Yuri Ivanovich Manin (russian: Ю́рий Ива́нович Ма́нин; born 16 February 1937) is a Russian mathematician, known for work in

algebraic geometry Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...

and

diophantine geometry In mathematics, Diophantine geometry is the study of Diophantine equations by means of powerful methods in algebraic geometry. By the 20th century it became clear for some mathematicians that methods of algebraic geometry are ideal tools to study ...

, and many expository works ranging from

mathematical logic Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of forma ...

theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experim ...

. Moreover, Manin was one of the first to propose the idea of a

quantum computer Quantum computing is a type of computation whose operations can harness the phenomena of quantum mechanics, such as superposition, interference, and entanglement. Devices that perform quantum computations are known as quantum computers. Thoug ...

1980 Events January * January 4 – U.S. President Jimmy Carter proclaims a grain embargo against the USSR with the support of the European Commission. * January 6 – Global Positioning System time epoch begins at 00:00 UTC. * January 9 ...

with his book ''Computable and Uncomputable''.

Life and career

Manin gained a doctorate in 1960 at the Steklov Mathematics Institute as a student of

Igor Shafarevich Igor Rostislavovich Shafarevich (russian: И́горь Ростисла́вович Шафаре́вич; 3 June 1923 – 19 February 2017) was a Soviet and Russian mathematician who contributed to algebraic number theory and algebraic geometry. ...

. He is now a Professor at the Max-Planck-Institut für Mathematik in

Bonn The federal city of Bonn ( lat, Bonna) is a city on the banks of the Rhine in the German state of North Rhine-Westphalia, with a population of over 300,000. About south-southeast of Cologne, Bonn is in the southernmost part of the Rhine-Ru ...

, and a professor

emeritus ''Emeritus'' (; female: ''emerita'') is an adjective used to designate a retired chair, professor, pastor, bishop, pope, director, president, prime minister, rabbi, emperor, or other person who has been "permitted to retain as an honorary title ...

Northwestern University Northwestern University is a private research university in Evanston, Illinois. Founded in 1851, Northwestern is the oldest chartered university in Illinois and is ranked among the most prestigious academic institutions in the world. Charte ...

. Manin's early work included papers on the arithmetic and

formal group In mathematics, a formal group law is (roughly speaking) a formal power series behaving as if it were the product of a Lie group. They were introduced by . The term formal group sometimes means the same as formal group law, and sometimes means one ...

s of

abelian varieties In mathematics, particularly in algebraic geometry, complex analysis and algebraic number theory, an abelian variety is a Algebraic variety#Projective variety, projective algebraic variety that is also an algebraic group, i.e., has a group law th ...

, the

Mordell conjecture Louis Joel Mordell (28 January 1888 – 12 March 1972) was an American-born British mathematician, known for pioneering research in number theory. He was born in Philadelphia, United States, in a Jewish family of Lithuanian extraction. Educ ...

in the function field case, and

algebraic differential equation In mathematics, an algebraic differential equation is a differential equation that can be expressed by means of differential algebra. There are several such notions, according to the concept of differential algebra used. The intention is to i ...

s. The

Gauss–Manin connection In mathematics, the Gauss–Manin connection is a connection on a certain vector bundle over a base space ''S'' of a family of algebraic varieties V_s. The fibers of the vector bundle are the de Rham cohomology groups H^k_(V_s) of the fibers V_s o ...

is a basic ingredient of the study of

cohomology In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups, usually one associated with a topological space, often defined from a cochain complex. Cohomology can be view ...

in families of

algebraic varieties Algebraic varieties are the central objects of study in algebraic geometry, a sub-field of mathematics. Classically, an algebraic variety is defined as the set of solutions of a system of polynomial equations over the real or complex numbers. ...

. He wrote a book on

cubic surface In mathematics, a cubic surface is a surface in 3-dimensional space defined by one polynomial equation of degree 3. Cubic surfaces are fundamental examples in algebraic geometry. The theory is simplified by working in projective space rather tha ...

s and

cubic form In mathematics, a cubic form is a homogeneous polynomial of degree 3, and a cubic hypersurface is the zero set of a cubic form. In the case of a cubic form in three variables, the zero set is a cubic plane curve. In , Boris Delone and Dmitry ...

s, showing how to apply both classical and contemporary methods of algebraic geometry, as well as

nonassociative algebra A non-associative algebra (or distributive algebra) is an algebra over a field where the binary multiplication operation is not assumed to be associative. That is, an algebraic structure ''A'' is a non-associative algebra over a field ''K'' if ...

. He also indicated the role of the

Brauer group Brauer or Bräuer is a surname of German origin, meaning "brewer". Notable people with the name include:- * Alfred Brauer (1894–1985), German-American mathematician, brother of Richard * Andreas Brauer (born 1973), German film producer * Arik ...

, via Grothendieck's theory of global

Azumaya algebra In mathematics, an Azumaya algebra is a generalization of central simple algebras to ''R''-algebras where ''R'' need not be a field. Such a notion was introduced in a 1951 paper of Goro Azumaya, for the case where ''R'' is a commutative local rin ...

s, in accounting for obstructions to the

Hasse principle In mathematics, Helmut Hasse's local–global principle, also known as the Hasse principle, is the idea that one can find an diophantine equation, integer solution to an equation by using the Chinese remainder theorem to piece together solutions mod ...

, setting off a generation of further work. He pioneered the field of

arithmetic topology Arithmetic topology is an area of mathematics that is a combination of algebraic number theory and topology. It establishes an analogy between number fields and closed, orientable 3-manifolds. Analogies The following are some of the analogies used ...

(along with

John Tate John Tate may refer to: * John Tate (mathematician) (1925–2019), American mathematician * John Torrence Tate Sr. (1889–1950), American physicist * John Tate (Australian politician) (1895–1977) * John Tate (actor) (1915–1979), Australian a ...

David Mumford David Bryant Mumford (born 11 June 1937) is an American mathematician known for his work in algebraic geometry and then for research into vision and pattern theory. He won the Fields Medal and was a MacArthur Fellow. In 2010 he was awarded t ...

Michael Artin Michael Artin (; born 28 June 1934) is a German-American mathematician and a professor emeritus in the Massachusetts Institute of Technology mathematics department, known for his contributions to algebraic geometry.Barry Mazur Barry Charles Mazur (; born December 19, 1937) is an American mathematician and the Gerhard Gade University Professor at Harvard University. His contributions to mathematics include his contributions to Wiles's proof of Fermat's Last Theorem ...

). He also formulated the

Manin conjecture In mathematics, the Manin conjecture describes the conjectural distribution of rational points on an algebraic variety relative to a suitable height function. It was proposed by Yuri I. Manin and his collaborators in 1989 when they initiated a p ...

, which predicts the asymptotic behaviour of the number of rational points of bounded height on algebraic varieties. He has further written on

Yang–Mills theory In mathematical physics, Yang–Mills theory is a gauge theory based on a special unitary group SU(''N''), or more generally any compact, reductive Lie algebra. Yang–Mills theory seeks to describe the behavior of elementary particles using t ...

quantum information Quantum information is the information of the state of a quantum system. It is the basic entity of study in quantum information theory, and can be manipulated using quantum information processing techniques. Quantum information refers to both ...

, and

mirror symmetry In mathematics, reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry is symmetry with respect to a reflection. That is, a figure which does not change upon undergoing a reflection has reflectional symmetry. In 2D ther ...

. Manin had over 40 doctoral students, including

Vladimir Berkovich Vladimir Berkovich is a mathematician at the Weizmann Institute of Science who introduced Berkovich spaces. His Ph.D. advisor was Yuri I. Manin. Berkovich was a visiting scholar at the Institute for Advanced Study in 1991-92 and again in the summe ...

Mariusz Wodzicki Mariusz Wodzicki (Count Wodzicki) (born 1956) is a Polish mathematician and nobleman, whose works primarily focus on analysis, algebraic k-theory, noncommutative geometry, and algebraic geometry. Wodzicki was born in Bytom, Poland in 1956. He rec ...

Alexander Beilinson Alexander A. Beilinson (born 1957) is the David and Mary Winton Green University professor at the University of Chicago and works on mathematics. His research has spanned representation theory, algebraic geometry and mathematical physics. In 1 ...

Ivan Cherednik Ivan Cherednik (Иван Владимирович Чередник) is a Russian-American mathematician. He introduced double affine Hecke algebras, and used them to prove Macdonald's constant term conjecture in . He has also dealt with algebr ...

Alexei Skorobogatov Alexei Nikolaievich Skorobogatov (russian: Алексе́й Никола́евич Скоробога́тов) is a British-Russian mathematician and Professor in Pure Mathematics at Imperial College London specialising in algebraic geometry. His ...

Vladimir Drinfeld Vladimir Gershonovich Drinfeld ( uk, Володи́мир Ге́ршонович Дрінфельд; russian: Влади́мир Ге́ршонович Дри́нфельд; born February 14, 1954), surname also romanized as Drinfel'd, is a renowne ...

Mikhail Kapranov Mikhail Kapranov, (Михаил Михайлович Капранов, born 1962) is a Russian mathematician, specializing in algebraic geometry, representation theory, mathematical physics, and category theory. He is currently a professor of the ...

Vyacheslav Shokurov Vyacheslav Vladimirovich Shokurov (russian: Вячеслав Владимирович Шокуров; born 18 May 1950) is a Russian mathematician best known for his research in algebraic geometry. The proof of the Noether–Enriques–Petri the ...

, Arend Bayer and Victor Kolyvagin, as well as foreign students including Hà Huy Khoái.

Awards

He was awarded the Brouwer Medal in 1987, the first

Nemmers Prize in Mathematics The Frederic Esser Nemmers Prize in Mathematics is awarded biennially from Northwestern University. It was initially endowed along with a companion prize, the Erwin Plein Nemmers Prize in Economics, as part of a $14 million donation from the Nemme ...

in 1994, the

Schock Prize The Rolf Schock Prizes were established and endowed by bequest of philosopher and artist Rolf Schock (1933–1986). The prizes were first awarded in Stockholm Stockholm () is the capital and largest city of Sweden as well as the largest ...

of the

Royal Swedish Academy of Sciences The Royal Swedish Academy of Sciences ( sv, Kungliga Vetenskapsakademien) is one of the royal academies of Sweden. Founded on 2 June 1739, it is an independent, non-governmental scientific organization that takes special responsibility for prom ...

in 1999, the Cantor Medal of the

German Mathematical Society The German Mathematical Society (german: Deutsche Mathematiker-Vereinigung, DMV) is the main professional society of German mathematicians and represents German mathematics within the European Mathematical Society (EMS) and the International Math ...

in 2002, the

King Faisal International Prize The King Faisal Prize ( ar, جائزة الملك فيصل, formerly King Faisal International Prize), is an annual award sponsored by King Faisal Foundation presented to "dedicated men and women whose contributions make a positive difference". T ...

in 2002 and the

Bolyai Prize The International János Bolyai Prize of Mathematics is an international prize founded by the Hungarian Academy of Sciences. The prize is named after János Bolyai and is awarded every five years to mathematicians for monographs with important new r ...

of the

Hungarian Academy of Sciences The Hungarian Academy of Sciences ( hu, Magyar Tudományos Akadémia, MTA) is the most important and prestigious learned society of Hungary. Its seat is at the bank of the Danube in Budapest, between Széchenyi rakpart and Akadémia utca. Its ma ...

in 2010. In 1990 he became a foreign member of the

Royal Netherlands Academy of Arts and Sciences The Royal Netherlands Academy of Arts and Sciences ( nl, Koninklijke Nederlandse Akademie van Wetenschappen, abbreviated: KNAW) is an organization dedicated to the advancement of science and literature in the Netherlands. The academy is housed ...

Works

* Manin: ''Selected works with commentary'', World Scientific 1996 * Manin:
Mathematics as metaphor - selected essays
', American Mathematical Society 2009 * Manin:
Rational points of algebraic curves over function fields
'. AMS translations 1966 (Mordell conjecture for function fields) * Manin:
Algebraic topology of algebraic varieties
'. Russian Mathematical Surveys 1965 * Manin: ''Modular forms and Number Theory''. International Congress of Mathematicians, Helsinki 1978 * Manin:
Frobenius manifolds, quantum cohomology, and moduli spaces
', American Mathematical Society 1999 * Manin:
Quantum groups and non commutative geometry
', Montreal, Centre de Recherches Mathématiques, 1988 * Manin:
Topics in non-commutative geometry
', Princeton University Press 1991 * Manin:
Gauge field theory and complex geometry
'. Springer 1988 (Grundlehren der mathematischen Wissenschaften) * Manin:
Cubic forms - algebra, geometry, arithmetics
', North Holland 1986 * Manin:
A course in mathematical logic
', Springer 1977, second expanded edition with new chapters by the author and

Boris Zilber Boris Zilber (russian: Борис Иосифович Зильбер, born 1949) is a Soviet-British mathematician who works in mathematical logic, specifically model theory. He is a professor of mathematical logic at the University of Oxford. H ...

, Springer 2010. * Manin: ''The provable and the unprovable'' (Russ.), Moscow 1979 * Manin: ''Computable and Uncomputable'' (Russ.), Moscow 1980 * Manin:
Mathematics and physics
', Birkhäuser 1981 * Manin:
New dimensions in geometry
'. in Arbeitstagung Bonn 1984, Lectures Notes in Mathematics Vol. 1111, Springer Verlag * Manin,

Alexei Ivanovich Kostrikin Alexei Ivanovich Kostrikin (russian: Алексей Иванович Кострикин) (12 February 1929 – 22 September 2000) was a Russian mathematician, specializing in algebra and algebraic geometry. Life Kostrikin graduated from the ...

: '' Linear algebra and geometry'', Gordon and Breach 1989 * Manin, Sergei Gelfand:
Homological algebra
', Springer 1994 (Encyclopedia of mathematical sciences). * Manin, Sergei Gelfand:
Methods of Homological algebra
', Springer 1996 * Manin, Igor Kobzarev:
Elementary Particles: mathematics, physics and philosophy
', Dordrecht, Kluwer, 1989 (This book is introductory.) * Manin, Alexei A. Panchishkin:
Introduction to Number theory
', Springer Verlag 1995, 2nd edn. 2005 * Manin
Moduli, Motives, Mirrors
', 3. European Congress Math. Barcelona 2000, Plenary talk * Manin
Classical computing, quantum computing and Shor´s factoring algorithm
', Bourbaki Seminar 1999 * Manin
Von Zahlen und Figuren
' 2002 * Manin,

Matilde Marcolli Matilde Marcolli is an Italian and American mathematical physicist. She has conducted research work in areas of mathematics and theoretical physics; obtained the Heinz Maier-Leibnitz-Preis of the Deutsche Forschungsgemeinschaft, and the Sofia Ko ...

Holography principle and arithmetic of algebraic curves
', 2002 * Manin
3-dimensional hyperbolic geometry as infinite-adic Arakelov geometry
', Inventiones Mathematicae 1991 * Manin:

', e-enterprise, 2014

References

External links

*
Manin's page at Max-Planck-Institut für Mathematik website
*

', interview by Martin Aigner and Vasco A. Schmidt
Biography
{{DEFAULTSORT:Manin, Yuri 1937 births Living people Scientists from Simferopol Algebraic geometers Algebraists Moscow State University alumni Northwestern University faculty Members of the Pontifical Academy of Sciences Members of the French Academy of Sciences Members of the Royal Netherlands Academy of Arts and Sciences Corresponding Members of the Russian Academy of Sciences Rolf Schock Prize laureates Brouwer Medalists Soviet mathematicians 21st-century Russian mathematicians 20th-century Russian mathematicians Knights Commander of the Order of Merit of the Federal Republic of Germany Recipients of the Pour le Mérite (civil class) Quantum information scientists Max Planck Institute directors

Life and career

Awards

Works

See also

References

Further reading

External links