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Late style: Yuri I. Manin looking back on a life in mathematics
Handwerk, A; Willems, H.00:55:00,published onJan 1, 2012,Springer,http://www.springer.com/us/book/9783642244827.Type:Video
Date Reviewed: May 17 2016

This is a biographical documentary about Yuri Manin, one of the greatest and most interesting mathematicians of our time, with a clear emphasis on the social and political context.

Together with Manin, we look at his alma mater, the legendary “Mech-Mat” (Faculty of Mechanics and Mathematics of the Moscow State University) characterized by him as follows: “nothing like Mech-Mat [in those days] existed anywhere in the world … maybe [only] in Paris during the best years.” Manin’s career, in his own words, was “swift and smooth.” At the International Congress of Mathematicians in Moscow in 1966, Leon Motchane, the founder of the Institut des Hautes Etudes Scientifiques, invited Manin to work there where he was substantially influenced by Grothendieck, an outstanding mathematician who “introduced a lot of new mathematics … and was very critical about many things.” Manin recalls: “meeting with him was one of great events in my life.”

Manin remembers the student revolt (1967) in Paris: “I was somewhat sad because they were doing propaganda for things not worthy of their enthusiasm. [...] We knew very well what ... Mao Zedong [was]. He was a much worsened version of Stalin. […] To take him as [an] ideal meant that they just did not understand anything about [the] realities of this world [...] and that saddened me very much.”

Manin was highly recognized by Soviet authorities and was awarded the Lenin Prize in 1967, but he did not want to be considered as “theirs.” He recalls: “I had to do something to show them that I am not theirs, but I did not want to do anything more.” In 1968, he co-signed a letter of 99 Soviet mathematicians against the forcible incarceration of Alexander Esenin-Volpin, a mathematician and a dissident, in a psychiatric hospital. For the next 20 years Manin was not allowed to travel abroad, “not allowed to teach standard courses, only special seminars ... but the best students came to me anyway”; so in his opinion, “it was not a great punishment.” He kept his small community of students, of family, of mathematics, and enjoyed it, and he obviously enjoyed working in Moscow: “the best place for doing mathematics.” An essential aspect of Manin’s personality, “inner freedom,” is described by Beilinson as “light breathing”: “he did not force his personality on anyone.”

In the late 1980s, Manin was finally able to accept invitations from foreign universities. Friedrich Hirzebruch, the founder of Max Planck Institute for Mathematics (MPIM), asked Manin to become his successor there. Manin worked as a co-director of MPIM from 1995 to 2007. Don Zagier, another co-director of MPIM, tells us that Manin was able to see unexpected and surprising connections between different branches of mathematics where no connections were seen before and that “this requires a very high level of thinking that most of us don’t possess.”

Manin and his colleagues discuss the intellectual environment in the Soviet Union when “you could completely forget about Marx, Engels, Lenin and Stalin [when] doing mathematics” (Manin); therefore, “many best and brightest people who could go to literature, humanities, business, etc. ... had to go to an area far from ideology, and they chose mathematics and physics” (Vershik). However, getting into Mech-Mat was very difficult for many because the undesirable applicants were screened out. For example, Michael Tsfasman recalls that two-thirds of the graduates of Moscow High School no. 2 (probably the best high school in Moscow in the 1960s and 1970s) were not allowed at the top universities because they were Jews, not communists, or independent thinkers (not even dissidents). (Manin notes that his mother lost her job in the late 1940s because of “cosmopolitanism” (being Jewish), leading to “a problem of how to live from one day to another day.”)

At the end of the video, Manin recalls that at the age of 4 he asked his father about the meaning of football, and the father explained that it was like trying to push a ball with a foot under a chair. Manin reacted, “I did not want to push the ball under the chair, I wanted to know what ‘football’ is.” This metaphor of trying to find out the structure of things and relationships among them characterizes very well Manin’s work in mathematics and, more generally, in culture [1]. We see a fragment about the Moscow Center of Continuous Mathematical Education (MCCME), the contemporary alma mater of future Russian mathematicians where Manin proudly notes that an excerpt from the Russian edition of [1] published by MCCME was included in a manual of Russian language for high school students, to be analyzed “as a very good example of a Russian literary text.” However, the authors did not stress Manin’s contributions to culture, and this is a pity because, while the strictly technical contributions by Manin may be understood only by some mathematicians, his cultural contributions may be understood and appreciated by many, both mathematicians and non-mathematicians.

Some very interesting fragments of the video are difficult to comprehend by an uninitiated viewer. For example, we see Manin and his wife visiting the offices of “Memorial,” a Russian history and human rights society, to study some documents. These episodes are of substantial semiotic value but may not be completely accessible to viewers unaware of the importance and role of “Memorial.” For another example, at the beginning of the video we see, without any comments and without any indication of what it is, a painting by Manin (Owl and Sun) prominently presented and discussed by Manin himself in [2]. I think that such fragments ought to have been explained.

The DVD is accompanied by a well-written 16-page brochure where Handwerk and Willems explain their work on the video and include short essays about Manin by his colleagues. Of note, Vershik stresses Manin’s ability to “discern something more important in a text than just a logically flawless argument ... [which allowed him] ... to embrace a larger spectrum of the intellectual world”; Ziegler emphasizes the title of one of Manin’s interviews (“Good Proofs Are Proofs That Make Us Wiser”): “this single, simple sentence contains so much truth and so much poetry about mathematics!”

Reviewer:  H. I. Kilov Review #: CR144416 (1609-0697)
1) Manin, Y. Mathematics as metaphor: selected essays. American Mathematical Society, Providence, RI, 2007.
2) Manin,Y. Dynamic functional asymmetry of brain hemispheres as a civilizational factor 7iskusstv.com/2013/Nomer11/Manin1.php (04/17/2016).
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