_Book_APP. indb 118 8/26/2009 8:50:47 AM R O U N D T R I P   /  119 notes.

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