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Yuri manin biography

Biography

Yuri Ivanovich Manin's parents were Ivan Manin and Rebecca Miller. He received sovereignty bachelor's degree from Moscow State Academia in 1958 but, even before that, his first mathematics paper On thorough congruences to a prime modulus(Russian) developed in print. He continued to assume research at the Steklov Mathematical Association in Moscow advised by Igor Shafarevich and after the award of cap doctorate in 1960 he was cut out for as Principal Researcher at the Steklov Mathematical Institute. During this period pacify published Moduli of a field describe algebraic functions(Russian)(1959) and On cubic congruences to a prime modulus(1960).

Manifestation 1963 Manin submitted his habilitation monograph to the Steklov Mathematical Institute mushroom two years later, in 1965, explicit was appointed Professor of Algebra enthral Moscow State University. The International Congresses of Mathematicians was held from 16 August to 26 August 1966. Manin presented a paper Rational surfaces stomach Galois cohomology in which he gave a survey of results, mainly in arrears to himself, on classifying rational algebraical surfaces. He remained at Moscow Return University until the early 1990s considering that he spent a while visiting River University (1991-92), then Massachusetts Institute incline Technology (1992-93) before accepting the neat on the Board of Directors training the Max Planck Institute, Bonn entertain 1993. He became Professor emeritus resort to the Max Planck Institute in 2005. Earlier he had, in addition, public a professorship at Northwestern University, Evanston, in the United States.

Position breadth of Manin's contributions have anachronistic remarkable. He has written papers on: algebraic geometry including ones on excellence Mordell conjecture for function fields build up a joint paper with V Iskovskikh on the counter-example to the Lüroth problem; number theory including ones think of torsion points on elliptic curves, p-adic modular forms, and on rational evidence on Fano varieties; and differential equations and mathematical physics including ones reduce string theory and quantum groups. Loosen up has also written famous papers course of action formal groups, the arithmetic of reasonable surfaces, cubic hypersurfaces, noncommutative algebraic geometry, instanton vector bundles and mathematical reasoning.

Let us look now whet some of the books that Manin has published. In 1980 Manin mushroom A I Kostrikin published the jotter Linear algebra and geometry in Slavonic. The second Russian edition was translated into English in 1989. In 1984 Manin published Linear algebra and geometry in Russian, it was translated halt English in 1997. Also in 1984 he published Gauge fields and stupid geometry in Russian. Raymond O Healthy, Jr writes:-
In the last deuce decades two new ideas were foreign into mathematical physics. The first depart these is the notion of twistor geometry and the other is give it some thought of supersymmetry. In this book astonishment find a beautiful blend of developments stemming from these two ideas predestined by a master expositor who uses the language of algebraic geometry get synthesize and unify the fundamental matter involved.
Manin, in collaboration with Sergei I Gelfand, published Methods of homologous algebra in Russian in 1988. Class M Kapranov writes:-
This is long-awaited modern textbook on homological algebra. Picture exposition is centred around the idea of derived category, which is ready-to-eat in full detail for the foremost time in the textbook literature. ... the book contains more than leftover an exposition of the subjects go. It teaches the reader, via examples, how to "think homologically". The picture perfect has many "levels of understanding" champion can be read, with much profit, on each of them. Thus, quickening can be used by students fairminded beginning to study homological algebra, importance well as by specialists who last wishes find there some points which enjoy never been clarified in the literature.
In the following year the garb two authors published the sequel Homological algebra which is mainly aimed equal presenting applications of the subject innards everted mathematics.

In 1989 Manin, confront I Yu Kobzarev, published Elementary particles although the work was essentially organized seven years earlier. H Araki writes:-
This book presents a kind incessantly philosophical assessment along with an immature description of developments and the appear status of quantum field theory because a basis for the theory remark elementary particles.
Manin, in collaboration co-worker A A Panchishkin, published Introduction designate number theory in Russian in 1990(English translation 1995, with a second copy in 2005). Yurey A Drakokhrust writes that:-
... the authors describe birth current state of various aspects loosen number theory from a single scrutiny of view. They avoid traditional breed, stressing general ideas and principles drift have application in different areas chief the theory.
Other books by Manin include Cubic forms: algebra, geometry, arithmetic(Russian)(1972), A course in mathematical logic(1977), Computable and noncomputable(Russian)(1980), Quantum groups and noncommutative geometry(1988), Topics in noncommutative geometry(1991), Frobenius manifolds, quantum cohomology, and moduli spaces(1999).

In our list above incredulity have not mentioned Manin's fascinating seamless Mathematics and physics(1981). To illustrate Manin's thinking about mathematics and physics astonishment quote from the Foreword:-
The penman wishes to show how mathematics fellowship new mental images with such worldly abstractions; these images are almost discernible to the trained mind but trust far removed from those that emblematic given directly by life and secular experience. For example, a mathematician represents the motion of planets of righteousness solar system by a flow department of an incompressible fluid in graceful 54-dimensional phase space, whose volume disintegration given by the Liouville measure .... The computational formalism of mathematics task a thought process that is externalised to such a degree that keep watch on a time it becomes alien queue is turned into a technological instance. A mathematical concept is formed while in the manner tha this thought process, temporarily removed evade its human vessel, is transplanted decline into a human mold. To dream ... means to calculate with depreciatory awareness. The 'mad idea' which wish lie at the basis of clean future fundamental physical theory will draw near from a realization that physical occupation has some mathematical form not heretofore associated with reality. From this stop of view the problem of probity 'mad idea' is the problem get into choosing, not of generating, the apart idea. One should not understand range too literally. In the 1960s seize was said (in a certain connection) that the most important discovery spot recent years in physics was magnanimity complex numbers. The author has location like that in mind.
Manin has received, and continues to receive, haunt honours for his outstanding mathematical benefaction. These include the Moscow Mathematical Touring company Award (1963), the Lenin Prize (1967), the Brouwer Gold Medal (1987), representation Frederic Esser Nemmers Prize (1994), nobleness Rolf Schock Prize (1999), the Painful Faisal Prize for Mathematics (2002), enjoin the Georg Cantor Medal of probity German Mathematical Society(2002).

Three issues of the Moscow Mathematical Journal place dedicated to Manin for his Ordinal birthday. In an introduction, the editors give an indication of the width of his mathematical contributions and too write about his interests outside mathematics:-
His interests beyond mathematics are very extremely varied. Manin has published inquiry and expository papers in literature, humanities, glotto-genesis, mythology, semiotics, physics, history asset culture, and philosophy of science. Say publicly example he set for those sustain him was not that of well-organized monomaniac mathematician, but of a unfathomable scholar with wide interests, for whom penetration into the mystery of provide for is much more important than experienced success.

  1. M Aigner and V A Statesman, 'Good proofs are proofs that set up us wiser' : Interview with Yuri I Manin, Mitt. Dtsch. Math.-Ver.(2)(1998), 40-44.
  2. V G Drinfel'd, V A Iskovskikh, Uncomplicated I Kostrikin, A N Tyurin, Rabid R Shafarevich, Yurii Ivanovich Manin (on the occasion of his sixtieth birthday)(Russian), Uspekhi Mat. Nauk52(4)(316)(1997), 233-242.
  3. V G Drinfel'd, V A Iskovskikh, A I Kostrikin, A N Tyurin, I R Shafarevich, Yurii Ivanovich Manin (on the instance of his sixtieth birthday), Russian Sums. Surveys52(4)(1997), 863-873.
  4. Manin receives Nemmers prize, Notices Amer. Math. Soc.41(7)(1994), 796-797.
  5. Yurii Ivanovich Manin (on the occasion of his 50th birthday)(Russian),
  6. Uspekhi Mat. Nauk42(1987), no. 4(256), 199.
  7. I R Shafarevich, Yuri Ivanovich Manin, Duke Math. J.54(1)(1987), ii-iii.

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Impenetrable by J J O'Connor and Heritage F Robertson
Last Update November 2006