The Pillars of Russian Mathematics

This fall, I’ll spend the semester studying math in Russia. (I can hardly contain my excitement.) I’ll be in Moscow, to be precise, studying with the “Math in Moscow” program; this program invites North American undergraduates for a semester of study at the small, elite “Independent University of Moscow”. The Independent University offers advanced, research-oriented coursework in the Russian pedagogical tradition. Interesting in their own right, however, are the mathematicians behind the University – Russian mathematical greats with fascinating histories and overflowing personalities.

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Ya. Sinai (L) and V. Arnold (R), 1963

The institution itself carries quite a story. (1) Founded upon the fall of the Soviet Union by a small, dedicated group of Russia’s very best, the Independent University, in short, effected a lone blockade against the complete disintegration of the once-prodigious Russian mathematical tradition. This group of professors – including Nikolay Konstantinov and the towering Vladimir I. Arnold – selflessly, and at large risk of failure (they even funded the venture out-of-pocket), began offering seminars, taking students, and pursuing research. The precarious institution, over time, acquired a small campus of its own and occasional funding from generous contributors. Today, they continue to thrive; the IUM’s Moscow Mathematical Journal features (by far) the highest citation index in all of Russia.

The Russian mathematical tradition, then, is reborn. I offer brief depictions of two of its late pillars.

Vladimir Igorevich Arnold was born in 1937 in Odessa, Ukraine. At 19 years of age, Arnold suddenly became very famous: he produced an affirmative solution to Hilbert’s 13th problem, concerning the expression of a function of many variables as a superposition of functions of only two variables. Arnold studied under the eminent A. N. Kolmogorov, the best Russian mathematician of the twentieth century, and quickly rose, himself, to a position of universal regard.

Arnold had a singular personality. My own professor at UNC, Alexander Varchenko, studied under Arnold; Varchenko writes about his former teacher in a tribute published by the American Mathematical Society (2). Arnold, according to Varchenko, was an avid sportsman; the professor led a once-yearly winter cross country skiing expedition in Moscow’s outskirts. Few could keep up with Arnold. The mathematician blazed ahead in the front of the pack, “dressed only in swimming trunks” and covering an incredible 50km (about 30m) per day. Arnold, writes Varchenko, “ran at a speed a bit above the maximal possible speed of the slowest of the participants,” and “those who were able to finish the skiing were very proud of themselves.” Perhaps most unbelievable of all is the mathematicians’ tradition – initiated (according to legend) by Kolmogorov himself, and passed along to Arnold and his own students – of bathing in the “few small rivers which [were] not frozen even in winter.” The mathematicians “certainly did not use bathing suits, and there were no towels,” writes Varchenko. Unbelievable.

Finally, Arnold was a classic polymath, who (according to another student, Dimitry Fuchs) seemed to offer “universal knowledge of everything.” (2) I include a segment of a letter sent from Arnold to Fuchs. (The entirety of the continuously spectacular letter can be found in (2)).

I have recently returned to Paris from Italy where I wandered, for three months, in karstic mountains working at ICPT (the International Center for Theoretical Physics) at Miramare, the estate of the Austrian prince Maximilian who was persuaded by Napoleon III to become the Emperor of Mexico (for which he was shot around 1867 as shown in the famous and blood-drenched picture of Edouard Manet).

Arnold, in an interview, states that “Mathematicians differ dramatically by their time scale: some are very good tackling 15-minute problems, some are good with the problems that require an hour, a day, a week, the problems that take a month, a year, decades of thinking… B. N. Delaunay used to say, ‘A good theorem takes not 5 hours, as in an Olympiad, but 5,000 hours’.”

Israel Moiseevich Gelfand was another Russian mathematical great, born in 1913 in Odessa. The AMS, in a tribute, writes that Gelfand “was expelled in the ninth grade as a son of a ‘bourgeois element’ (‘netrudovoi element’ in Soviet parlance)—his father was a mill manager” and that the mathematician, at age 16, “decided to go to Moscow, where he had some distant relatives.” (3) Before his move to Moscow, Gelfand grew up in complete mathematical isolation.

UNC’s Professor Varchenko, in personal discussions, has supplemented the official narrative of the AMS (Professor Varchenko actually co-wrote with Gelfand, near the end of the latter’s life). Gelfand, uneducated and unable to study at Moscow State University, instead found a job in the university’s library, where he began reading advanced mathematical texts. One day, a student searched for a particular book in vain; leaving the room in exasperation, he saw the very book in the hand of the lowly cashier. He was shocked. This student became Gelfand’s ticket into the PhD program (though Gelfand had neither a high school nor a college education!). Gelfand too eventually earned his doctorate under Kolmogorov.

Varchenko remembers Gelfand’s response to a question: “What if you had grown up with an education?” Gelfand, as he was apt to do, launched into a story. Gelfand described a boy who, born into poverty, was offered a job sweeping the basement of a church. The boy, however, was expelled from his job for showing up in rags. He was forced to work odds and ends; pulling things together, he grew up to become a rich businessman. “What if I had been educated?” Gelfand responded. “I would still be the boy sweeping the church.” Varchenko remembers Gelfand with fond nostalgia.

Vladimir Retakh, in the AMS tribute, remembers a talk by mathematician Lipman Bers. “[Bers] mentioned a theorem by Maskit and added, ‘I am proud that Maskit is my former student.’ Gelfand reacted immediately, ‘You cannot say ‘my former student’. This is like saying ‘my former son’.”

I am proud to be even a minuscule part of this academic and cultural tradition.

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  1. Y. Ilyashenko and A. Sossinsky write about the Independent University of Moscow
  2. Tribute to Vladimir Arnold (Part I)
    Memories of Vladimir Arnold (Part II)
  3. Israel Moiseevich Gelfand, Part I
    Israel Moiseevich Gelfand, Part II
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2 comments on “The Pillars of Russian Mathematics

  1. mariyaboyko says:

    great post! i am a PhD student in History of Math and my research has EVERYTHING to do (directly and indirectly) with the people mentioned above :):)

  2. Ben says:

    Awesome and thank you! If you have any more cool stories, I’d be glad to hear them.

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