DVD Review

Late Style—Yuri I. Manin Looking Back on a Life in Mathematics Reviewed by Gunther Cornelissen

Late Style—Yuri I. Manin Looking Back on a Life algebraic geometry. in Mathematics He supervised more Springer VideoMATH, 2012 than fifty Ph.D. US$39.95, Duration: 60 minutes students, many of ISBN-13: 978-3642244827 whom went on to do Directed by Agnes Handwerk and Harrie Willems great things. Apart from that, Manin published not only The expression “Late Style” derives from Adorno’s in the philosophy 1937 essay on the Spätstil of Beethoven. The phrase of mathematics and was used as the title of a course at Columbia Uni- physics but also in versity and later of a posthumous book by Edward socio-linguistics and Said, who explained that “Late Style” refers to “the Jungian psychol- way in which the work of some great artists and writers acquires a new idiom towards the end of ogy, and he wrote their lives.” Here one is viewing, however, “artistic a few collections of lateness not [necessarily] as harmony and resolu- poems and literary tion, but as intransigence, difficulty, and unre- reviews. This nonmathematical part of his works solved contradiction.” With the subtitle “Looking has now been preserved by the publication of his Back on a Life in Mathematics”, it is also the chosen book Mathematics as Metaphor; an English trans- title for a documentary about Yuri Manin. lation was published by the AMS, unfortunately Yuri Manin’s (1937–) variegated works span leaving out the literary works. In a foreword to much of diophantine geometry (including a proof this book, Freeman Dyson identified Manin as the of the Mordell conjecture over function fields, prototype of a “Bird”, a scientist possessing over- and pioneering the use of modular symbols, view and acting as a painter of large landscapes, p-adic automorphic forms, and noncommutative by contrast calling himself a “Frog”, more the sort geometry), algebraic geometry (Fano varieties, of animal that digs around locally in the mud (thus cubic surfaces), and mathematical physics (he is downplaying his own tremendous contributions the “M” in the ADHM construction of instantons, to science). was at the cradle of quantum computing and quan- From the current documentary, we pick up two tum cohomology, etc.). He wrote influential text- related viewpoints. Don Zagier, one of several books on mathematical logic, homological algebra, mathematicians who appear in the documentary, cubic forms, gauge theory, and noncommutative sees the work of Manin guided by the following principle: if one detects a similar structure in seemingly different areas, one should search for an Gunther Cornelissen is professor of mathematics at actual mathematical structure that bridges these Utrecht University, The Netherlands. His email address is [email protected]. fields. In the movie, Anatoly Vershik describes Manin as a product of the Soviet system, in which DOI: http://dx.doi.org/10.1090/noti932 many great minds that in freedom would choose

84 Notices of the AMS Volume 60, Number 1 literature, poetry, or psychology were scared away Without any concerns and efforts, and somehow from such pursuits by the need to embed their unnoticed, she came to possess all that set her so thoughts in Communist Party ideology. These far apart from the rest of the schoolgirls in the last minds turned to mathematics, where no such two years—gracefulness, elegance, litheness, and embedding was required, thereby enlarging the a clear brilliance in her eyes.” But it seems “light pool of different styles of doing mathematics. I breathing” does not create captivating movie char- very much view mathematics as possessing (or acters. By contrast, when Grothendieck enters the even being) a variety of different ways of speech. scene—certainly a person of rather heavy breath- Some of these are philosophical or poetical, while ing, if I may use this expression—he instantly others, equally valuable, are visual, formalistic, or becomes the dominant character even though computational. In this sense, Vershik’s description physically absent. reveals Moscow mathematics as a kaleidoscopic The first reaction to the movie by some of my potpourri of unparalleled variation. In an interview nonmathematical friends was that they found it in the Berlin Intelligencer (published for the Inter- unclear why they should watch a documentary national Congress of Mathematicians held in Berlin about this person. This shows the project largely in 1998), Manin described one of his life values by failed in revealing Manin as what he is: one of the the Renaissance term varietà, and we see a coher- most interesting mathematicians of our time. My ent reflection of this value in his work, which is first impression was that the movie missed its tar- always imbued with his own distinctively “literary” get, but I now believe that, rather than missing the style. Manin reflects on all of this in a fascinating target, the target itself went missing: the depiction interview with David Eisenbud that can be seen on of Manin as a character in this rendition of his life the website of the Simons Foundation’s “Science is ineffective. This stands in great contrast with the Lives” project. Despite the fact that the interview wealth of scientific, artistic, and literary ideas that is artificially cut up into fragments of ten minutes he has generated. Actually, Manin’s own thoughts or less, I would recommend anyone to watch it. about his life make an interesting meta-subject. My feelings about the movie under review are Also, the technical execution of the (obviously less positive. It is less contemplative, more bio- low-budget) project leaves something to be de- sired, despite the interesting musical score of graphical in the narrow sense, and also does not Tom Willems. For example, many transitions are explain any actual mathematics—not that this is images of Manin and his wife walking away from necessarily bad. In it, we see Manin go back to the camera in some outdoor scenery. Actually, his early university education in Moscow, and we the moviemakers seem to have a preference for experience his rise to fame and his visits to Paris, depicting—preferably old—people from the back where he interacted with Grothendieck. We also and for the use of backlighting and shaky hand- learn about his deliberate choice to sign the letter held cameras, which at first I found amusing but, to release Alexander Esenin-Volpin from involun- as the film progressed, irritated me more and tary psychiatric imprisonment, which led to the more. The movie contains pictures of and short withdrawal of Manin’s teaching rights and travel interviews with quite a few celebrated mathemati- permits. We see hints of the singularly lively sci- cians; recognizing them is pleasant, at least for the entific and cultural life in Moscow after the Stalin In Crowd, but maybe it is just too many faces and era, and we discover how Manin’s life was affected too little discourse. by the destruction of the iron curtain, followed As I mentioned before, I believe Manin is exactly by his subsequent travels, and his settlement in the person who could arrive at a very interesting Germany. After this, we switch to scenes from his reflection upon his own life, but such a reflection earliest youth in Crimea, including the story of is only alluded to in the present movie. Maybe it his father, who died young in the Second World was just too early, for what would the embodiment War, and his mother, a victim of the “rootless cos- of such a reflection be? Surely Yuri Manin is not mopolitanism” action, an anti-Semitic campaign the Beethoven of mathematics; from the aforemen- during the Stalin era. tioned book of Said, we extract musicologist Ruth The movie describes the life of an outstanding Subotnik’s description of Beethoven realizing, as and scrupulous scientist in a tumultuous environ- an older man facing death, that his work proclaims ment. This scientist, Manin, is a man of subtle that “no synthesis is conceivable.” By contrast, ideas, not an active dissident, though not without everything seems to point to Manin’s continuing influence. One aspect of his personality, “inner interest to see mathematics, and the whole intellec- freedom”, is described in the movie by Beilinson as tual project of humanity, as one big superstructure “light breathing”, apparently referring to the story to be revealed, analyzed, described, painted, sung of the same name by Ivan Bunin. In the story, Bunin about, and calculated in. Let us hope that he will describes one of his female characters as “afraid be with us much longer to help us uncover many of nothing—neither of ink stains on her fingers, more untrodden paths—that his Late Style is still nor of her face flushing; neither of her hair being to come. untidy, nor of exposing her knee when running.

January 2013 Notices of the AMS 85