Perfect Rigour
Page 23
Some of his students believed the illnesses were set off: Abramov, 54; Abramov interview.
his students, who for the preceding couple of years had taken turns: Prohorov interview.
everyone was to be taught the same thing at the same time: Abramov, 48.
“elite education is not allowable in our society”: Egorov, 166.
Moscow’s School 2 was apparently the object of many denunciations: Leonid Ashkinazi, “Shkola kak fenomen kultury,” Himiya i zhizn 1 (1991): 16.
School 239 lost some of its most popular teachers to KGB pressure: Mikhail Ivanov, principal of the Physics in Mathematics Lyceum and former teacher at School 239, interview with the author, St. Petersburg, October 23, 2007.
its principal was frequently reprimanded for admitting too many Jewish children: Tamara Yefimova, principal of School 239, interview with the author, St. Petersburg, October 17, 2007.
two out of four Leningrad math schools were shut down: Tatyana Hein, education activist and Leningrad School 317 graduate, interview with Katerina Belenkina, Moscow, April 2007.
those parents who were college instructors: Aleksandr Krauz, “Zapiski o vtoroy shkole,” http://ilib.mirror1.mccme.ru/2/07-krauz.htm, accessed September 16, 2008.
the school’s bulletin boards overflowed with announcements: Ashkinazi.
“What made the school different”: Boris Levit, interview with Katerina Belenkina, April 2007.
some schools allowed students not to wear uniforms: Arkady Tsurkov, Israeli mathematician and former Soviet dissident, interview with Katerina Belenkina, April 2007.
some teachers read forbidden works of literature aloud in class: Ivanov.
“What can be more beneficial at sixteen or seventeen”: Mikhail Berg, “Tridtsat let spustya,” http://litpromzona.narod.ru/berg/30let.html, accessed September 16, 2008.
“Because of him, we felt like gods”: Viktor Kistlerov, Moscow computer scientist, interview with Katerina Belenkina, April 2007.
forge a relationship with a second-tier college: Yefimova interview.
he made no secret of his fear of the secret police: Arnold in Kolmogorov v vospominaniyakh, 37; Abramov interview.
in 1957 he was fired as dean: Arnold in Kolmogorov v vospominaniyakh, 45.
He parted with his ideas with famous ease: Prohorov interview.
He claimed little interest in the authorship of solutions: “Posledneye interview,” in Yavleniye, 191.
I spoke with a Russian Israeli psychologist: Viktoria Sudakova, phone interview with the author, Jerusalem, December 31, 2007.
her support for a math-club class apparently struck some of the teachers: Yefimova, Rukshin, Ivanov interviews.
Valery Ryzhik: Valery Ryzhik, interview with the author, St. Petersburg, Russia, February 28, 2008; biographical information retrieved from a website devoted to the memoirs of School 239 teachers and graduates, http://club.sch239.spb.ru:8001/club/htdocs/teach_page/ryzhik/, accessed March 23, 2008.
Students recalled that in ordinary years he picked five top students: Natalya Alexandrovna Konstantinova, recollections, http://club.sch239.spb.ru:8001/club/htdocs/teach_page/ryzhik/words.shtml, accessed March 23, 2008.
he would go to the bakery on Liteyniy Prospect: Golovanov interview.
what chess players call intuition is in fact the ability to grasp complex systems in a single take: Jonah Lehrer, How We Decide (Boston: Houghton Mifflin Harcourt, 2009), 44.
Rukshin focusing more on literature, music, and all-around erudition: Sergei Rukshin, interview with the author, St. Petersburg, October 17 and October 23, 2007, and February 13, 2008.
Ryzhik on chivalry, honesty, responsibility, and other universal values: Ryzhik interview; Yelena Vereshchagina, a former classmate of Perelman’s, interview with the author, St. Petersburg, February 13, 2008.
the student who had slipped his classmate the bomb: For example, see http://scholar-vit.livejournal.com/159422.html?thread=5221566#t5221566, accessed February 7, 2009.
turned away, apparently because the principal had come under increased pressure to cut the number of Jewish teachers: Ryzhik, Yefimova, Vereshchagina interviews.
criticized for violating every rule of Soviet teaching methodology: Golovanov interview.
Viktor Radionov was fired amid charges of pedophilia: Yefimova, Golovanov, Rukshin interviews.
impressed students with his willingness to entertain even risky political questions: Vereshchagina interview.
later exposed as a KGB informant: Memoir of 1970 graduate Alexander Kolotov, http://club.sch239.spb.ru:8001/club/HTDOCS/teach_page/ostrovsk/alternative.shtml, accessed March 23, 2008.
patiently explained any math issue to any of his classmates: Vereshchagina interview.
by the time he was in his last year of school, his fingernails were so long they curled: Rukshin interview.
4. A Perfect Score
Mathmech anti-Semitism: Valery Ryzhik, interview with the author, St. Petersburg, Russia, February 28, 2008; Alexander Golovanov, interview with the author, St. Petersburg, October 18 and October 23, 2008.
roughly eighty thousand conscripts were serving there at any given time: G. F. Krivosheev, ed., Rossiya i SSSR v voynakh XX veka, website of Zabytiy Polk, http://www.polk.ru/pl/afg1.php, accessed March 27, 2008.
all the boys who took prizes at the Leningrad citywide math olympiad at his grade level: In 1979 first place went to Alexander Levin and Grigory Perelman; second place went to Boris Sudakov and Nikolai Shubin; all four were members of Rukshin’s math club. In addition, Alterman (his first name is unknown) and Vadim Tsemekhman, who had taken first and second place respectively the preceding year, had honorable mentions. Information supplied by Dmitry Fomin, historian of the St. Petersburg/Leningrad mathematics olympiads, in an e-mail to the author, March 14 and 15, 2008.
those who took first and second places in the city olympiad would advance to another round of competition: See http://www.mathcenter.spb.ru/history/fomin.html, accessed March 14, 2008.
Alexander Vasilyev and Nikolai Shubin took first place: Fomin e-mail, March 14, 2008.
He named two people: Perelman and Levin: Alexander Abramov, interview with the author, Moscow, December 5, 2007.
Alexander Levin had not come to the club that particular day: Sergei Rukshin, interview with the author, St. Petersburg, October 17 and October 23, 2007, and February 13, 2008; Golovanov interview.
Competition description: Fomin, “Istoricheskiy ocherk.”
“Wait!” he shouted: Rukshin interview.
The solution turned out to contain a serious flaw: Simon Singh, Fermat’s Enigma: The Epic Quest to Solve the World’s Greatest Mathematical Problem (New York: Anchor, 1998).
for Perelman it was split into time devoted to solving problems: Yelena Vereshchagina, interview with the author, St. Petersburg, February 13, 2008.
One student recalled waking up in the morning: Alexander Spivak, 1982 Soviet IMO team member and later mathematics teacher, interview with the author, Moscow, February 7, 2008.
Another recalled arriving by bus in Chernogolovka: Sergei Samborsky, 1982 Soviet IMO team reserve member and later computer scientist, interview with the author, Moscow, February 14, 2008.
Preparedness for Labor and Defense of the USSR requirements: http://russiansport.narod.ru/files/norms_gto.html, accessed April 1, 2008.
the only nonperfect grade on his graduating transcript: Yefimova interview.
Both he and Spivak had perfect scores: Abramov, Spivak interviews.
shortly before the planned trip she was told that her travel documents could not be processed in time: Abramov interview.
took ninth place with 230 points: Information from the official IMO website, http://www.imo-official.org/year_country_r
.aspx?year=1981, accessed April 7, 2008.
a professor of mathematics at Karlsruhe University: http://www.mathematik.uni-karlsruhe.de/iag1/~grinberg/en, accessed April 7, 2008.
represented Germany at the IMO three times between 2004 and 2006: http://www.imo-official.org/participant_r.aspx?id=7901, accessed April 7, 2008.
“Natalia Grinberg, former number 1”: http://www.mathlinks.ro/Forum/viewtopic.php?t=101785, accessed April 7, 2008.
IMO team: http://www.imo-official.org/year_country_r.aspx?year=1978, accessed April 7, 2008; rumor comes from Rukshin interview.
The students were now on their own: A. Abramov and A. Savin, “XXXIII mezhdunarodnaya matematicheskaya olimpiada,” Kvant 12 (1982): 46–48, http://kvant.mirror1.mccme.ru/1982/12/XXIII_mezhdunarodnaya_matemati.htm.; Spivak interview.
The judging process: Abramov, Savin; Spivak interview.
Perelman showed no interest in the sights: Abramov, Spivak interviews.
Perelman’s results: See http://imo-official.org/participant_r.aspx?id=10481, accessed April 16, 2008.
5. Rules for Adulthood
the group represented a sort of elite learning center: Alexander Golovanov, interview with the author, St. Petersburg, October 18 and October 23, 2008; Mehmet Muslimov, interview with the author, St. Petersburg, February 27, 2008. (Back in his university and math-club days Muslimov had been known as Aleksei Pavlov, but he later converted to Islam and took a new name, in addition to becoming a linguist.)
in the 1970s Leningrad University had moved its science departments: http://www.naukograd-peterhof.ru/peterhof-history.html, accessed April 17, 2008.
He was, however, unwilling to entertain them: Muslimov interview.
He was strongly drawn to Viktor Zalgaller: Golovanov interview.
I interviewed Zalgaller: Viktor Zalgaller, interview with the author, Rehovot, Israel, March 16, 2008.
Zalgaller was a World War II veteran: Mikhail Ivanov, ed., Sbornik vospominaniy o 239 shkole, unpublished manuscript.
Alexander Danilovich Alexandrov: Biography of A. D. Alexandrov at http://www.univer.omsk.su/LGS/#s2, accessed April 24, 2008.
A. D. Alexandrov and graduate school: O. A. Ladyzhenskaya, “Ocherk o zhizni I deyatelnosti A. D. Aleksandrova,” in G. M. Idlis, O. A. Ladyzhenskaya, eds., Akademik Aleksandr Danilovch Aleksandrov. Vospominaniya, publikatsii, materialy (Moscow: Nauka, 2002), 7.
He was also a member of the Communist Party and remained one: A. M. Vershik, “A. D., kakim ya yego znal,” http://www.pdmi.ras.ru/~vershik/B22.pdf, accessed April 24, 2008.
He managed, almost single-handedly, to reframe it: Idlis, Ladyzhenskaya, 8–10.
Then one of the mathematicians dared ask Alexandrov: Ibid., 74.
The former student, a very prominent mathematician: Vershik.
still amounted to exile: Idlis, Ladyzhenskaya.
he wanted to fill a vacant chair in geometry: Vershik.
Alexandrov’s hopes of obtaining the chair in geometry were dashed: Ibid.
was generally considered unhirable: Lev Pontryagin, Zhizneopisaniye Lva Semenovicha Pontryagina, matematika, sostavlennoye im samim (Moscow: Komkniga, 2006), 113.
managed to provide him not only with a teaching job: Ladyzhenskaya, “Borba,” 75–76.
Rokhlin would see twelve of his students’ dissertations to completion: Mathematics Genealogy Project, http://www.genealogy.math.ndsu.nodak.edu/id.php?id=42580, accessed April 24, 2008.
the man who would be largely responsible for introducing Perelman: Zalgaller interview; Jeff Cheeger, New York University professor, interview with the author, New York City, April 1, 2008.
“He would give topics and promising ideas away to his students”: V. A. Zalgaller, “Vospominaniya ob A. D. Alexandrove i yego leningradskom geometricheskom seminare,” in Idlis, Ladyzhenskaya, 16.
“‘So have you proved it?’ Alexandrov asked”: A. V. Kuzminykh, “Pamiati uchitelya,” in ibid., 120.
Alexandrov’s reaction to a request to write a history of Soviet geometry: M. A. Rozov, “Lev v kresle,” in ibid., 155.
he had chosen to become a geometer after hearing another professor’s words: Yu. G. Reshetnyak, “Vospominaniya o nashem uchitele: A. D. Aleksandrov i yego geometricheskaya shkola,” in ibid., 40.
Alexandrov was said to have made the following comment: O. M. Kosheleva, “My otvetstvenny za vsyo,” in ibid., 125–26.
“In the end, through the general interconnectedness of events”: Quoted in ibid., 126.
Fedja Nazarov: Nazarov’s faculty page at http://www.math.wisc.edu/~nazarov/, accessed April 27, 2008.
Anna Bogomolnaia: Bogomolnaia’s faculty page at http://www.ruf.rice.edu/~econ/faculty/bogomolnaia.html, accessed April 27, 2008.
Evgeny Abakumov: Directory of French mathematicians, http://wwwmaths.anu.edu.au/people/past_visitors.html, accessed September 23, 2008.
Those banished included Bogomolnaia, Nazarov: Rukshin interview.
Konstantin Kohas: Kohas’s faculty page at http://www.math.spbu.ru/user/analysis/pers/kohas.html, accessed April 27, 2008.
terminology from Laurence Peter and Raymond Hull’s The Peter Principle: Laurence J. Peter, Raymond Hull, The Peter Principle (New York: Buccaneer Books, 1996), 46.
“He just didn’t quite have the temperament”: Anna Bogomolnaia, telephone interview with the author, April 18, 2008.
6. Guardian Angels
An open letter circulated by a group of American mathematicians: Khronika tekushikh sobytiy 51, December 1, 1978, http://www.memo.ru/history/DISS/chr/XTC51-60.htm, accessed July 31, 2008; quoted according to G. A. Freiman, It Seems I Am a Jew: A Samizdat Essay, trans. and ed. Melvyn B. Nathanson (Carbondale, IL: Southern Illinois University Press, 1980), 87.
Zalgaller and Burago concocted a plan: Viktor Zalgaller, interview with the author, Rehovot, Israel, March 16, 2008.
Aleksei Verner: Aleksei Verner and Valery Ryzhik, interview with the author, St. Petersburg, February 27, 2008.
his adviser was Vladimir Rokhlin: Mathematics Genealogy Project, http://www.genealogy.math.ndsu.nodak.edu/id.php?id=14999, accessed August 4, 2008.
Gromov . . . despaired of getting a research position: Olga Orlova, “Pochemu ucheniye prodolzhayut uezzhat’ iz Rossii,” an interview with Anatoly Vershik, http://www.svobodanews.ru/Article/2007/11/22/20071122161321910.html, accessed August 4, 2008.
So said the university’s website: http://www.ihp.jussieu.fr/, accessed August 4, 2008.
As I arrived in the cafeteria: Mikhail Gromov, interview with the author, Paris, June 24, 2008.
Geometry Festival: http://www.math.duke.edu/conferences/geomfest97/PreviousSpeakers.html, accessed August 4, 2008.
his first major published work: G. Perelman, Yu. Burago, M. Gromov, “Aleksandrov Spaces with Curvatures Bounded Below,” Russian Math Surveys 47, no. 2 (1992): 1–58.
Gromov mentioned Perelman to all the right people: Jeff Cheeger, New York University professor, interview with the author, New York City, April 1, 2008.
a French mathematician and historian of science: Jean-Michel Kantor, mathematician at the Institut Mathématiques à Jussieu, Université de Paris.
7. Round Trip
Gang Tian: Gang Tian, interview with the author, Princeton, NJ, November 9, 2007.
Lena . . . obtained her PhD in mathematics from the Weizmann Institute: http://www.weizmann.ac.il/acadaff/Scientific_Activities/2004/feinberg_degrees.html, accessed August 9, 2008.
Western mathematicians, while suffering from too narrow a focus: Andrei Minarsky, interview with the author, St. Petersburg, October 23, 2008.
Cheeger and his coauthor Detlef Gromoll: Jeff Cheeger and Detlef Gromoll, “On the Structure of Complete Manifolds of Nonnegative Curvature,” Annals of Mat
hematics 96 (1972): 413–43.
His paper was four pages long: Grigory Perelman, “Proof of the Soul Conjecture of Cheeger and Gromoll,” Journal of Differential Geometry 40 (1994): 209–12.
one of the best American graduate programs in mathematics: U.S. News & World Report rankings, http://grad-schools.usnews.rankingsandreviews.com/grad/mat/items/45094, accessed August 14, 2008.
Michael Anderson: Faculty page at http://www.math.sunysb.edu/~anderson/, accessed August 14, 2008; Michael Anderson, interview with the author, Stony Brook, NY, November 8, 2007.
Alexandrov spaces at the International Congress of Mathematicians: G. Perelman, “Spaces with Curvature Bounded Below,” http://www.ams.org/mathweb/icm94/04.perelman.html, accessed August 9, 2008.
fifty-five of the world’s top mathematicians: List of speakers at http://www.ams.org/mathweb/icm94/, accessed August 14, 2008.
four Fields Medalists, past and future: Richard Borcherds (1998), Gerd Faltings (1986), Maxim Kontsevich (1998), and Jean-Christophe Yoccoz (1994).
His speech seemed vague and disconnected: Two of the mathematicians quoted elsewhere in this book told me this, but neither one wanted the opinion attributed to him.
geometer Bruce Kleiner: Bruce Kleiner, interview with the author, New York City, April 9, 2008.
the conditions of the fellowship stated explicitly: Miller Fellowship description, http://millerinstitute.berkeley.edu/page.php?nav=11, accessed August 14, 2008.
Peter Sarnak: Peter Sarnak’s CV at http://www.math.ias.edu/media/SarnakCV.pdf, accessed August 15, 2008.
Sarnak recalled in an e-mail message: Peter Sarnak, e-mail to the author, June 1, 2008.
Perelman told several people at the time: Jeff Cheeger, New York University professor, interview with the author, New York City, April 1, 2008; Sarnak e-mail.
the European Mathematical Society held its second quadrennial congress: History of the European Mathematical Society at http://www.btinternet.com/~d.a.r.wallace/EMSHISTORY99.html, accessed September 25, 2008.
Anatoly Vershik submitted Perelman’s name: Anatoly Vershik, interview with the author, St. Petersburg, May 24, 2008.