Saturday, November 7, 2009
It may be no accident that, while some of the best American mathematical minds worked to solve one of the century's hardest problems—the Poincaré Conjecture—it was a Russian mathematician working in Russia who, early in this decade, finally triumphed.
Decades before, in the Soviet Union, math placed a premium on logic and consistency in a culture that thrived on rhetoric and fear; it required highly specialized knowledge to understand; and, worst of all, mathematics lay claim to singular and knowable truths—when the regime had staked its own legitimacy on its own singular truth. All this made mathematicians suspect. Still, math escaped the purges, show trials and rule by decree that decimated other Soviet sciences.
Three factors saved math. First, Russian math happened to be uncommonly strong right when it might have suffered the most, in the 1930s. Second, 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). And third, at a critical moment math proved immensely useful to the state.
Three weeks after Nazi Germany invaded the Soviet Union in June 1941, the Soviet air force had been bombed out of existence. The Russian military set about retrofitting civilian airplanes for use as bombers. The problem was, the civilian airplanes were much slower than the military ones, rendering moot everything the military knew about aim.
What was needed was a small army of mathematicians to recalculate speeds and distances to let the air force hit its targets.
The greatest Russian mathematician of the 20th century, Andrei Kolmogorov, led a classroom of students, armed with adding machines, in recalculating the Red Army's bombing and artillery tables. Then he set about creating a new system of statistical control and prediction for the Soviet military.
Following the war, the Soviets invested heavily in high-tech military research, building over 40 cities where scientists and mathematicians worked in secret. The urgency of the mobilization recalled the Manhattan Project—only much bigger and lasting much longer. Estimates of the number of people engaged in the Soviet arms effort in the second half of the century range up to 12 million people, with a couple million of them employed by military-research institutions.
These jobs spelled nearly total scientific isolation: For defense employees, any contact with foreigners would be considered treasonous rather than simply suspect. In addition, research towns provided comfortably cloistered social environments but no possibility for outside intellectual contact. The Soviet Union managed to hide some of its best mathematical minds away in plain sight.
In the years following Stalin's death in 1953, the Iron Curtain began to open a tiny crack—not quite enough to facilitate much-needed conversation with non-Soviet mathematicians but enough to show off some of Soviet mathematics' proudest achievements.
By the 1970s, a Soviet math establishment had taken shape. A totalitarian system within a totalitarian system, it provided its members not only with work and money but also with apartments, food, and transportation. It determined where they lived and when, where, and how they traveled for work or pleasure. To those in the fold, it was a controlling and strict but caring mother: Her children were undeniably privileged.
Even for members of the math establishment, though, there were always too few good apartments, too many people wanting to travel to a conference. So it was a vicious, back-stabbing little world, shaped by intrigue, denunciations and unfair competition.
Math not only held out the promise of intellectual work without state interference (if also without its support) but also something found nowhere else in late-Soviet society: a knowable singular truth. "If I had been free to choose any profession, I would have become a literary critic," says Georgii Shabat, a well-known Moscow mathematician. "But I wanted to work, not spend my life fighting the censors." The search for that truth could take long years—but in the late Soviet Union, time seemed to stand still.
When it all collapsed, the state stopped investing in math and holding its mathematicians hostage. It's hard to say which of these two factors did more to send Russian mathematicians to the West, primarily the U.S., but leave they did, in what was probably one of the biggest outflows of brainpower the world has ever known. Even the older Mr. Gelfand moved to the U.S. and taught at Rutgers University for nearly 20 years, almost until his death in October at the age of 96. The flow is probably unstoppable by now: A promising graduate student in Moscow or St. Petersburg, unable to find a suitable academic adviser at home, is most likely to follow the trail to the U.S.
But the math culture they find in America, while less back-stabbing than that of the Soviet math establishment, is far from the meritocratic ideal that Russia's unofficial math world had taught them to expect. American math culture has intellectual rigor but 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. This culture offers the kinds of opportunities for professional communication that a Soviet mathematician could hardly have dreamed of, but it doesn't foster the sort of luxurious, timeless creative work that was typical of the Soviet math counterculture.
For example, the American model may not be able to produce a breakthrough like the proof of the Poincaré Conjecture, carried out by the St. Petersburg mathematician Grigory Perelman.
Mr. Perelman came to the United States as a young postdoctoral student in the early 1990s and immediately decided that America was math heaven; he wrote home demanding that his mother and his younger sister, a budding mathematician, move here. But three years later, when his postdoc hiatus was over and he was faced with the pressures of securing an academic position, he returned home, disillusioned.
In St. Petersburg he went on the (admittedly modest) payroll of the math research institute, where he showed up infrequently and generally kept to himself for almost seven years, one of the greatest mathematical discoveries of at least the last hundred years. 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.
After posting his proof on the Web, Mr. Perelman traveled to the U.S. in the spring of 2003, to lecture at a couple of East Coast universities. He was immediately showered with offers of professorial appointments and research money, and, by all accounts, he found these offers gravely insulting, as he believes the monetization of achievement is the ultimate insult to mathematics. So profound was his disappointment with the rewards he was offered that, I believe, it contributed a great deal to his subsequent decision to quit mathematics altogether, along with the people who practice it. (He now lives with his mother on the outskirts of St. Petersburg.)
A child of the Soviet math counterculture, he still held a singular truth to be self-evident: Math as it ought to be practiced, math as the ultimate flight of the imagination, is something money can't buy.Russia's Conquering Zeros
by Masha Gessen
author of Perfect Rigor: A Genius and the Mathematical Breakthrough of the Century
It's hard to believe that any change could happen in our full-inclusion town. I've talked in the past how I came to the realization that when push comes to shove, schools will admit that Singapore Math is stronger in all ways, but the schools have to teach all kids. ("Everyday Math is better for our mix of students.") Since they won't separate or track, they pretend that differentiated instruction will solve the problem. It doesn't. They know it doesn't, but they don't have any acceptable solution. They continue to focus on small relative changes in test scores, point to the few students who do well, and don't dare ask their parents why that is the case.
Has any town tried to quantify how much help their best students get at home? I thought there was one town (in NJ?) that sent out a questionnaire about this. What happened there? Why should schools try to find out if there is a problem for which they have no solution? When our son was in a private school that used Everyday Math, it seemed like it was normal and good for families to provide whatever support that was needed. We paid a lot of money, but our home support was not less.
Is there any hope?
Wednesday, November 4, 2009
as an education professor, my goal isn't to teach the students who all score the highest on the SAT. perhaps Roger and "Common Sense" posters want that, but i find that having a diverse class helps me teach my curriculum far more effectively. we are required by our accrediting body to prepare teachers to teach in a heterogeneous world and having a homogeneous student body runs counter to our goals. i can try and prepare my students to teach in an inner city school but it's far more effective if a student actually attended this school who can share her experiences and give that extra rationale for the classroom management or learning strategies i am teaching. the same can be said for having students who attended a private Christian school or a school in a rural setting, etc. -- the diverse student body helps the curriculum i teach and that value is lost if a university goes on test scores alone.
The educationists are living in a completely different universe from the rest of us.