Sergei Petrovich Novikov (

Russian Russian(s) may refer to: *Russians (), an ethnic group of the East Slavic peoples, primarily living in Russia and neighboring countries *A citizen of Russia *Russian language, the most widely spoken of the Slavic languages *''The Russians'', a b ...

: Серге́й Петро́вич Но́виков ; 20 March 19386 June 2024) was a Soviet and Russian mathematician, noted for work in both

algebraic topology Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariant (mathematics), invariants that classification theorem, classify topological spaces up t ...

and soliton theory. He became the first Soviet mathematician to receive the

Fields Medal The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of Mathematicians, International Congress of the International Mathematical Union (IMU), a meeting that takes place e ...

in 1970.

Biography

Novikov was born on 20 March 1938 in Gorky,

Soviet Union The Union of Soviet Socialist Republics. (USSR), commonly known as the Soviet Union, was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 until Dissolution of the Soviet ...

(now

Nizhny Novgorod Nizhny Novgorod ( ; rus, links=no, Нижний Новгород, a=Ru-Nizhny Novgorod.ogg, p=ˈnʲiʐnʲɪj ˈnovɡərət, t=Lower Newtown; colloquially shortened to Nizhny) is a city and the administrative centre of Nizhny Novgorod Oblast an ...

Russia Russia, or the Russian Federation, is a country spanning Eastern Europe and North Asia. It is the list of countries and dependencies by area, largest country in the world, and extends across Time in Russia, eleven time zones, sharing Borders ...

). He grew up in a family of talented mathematicians. His father was Pyotr Sergeyevich Novikov, who gave a negative solution to the

word problem for groups A word is a basic element of language that carries meaning, can be used on its own, and is uninterruptible. Despite the fact that language speakers often have an intuitive grasp of what a word is, there is no consensus among linguists on its ...

. His mother, Lyudmila Vsevolodovna Keldysh, and maternal uncle,

Mstislav Vsevolodovich Keldysh Mstislav Vsevolodovich Keldysh (; – 24 June 1978) was a Soviet mathematician who worked as an engineer in the Soviet space program. He was the academician of the Academy of Sciences of the Soviet Union (1946), President of the Academy of Sci ...

, were also important mathematicians. Novikov entered

Moscow State University Moscow State University (MSU), officially M. V. Lomonosov Moscow State University,. is a public university, public research university in Moscow, Russia. The university includes 15 research institutes, 43 faculties, more than 300 departments, a ...

in 1955 and graduated in 1960. In 1964, he received the

Moscow Mathematical Society The Moscow Mathematical Society (MMS) is a society of Moscow mathematicians aimed at the development of mathematics in Russia. It was created in 1864, and Victor Vassiliev is the current president. History The first meeting of the society w ...

Award for young mathematicians and defended a dissertation for the ''Candidate of Science in Physics and Mathematics'' degree (equivalent to the

PhD A Doctor of Philosophy (PhD, DPhil; or ) is a terminal degree that usually denotes the highest level of academic achievement in a given discipline and is awarded following a course of graduate study and original research. The name of the deg ...

) under

Mikhail Postnikov Mikhail Mikhailovich Postnikov (; 27 October 1927 – 27 May 2004) was a Soviet mathematician, known for his work in algebraic and differential topology. Biography He was born in Shatura, near Moscow. He received his Ph.D. from Moscow State ...

at Moscow State University. In 1965, he defended a dissertation for the ''Doctor of Science in Physics and Mathematics'' degree there. Novikov died on 6 June 2024, at the age of 86.

Career

In 1966, Novikov became a corresponding member of the

Academy of Sciences of the Soviet Union The Academy of Sciences of the Soviet Union was the highest scientific institution of the Soviet Union from 1925 to 1991. It united the country's leading scientists and was subordinated directly to the Council of Ministers of the Soviet Union (un ...

. In 1971, he became head of the Mathematics Division of the

Landau Institute for Theoretical Physics Landau (), officially Landau in der Pfalz (, ), is an autonomous (''kreisfrei'') town surrounded by the Südliche Weinstraße ("Southern Wine Route") district of southern Rhineland-Palatinate, Germany. It is a university town (since 1990), a long ...

of the USSR Academy of Sciences. In 1983, Novikov was also appointed the head of the Department of Higher Geometry and Topology at

. He became President of the

in 1985 and remained in that role until 1996, when he moved to the

University of Maryland College of Computer, Mathematical, and Natural Sciences The College of Computer, Mathematical, and Natural Sciences (CMNS) at the University of Maryland, College Park, is home to ten academic departments and a dozen interdisciplinary research centers and institutes. CMNS is one of 13 schools and colle ...

at the

University of Maryland, College Park The University of Maryland, College Park (University of Maryland, UMD, or simply Maryland) is a public university, public Land-grant university, land-grant research university in College Park, Maryland, United States. Founded in 1856, UMD i ...

. He continued to maintain research appointments at the Landau Institute for Theoretical Physics, Moscow State University, and the Department of Geometry and Topology at the

Steklov Mathematical Institute Steklov Institute of Mathematics or Steklov Mathematical Institute () is a premier research institute based in Moscow, specialized in mathematics, and a part of the Russian Academy of Sciences. The institute is named after Vladimir Andreevich Ste ...

after his move to Maryland.

Research

Novikov's early work was in

cobordism theory In mathematics, cobordism is a fundamental equivalence relation on the class of compact manifolds of the same dimension, set up using the concept of the boundary (French '' bord'', giving ''cobordism'') of a manifold. Two manifolds of the same d ...

, in relative isolation. Among other advances he showed how the

Adams spectral sequence In mathematics, the Adams spectral sequence is a spectral sequence introduced by which computes the stable homotopy groups of topological spaces. Like all spectral sequences, it is a computational tool; it relates homology theory to what is now c ...

, a powerful tool for proceeding from

homology theory In mathematics, the term homology, originally introduced in algebraic topology, has three primary, closely-related usages. The most direct usage of the term is to take the ''homology of a chain complex'', resulting in a sequence of abelian grou ...

to the calculation of

homotopy group In mathematics, homotopy groups are used in algebraic topology to classify topological spaces. The first and simplest homotopy group is the fundamental group, denoted \pi_1(X), which records information about loops in a space. Intuitively, homo ...

s, could be adapted to the new (at that time)

cohomology theory 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 viewed ...

typified by cobordism and

K-theory In mathematics, K-theory is, roughly speaking, the study of a ring generated by vector bundles over a topological space or scheme. In algebraic topology, it is a cohomology theory known as topological K-theory. In algebra and algebraic geometr ...

. This required the development of the idea of

cohomology operation In mathematics, the cohomology operation concept became central to algebraic topology, particularly homotopy theory, from the 1950s onwards, in the shape of the simple definition that if ''F'' is a functor defining a cohomology theory, then a cohomo ...

s in the general setting, since the basis of the spectral sequence is the initial data of

Ext functor In mathematics, the Ext functors are the derived functors of the Hom functor. Along with the Tor functor, Ext is one of the core concepts of homological algebra, in which ideas from algebraic topology are used to define invariants of algebraic stru ...

s taken with respect to a ring of such operations, generalising the

Steenrod algebra Norman Earl Steenrod (April 22, 1910October 14, 1971) was an American mathematician most widely known for his contributions to the field of algebraic topology. Life He was born in Dayton, Ohio, and educated at Miami University and University of ...

. The resulting

Adams–Novikov spectral sequence In mathematics, the Adams spectral sequence is a spectral sequence introduced by which computes the stable homotopy groups of topological spaces. Like all spectral sequences, it is a computational tool; it relates homology theory to what is now c ...

is now a basic tool in

stable homotopy theory In mathematics, stable homotopy theory is the part of homotopy theory (and thus algebraic topology) concerned with all structure and phenomena that remain after sufficiently many applications of the suspension functor. A founding result was the ...

. Novikov also carried out important research in

geometric topology In mathematics, geometric topology is the study of manifolds and Map (mathematics)#Maps as functions, maps between them, particularly embeddings of one manifold into another. History Geometric topology as an area distinct from algebraic topo ...

, being one of the pioneers with William Browder,

Dennis Sullivan Dennis Parnell Sullivan (born February 12, 1941) is an American mathematician known for his work in algebraic topology, geometric topology, and dynamical systems. He holds the Albert Einstein Chair at the Graduate Center of the City University ...

, and

C. T. C. Wall Charles Terence Clegg "Terry" Wall (born 14 December 1936) is a British mathematician, educated at Marlborough and Trinity College, Cambridge. He is an emeritus professor of the University of Liverpool, where he was first appointed professor in ...

of the

surgery theory In mathematics, specifically in geometric topology, surgery theory is a collection of techniques used to produce one finite-dimensional manifold from another in a 'controlled' way, introduced by . Milnor called this technique ''surgery'', while An ...

method for classifying high-dimensional manifolds. He proved the topological invariance of the rational

Pontryagin class In mathematics, the Pontryagin classes, named after Lev Pontryagin, are certain characteristic classes of real vector bundles. The Pontryagin classes lie in cohomology groups with degrees a multiple of four. Definition Given a real vector bundl ...

es, and posed the

Novikov conjecture The Novikov conjecture is one of the most important unsolved problems in topology. It is named for Sergei Novikov who originally posed the conjecture in 1965. The Novikov conjecture concerns the homotopy invariance of certain polynomials in th ...

. From about 1971, he moved to work in the field of isospectral flows, with connections to the theory of

theta function In mathematics, theta functions are special functions of several complex variables. They show up in many topics, including Abelian varieties, moduli spaces, quadratic forms, and solitons. Theta functions are parametrized by points in a tube ...

s. Novikov's conjecture about the Riemann–Schottky problem (characterizing principally polarized abelian varieties that are the Jacobian of some algebraic curve) stated, essentially, that this was the case if and only if the corresponding theta function provided a solution to the

Kadomtsev–Petviashvili equation In mathematics and physics, the Kadomtsev–Petviashvili equation (often abbreviated as KP equation) is a partial differential equation to describe nonlinear wave motion. Named after Boris Kadomtsev, Boris Borisovich Kadomtsev and Vladimir Iosifovi ...

of soliton theory. This was proved by Takahiro Shiota (1986), following earlier work by

Enrico Arbarello Enrico Arbarello is an Italian mathematician who is an expert in algebraic geometry. Career He earned a Ph.D. at Columbia University in New York in 1973. He was a visiting scholar at the Institute for Advanced Study from 1993 to 1994. He is n ...

and

Corrado de Concini Corrado de Concini (born 28 July 1949, in Rome) is an Italian mathematician and professor at the Sapienza University of Rome. He studies algebraic geometry, quantum groups, invariant theory, and mathematical physics. Life and work He was born ...

(1984), and by Motohico Mulase (1984).

Awards and honours

In 1967, Novikov received the

Lenin Prize The Lenin Prize (, ) was one of the most prestigious awards of the Soviet Union for accomplishments relating to science, literature, arts, architecture, and technology. It was originally created on June 23, 1925, and awarded until 1934. During ...

. In 1970, Novikov became the first Soviet mathematician to be awarded the

. He was not allowed to travel to the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the IMU Abacus Medal (known before ...

Nice Nice ( ; ) is a city in and the prefecture of the Alpes-Maritimes department in France. The Nice agglomeration extends far beyond the administrative city limits, with a population of nearly one million International Mathematical Union The International Mathematical Union (IMU) is an international organization devoted to international cooperation in the field of mathematics across the world. It is a member of the International Science Council (ISC) and supports the International ...

met in Moscow. In 2005, he was awarded the

Wolf Prize The Wolf Prize is an international award granted in Israel, that has been presented most years since 1978 to living scientists and artists for "achievements in the interest of mankind and friendly relations among people ... irrespective of natio ...

for his contributions to

differential topology In mathematics, differential topology is the field dealing with the topological properties and smooth properties of smooth manifolds. In this sense differential topology is distinct from the closely related field of differential geometry, which ...

and to

mathematical physics Mathematical physics is the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the de ...

. He is one of just eleven mathematicians who received both the Fields Medal and the Wolf Prize. In 2020, he received the

Lomonosov Gold Medal The Lomonosov Gold Medal ( ''Bol'shaya zolotaya medal' imeni M. V. Lomonosova''), named after Russian scientist and polymath Mikhail Lomonosov, is awarded each year since 1959 for outstanding achievements in the natural sciences and the humaniti ...

of the Russian Academy of Sciences. In 1981, he was elected a full member of the USSR Academy of Sciences (

Russian Academy of Sciences The Russian Academy of Sciences (RAS; ''Rossíyskaya akadémiya naúk'') consists of the national academy of Russia; a network of scientific research institutes from across the Russian Federation; and additional scientific and social units such ...

since 1991). He was elected to the

London Mathematical Society The London Mathematical Society (LMS) is one of the United Kingdom's Learned society, learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh ...

(honorary member, 1987),

Serbian Academy of Sciences and Arts The Serbian Academy of Sciences and Arts (; , SANU) is a national academy and the most prominent academic institution in Serbia, founded in 1841 as Society of Serbian Letters (, DSS). The Academy's membership has included Nobel Prize, Nobel la ...

(honorary member, 1988),

Accademia dei Lincei The (; literally the "Academy of the Lynx-Eyed"), anglicised as the Lincean Academy, is one of the oldest and most prestigious European scientific institutions, located at the Palazzo Corsini on the Via della Lungara in Rome, Italy. Founded in ...

(foreign member, 1991),

Academia Europaea The Academia Europaea is a pan-European Academy of humanities, letters, law, and sciences. The Academia was founded in 1988 as a functioning Europe-wide Academy that encompasses all fields of scholarly inquiry. It acts as co-ordinator of Europe ...

(member, 1993),

National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, NGO, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the ...

(foreign associate, 1994),

Pontifical Academy of Sciences The Pontifical Academy of Sciences (, ) is a Academy of sciences, scientific academy of the Vatican City, established in 1936 by Pope Pius XI. Its aim is to promote the progress of the mathematical, physical, and natural sciences and the study ...

(member, 1996), (fellow, 2003), and

Montenegrin Academy of Sciences and Arts Montenegrin Academy of Sciences and Arts ( sh-Cyrl, Црногорска академија наука и умјетности, ЦАНУ; ) is the most important scientific institution of Montenegro. History It was founded in 1973 as the Montene ...

(honorary member, 2011). He received honorary doctorates from the

University of Athens The National and Kapodistrian University of Athens (NKUA; , ''Ethnikó kai Kapodistriakó Panepistímio Athinón''), usually referred to simply as the University of Athens (UoA), is a public university in Athens, Greece, with various campuses alo ...

(1988) and

University of Tel Aviv Tel Aviv University (TAU) is a public research university in Tel Aviv, Israel. With over 30,000 students, it is the largest university in the country. Located in northwest Tel Aviv, the university is the center of teaching and research of the ci ...

(1999).

Writings

* * * with Dubrovin and Fomenko: ''Modern geometry- methods and applications'', Vol.1-3, Springer, Graduate Texts in Mathematics (originally 1984, 1988, 1990, V.1 The geometry of surfaces and transformation groups, V.
The geometry and topology of manifolds
V.3 Introduction to homology theory)
''Topics in Topology and mathematical physics''
AMS (American Mathematical Society) 1995 * ''Integrable systems – selected papers'',

Cambridge University Press Cambridge University Press was the university press of the University of Cambridge. Granted a letters patent by King Henry VIII in 1534, it was the oldest university press in the world. Cambridge University Press merged with Cambridge Assessme ...

1981 (London Math. Society Lecture notes) * * with V. I. Arnold as editor and co-author
''Dynamical systems''
1994, Encyclopedia of mathematical sciences, Springer * ''Topology I: general survey'', V. 12 of Topology Series of Encyclopedia of mathematical sciences, Springer 1996
2013 edition

''Solitons and geometry''
Cambridge 1994 * as editor, with Buchstaber
''Solitons, geometry and topology: on the crossroads''
AMS, 1997 * with Dubrovin and Krichever: ''Topological and Algebraic Geometry Methods in contemporary mathematical physics'' V.2, Cambridge , * ''My generation in mathematics'', Russian Mathematical Surveys V.49, 1994, p. 1

Notes

References

External links