Perelman's Seminal Proof Cited as Evidence of Russian-Soviet Mathematics Rigor

November 26, 2009

The recent celebration of the twentieth anniversary of the fall of the Berlin Wall has prompted some to reexamine the Cold War era. Mathematicians are no exception.

In a recent article for the Wall Street Journal, Russian journalist Masha Gessen examined the differences between the U.S. and U.S.S.R. by looking at their math cultures. She pointed to the Poincaré Conjecture, proved in Russia by Russian mathematician Grigory Perelman, as a modern example of these differences.  

In the Soviet Union, Gessen wrote, "math proved too obscure for the sort of meddling Joseph Stalin most liked to exercise: It was simply too difficult to ignite a passionate debate about something as inaccessible as the objective nature of natural numbers (although just such a campaign was attempted)."

After World War II, the Soviets invested heavily in high-tech military research, employing roughly 12 million people in the second half of the century. During that time the regime built more than 40 cities, which Gessen described as "research towns [that] provided comfortably cloistered social environments, but no possibility for outside intellectual contact."

Members of the Soviet math establishment were privileged. They were given work, money, and significant benefits over their fellow citizens. However, some were kept outside the establishment, specifically Jews, women, and others unwilling to join the Party. Gessen described them as "the mathematical counterculture" where "math was almost a hobby."

Mathematicians called it "math for math's sake," Gessen wrote.  "There was no material reward in this—no tenure, no money, no apartments, no foreign travel; all they stood to gain was the respect of their peers."

When the Soviet Union collapsed, investment in math declined precipitously, and Soviet mathematicians left for the West. Gessen described the movement as "probably one of the biggest outflows of brainpower the world has ever known."

The regime's absolute control over society and truth itself was a stark contrast to the open society in the U.S., so much so that Soviet mathematicians emigrating in the early 1990s described the U.S. as "math heaven." But for all its freedom, Gessen wrote, the U.S. "doesn't foster the sort of luxurious, timeless creative work that was typical of the Soviet math counterculture." Many, including Grigory Perelman, soon returned to Russia.

After his return to St. Petersburg, Perelman worked for the math research institute, "where he showed up infrequently and generally kept to himself for almost seven years," Gessen said. "It's all but impossible to imagine an American institution that could have provided Mr. Perelman with this kind of near-solitary existence, free of teaching and publishing obligations," she continued.

While America's culture, Gessen wrote, offers the kinds of opportunities for professional communication that Soviet mathematicians could hardly have imagined, "it also suffers from allegations of favoritism, small-time competitiveness, occasional plagiarism scandals, as well as the usual tenure battles, funding pressures, and administrative chores that characterize American academic life."

In the article, which was adapted from her latest book, Perfect Rigor: A Genius and the Mathematical Breakthrough of the Century, Gessen nonetheless neglected to credit the influence of Western mathematicians on Perelman's work:  Richard Hamilton (Columbia University); Andrew Wiles (Princeton University), who proved Fermat's Last Theorem; Ketan Mulmuley, who has been investigating P vs NP while shuttling between the University of Chicago and IIT Bombay; and Stephen Cook, who proved that SAT is NP-complete while at the University of Toronto.

Source: Wall Street Journal, Nov.  6, 2009.