Abstract
This is a personal view of and commentary on Yuri Manin’s relationship with mathematics, philosophy, literature, poetry, art, and culture. His life epitomized those of the great natural philosophers of yore.
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Notes
- 1.
I can tell the exact date because I keep a diary.
- 2.
In fact, Manin was hired as one of the directors. The Max Plank Institutes have no “permanent professors” but only directors. (I thank J.-P. Bourguignon for this clarification.)
- 3.
From Tarkovsky’s diary, one gets the impression that these troubles arose not because of an opposition to the authorities, but because of the spiritual themes that are present in his movies.
- 4.
For all these quotes from Tarkovsky’s book, I am using the English translation which appeared in 1994 (Tarkovsky 1994).
- 5.
[My note] The Lenin prize was one of the most prestigious prizes (maybe the most prestigious one) of the Soviet Union. Manin received it in 1967. Among the other recipients, let me mention Andrei Sakharov, Sergei Prokofiev, Dmitry Shostakovich, Sviatoslav Richter, and, among the mathematicians, Vladimir Arnol’d and Andrei Kolmogorov.
- 6.
I learned later on that Bulgakov was a medical doctor, just as Chekhov was. Incidentally, Bulgakov wrote a book titled A country doctor’s notebook, in a very classical style (unlike The master and Margarita), which he thought of as a parallel to Chekhov’s medical tales.
- 7.
I also know that the oncologist Léon Schwartzenberg, who was treating Manin and who, together with his partner Marina Vlady had become close to him during the last moments of his life, declared once that he could not do his treatment on Tarkovsky in an efficient manner because the latter refused to take the classical drugs.
- 8.
The passage is also included in the introduction of (Manin 2007).
- 9.
The joining of like to unlike was at the basis of the philosophies of Heraclitus, Anaximander, and the Pythagoreans.
- 10.
The passage is also included in the Introduction to his book Mathematics as metaphor (Manin 2007).
- 11.
The famous linguist Ferdinand de Saussure (1857–1913), considered as the founder of modern linguistics, in his Cours de linguistique générale, makes a distinction between the following three notions: langue, the result of a social convention transmitted by society to man and for which the latter does not play any important role, langage, as the capacity that allows human beings to communicate and interact with each other, and parole, as the personal use of language. Note that English makes no difference between “langue” and “langage.”
- 12.
Manin says that this expression is in Pushkin. Actually, I found it in Walter Scott’s Rob Roy (1817), and also in a poem by Dovid Knut (1900–1955), a Russian-Jewish emigre of the first generation who published his poems in Paris in the 1920s.
- 13.
Manin puts this expression in quotation marks, and it is not clear whether he intends the literal or the Freudian meaning of this expression; both may fit here (although, from what I know, Manin was not a strong supporter of Freud, maybe because of Freud’s materialistic side).
- 14.
The first terms \( {\sum \limits}_{n=1}^N\, {\mathrm{a}}_n{\mathrm{e}}^{inx} \) of the Fourier series is a trigonometric polynomial which can be put in parallel with Ptolemy’s superposition of periodic motions.
- 15.
To quote again Russian authors, I mention Sergei Bulgakov, who writes that man is a “microcosm, and his imprint therefore lies upon the entire world, the macrocosm,” and that “by his body man belongs to the creaturely world, which, he, as microcosm, has in himself and unifies and generalizes,” (Bulgakov 2008, pp. 173, 279), etc.
- 16.
The founder of cosmism is considered to be Nikolaï Fiodorov (1829–1903). The movement was developed especially in the first three decades of the twentieth century, before it was squashed brutally by Stalin. This movement inspired writers, philosophers, composers, theater directors, and artists, like Leo Tolstoi, Alexander Scriabin, Vassily Kandinsky, Casimir Malevic, Vladimir Soloviev, and Sergei Bulgakov.
- 17.
The word theory comes from the Greek word “theōria,” which means “contemplation.”
- 18.
The article is a joint work with Matilde Marcolli.
- 19.
The mathematician, theologian, physicist, philosopher, and historian of art Pavel Florensky (1882–1937) was dubbed the “Russian Leonardo” and the “Pascal of the Gulag.” Solzhenitsyn said about him that he was “perhaps the most remarkable person devoured by the Gulag.” The translation of his books and articles in French, English, Romanian, and other languages have taken an accelerated pace in the last two decades. I wrote an article on him for the present Handbook (Papadopoulos 2023).
- 20.
Since the Greeks, talking about mathematics means proving.
- 21.
The episode is told in a chapter titled Spontaneous Artistic Activity, Origin of logograms, and Mathematical Intuition. This chapter is not contained in the English version of the book.
- 22.
Manin was very happy of the fact that the French version of the book, which appeared in 2022, included the poems. The French translation of his book was done by Claire Vajou, but it is certain that the translation of his poems was done with his close collaboration, maybe by him alone (he was completely fluent in French).
- 23.
The passage is also reproduced in the Introduction of Mathematics as metaphor (Manin 2007).
- 24.
The idea that abstract mathematical objects exist independently of us and our knowledge of them is one of the basic teachings of Plato, who also considered that knowledge (which, for him, is, to a large extent, mathematical), is simply recollection (anamnesis) of innate knowledge, about preexisting things. The standard reference for this theory of anamnesis is Plato’s Meno 81e1–82b8. It is worth noting that in this passage, Plato, to illustrate his idea, brings in Socrates helping a slave boy recollecting a specific knowledge, which, in fact, is a mathematical knowledge: how to construct a square whose area is twice that of another given square. S. Negrepontis explained to me that the method Socrates uses for this recollection turns out to be anthyphaeretic division. Finally, let me recall that “Platonism,” as a belief in preexisiting objects (outside our thought), is contrary to the intuitionistic trend in mathematics (mostly represented, in the modern period, by Brouwer), which holds that mathematical objects exist only when we can construct them.
- 25.
As Plotnitsky rightly points out in his essay Continuity and discontinuity in, and between, mathematics and physics (Plotnitsky 2023): “mathematical Platonism (which is a twentieth-century conception) should not be confused with Plato’s own philosophy.” In fact, the term “Platonic” is often used and misused. A Japanese friend told me that in Japan, this word is used exclusively (as a Japanese word) as an adjective for a love relation, to say that it is purely mental.
- 26.
“[…] The Infinite occurs in the Saying […]” [My bad translation], from his book Autrement qu’être ou au-delà de l’essence (Levinas 1990, p. 230).
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Acknowledgments
I would like to thank Arkady Plotnitsky and Susumu Tanabé who kindly made several interesting comments on a previous version of this chapter. This work is supported by the lnterdisciplinary Thematic lnstitute CREAA, as part of the ITl 2021–2028 program of the University of Strasbourg, CNRS and Inserm (ldEx Unistra ANR-10-IDEX-0002), and the French lnvestments for the Future Program.
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Papadopoulos, A. (2023). Yuri Ivanovich Manin (1937–2023): Mathematics, Philosophy, and Poetry. In: Sriraman, B. (eds) Handbook of the History and Philosophy of Mathematical Practice. Springer, Cham. https://doi.org/10.1007/978-3-030-19071-2_143-1
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