Vladimir Igorevich Arnold (alternative spelling Arnol'd, russian: link=no, Влади́мир И́горевич Арно́льд, 12 June 1937 – 3 June 2010) was a Soviet and Russian mathematician. While he is best known for the Kolmogorov–Arnold–Moser theorem regarding the stability of

integrable system In mathematics, integrability is a property of certain dynamical systems. While there are several distinct formal definitions, informally speaking, an integrable system is a dynamical system with sufficiently many conserved quantities, or first ...

s, he made important contributions in several areas including

dynamical systems theory Dynamical systems theory is an area of mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theory is called '' ...

algebra Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary ...

catastrophe theory In mathematics, catastrophe theory is a branch of bifurcation theory in the study of dynamical systems; it is also a particular special case of more general singularity theory in geometry. Bifurcation theory studies and classifies phenomena c ...

topology In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ...

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 ...

symplectic geometry Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds equipped with a closed, nondegenerate 2-form. Symplectic geometry has its origins in the ...

differential equations In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...

classical mechanics Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classi ...

hydrodynamics In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) a ...

and

singularity theory In mathematics, singularity theory studies spaces that are almost manifolds, but not quite. A string can serve as an example of a one-dimensional manifold, if one neglects its thickness. A singularity can be made by balling it up, dropping it ...

, including posing the

ADE classification In mathematics, the ADE classification (originally ''A-D-E'' classifications) is a situation where certain kinds of objects are in correspondence with simply laced Dynkin diagrams. The question of giving a common origin to these classifications, r ...

problem, since his first main result—the solution of

Hilbert's thirteenth problem Hilbert's thirteenth problem is one of the 23 Hilbert problems set out in a celebrated list compiled in 1900 by David Hilbert. It entails proving whether a solution exists for all 7th-degree equations using algebraic (variant: continuous) fu ...

in 1957 at the age of 19. He co-founded two new branches of mathematics—

KAM theory Kaam ( Gurmukhi: ਕਾਮ ''Kāma'') in common usage, the term stands for 'excessive passion for sexual pleasure' and it is in this sense that it is considered to be an evil in Sikhism. In Sikhism it is believed that Kaam can be overcom ...

, and topological Galois theory (this, with his student Askold Khovanskii). Arnold was also known as a popularizer of mathematics. Through his lectures, seminars, and as the author of several textbooks (such as the famous '' Mathematical Methods of Classical Mechanics'') and popular mathematics books, he influenced many mathematicians and physicists. Many of his books were translated into English. His views on education were particularly opposed to those of Bourbaki.

Biography

Vladimir Igorevich Arnold was born on 12 June 1937 in

Odessa Odesa (also spelled Odessa) is the third most populous city and municipality in Ukraine and a major seaport and transport hub located in the south-west of the country, on the northwestern shore of the Black Sea. The city is also the administrativ ...

Soviet Union The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, it was nominally a federal union of fifteen nationa ...

(now

Odesa Odesa (also spelled Odessa) is the third most populous city and municipality in Ukraine and a major seaport and transport hub located in the south-west of the country, on the northwestern shore of the Black Sea. The city is also the administrati ...

Ukraine Ukraine ( uk, Україна, Ukraïna, ) is a country in Eastern Europe. It is the second-largest European country after Russia, which it borders to the east and northeast. Ukraine covers approximately . Prior to the ongoing Russian inva ...

). His father was Igor Vladimirovich Arnold (1900–1948), a mathematician. His mother was Nina Alexandrovna Arnold (1909–1986, ''

née A birth name is the name of a person given upon birth. The term may be applied to the surname, the given name, or the entire name. Where births are required to be officially registered, the entire name entered onto a birth certificate or birth re ...

'' Isakovich), a Jewish art historian. While a school student, Arnold once asked his father on the reason why the multiplication of two negative numbers yielded a positive number, and his father provided an answer involving the field properties of real numbers and the preservation of the distributive property. Arnold was deeply disappointed with this answer, and developed an aversion to the

axiomatic method In mathematics and logic, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems. A theory is a consistent, relatively-self-contained body of knowledge which usually contai ...

that lasted through his life. When Arnold was thirteen, his uncle Nikolai B. Zhitkov,''Swimming Against the Tide'', p. 3 who was an engineer, told him about

calculus Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizati ...

and how it could be used to understand some physical phenomena, this contributed to spark his interest for mathematics, and he started to study by himself the mathematical books his father had left to him, which included some works of

Leonhard Euler Leonhard Euler ( , ; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries ...

and

Charles Hermite Charles Hermite () FRS FRSE MIAS (24 December 1822 – 14 January 1901) was a French mathematician who did research concerning number theory, quadratic forms, invariant theory, orthogonal polynomials, elliptic functions, and algebra. ...

. While a student of

Andrey Kolmogorov Andrey Nikolaevich Kolmogorov ( rus, Андре́й Никола́евич Колмого́ров, p=ɐnˈdrʲej nʲɪkɐˈlajɪvʲɪtɕ kəlmɐˈɡorəf, a=Ru-Andrey Nikolaevich Kolmogorov.ogg, 25 April 1903 – 20 October 1987) was a Sovi ...

Moscow State University M. V. Lomonosov Moscow State University (MSU; russian: Московский государственный университет имени М. В. Ломоносова) is a public research university in Moscow, Russia and the most prestigious ...

and still a teenager, Arnold showed in 1957 that any continuous function of several variables can be constructed with a finite number of two-variable functions, thereby solving

. This is the

Kolmogorov–Arnold representation theorem In real analysis and approximation theory, the Kolmogorov-Arnold representation theorem (or superposition theorem) states that every multivariate continuous function can be represented as a superposition of the two-argument addition and continuou ...

. After graduating from Moscow State University in 1959, he worked there until 1986 (a professor since 1965), and then at Steklov Mathematical Institute. He became an academician of the Academy of Sciences of the Soviet Union ( Russian Academy of Science since 1991) in 1990.

Great Russian Encyclopedia The ''Great Russian Encyclopedia'' (GRE; russian: Большая российская энциклопедия, БРЭ, transliterated as ''Bolshaya rossiyskaya entsiklopediya'' or academically as ''Bolšaja rossijskaja enciklopedija'') is a ...

(2005), Moscow: Bol'shaya Rossiyskaya Enciklopediya Publisher, vol. 2. Arnold can be said to have initiated the theory of symplectic topology as a distinct discipline. The

Arnold conjecture The Arnold conjecture, named after mathematician Vladimir Arnold, is a mathematical conjecture in the field of symplectic geometry, a branch of differential geometry. Statement Let (M, \omega) be a compact symplectic manifold. For any smooth f ...

on the number of fixed points of Hamiltonian symplectomorphisms and Lagrangian intersections were also a major motivation in the development of

Floer homology In mathematics, Floer homology is a tool for studying symplectic geometry and low-dimensional topology. Floer homology is a novel invariant that arises as an infinite-dimensional analogue of finite-dimensional Morse homology. Andreas Floer in ...

. In 1999 he suffered a serious bike accident in Paris, resulting in

traumatic brain injury A traumatic brain injury (TBI), also known as an intracranial injury, is an injury to the brain caused by an external force. TBI can be classified based on severity (ranging from mild traumatic brain injury TBI/concussionto severe traumatic br ...

, and though he regained consciousness after a few weeks, he had amnesia and for some time could not even recognize his own wife at the hospital, but he went on to make a good recovery. Arnold worked at the Steklov Mathematical Institute in Moscow and at Paris Dauphine University up until his death. he was reported to have the highest

citation index A citation index is a kind of bibliographic index, an index of citations between publications, allowing the user to easily establish which later documents cite which earlier documents. A form of citation index is first found in 12th-century Hebre ...

among Russian scientists, and

h-index The ''h''-index is an author-level metric that measures both the productivity and citation impact of the publications, initially used for an individual scientist or scholar. The ''h''-index correlates with obvious success indicators such as ...

of 40. His students include Alexander Givental, Victor Goryunov, Sabir Gusein-Zade, Emil Horozov,

Boris Khesin Boris Aronovich Khesin (in Russian: Борис Аронович Хесин, born in 1964) is a Russian and Canadian mathematician working on infinite-dimensional Lie groups, Poisson geometry and hydrodynamics. He is a professor at the Universit ...

, Askold Khovanskii, Nikolay Nekhoroshev, Boris Shapiro, Alexander Varchenko, Victor Vassiliev and Vladimir Zakalyukin. To his students and colleagues Arnold was known also for his sense of humour. For example, once at his seminar in Moscow, at the beginning of the school year, when he usually was formulating new problems, he said:

Death

Arnold died of

acute pancreatitis Acute pancreatitis (AP) is a sudden inflammation of the pancreas. Causes in order of frequency include: 1) a gallstone impacted in the common bile duct beyond the point where the pancreatic duct joins it; 2) heavy alcohol use; 3) systemic disea ...

on 3 June 2010 in Paris, nine days before his 73rd birthday. He was buried on 15 June in Moscow, at the Novodevichy Monastery. In a telegram to Arnold's family,

Russian President The president of the Russian Federation ( rus, Президент Российской Федерации, Prezident Rossiyskoy Federatsii) is the head of state of the Russian Federation. The president leads the executive branch of the federal ...

Dmitry Medvedev Dmitry Anatolyevich Medvedev ( rus, links=no, Дмитрий Анатольевич Медведев, p=ˈdmʲitrʲɪj ɐnɐˈtolʲjɪvʲɪtɕ mʲɪdˈvʲedʲɪf; born 14 September 1965) is a Russian politician who has been serving as the dep ...

stated:

Popular mathematical writings

Arnold is well known for his lucid writing style, combining mathematical rigour with physical intuition, and an easy conversational style of teaching and education. His writings present a fresh, often

geometric Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is ca ...

approach to traditional mathematical topics like

ordinary differential equation In mathematics, an ordinary differential equation (ODE) is a differential equation whose unknown(s) consists of one (or more) function(s) of one variable and involves the derivatives of those functions. The term ''ordinary'' is used in contrast ...

s, and his many textbooks have proved influential in the development of new areas of mathematics. The standard criticism about Arnold's pedagogy is that his books "are beautiful treatments of their subjects that are appreciated by experts, but too many details are omitted for students to learn the mathematics required to prove the statements that he so effortlessly justifies." His defense was that his books are meant to teach the subject to "those who truly wish to understand it" (Chicone, 2007). Arnold was an outspoken critic of the trend towards high levels of abstraction in mathematics during the middle of the last century. He had very strong opinions on how this approach—which was most popularly implemented by the Bourbaki school in France—initially had a negative impact on French mathematical education, and then later on that of other countries as well.An Interview with Vladimir Arnol'd
by S. H. Lui, '' AMS Notices'', 1991. Arnold was very interested in the

history of mathematics The history of mathematics deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments ...

. In an interview, he said he had learned much of what he knew about mathematics through the study of

Felix Klein Christian Felix Klein (; 25 April 1849 – 22 June 1925) was a German mathematician and mathematics educator, known for his work with group theory, complex analysis, non-Euclidean geometry, and on the associations between geometry and grou ...

's book ''Development of Mathematics in the 19th Century'' —a book he often recommended to his students. He studied the classics, most notably the works of Huygens, Newton and Poincaré, and many times he reported to have found in their works ideas that had not been explored yet.

Work

Arnold worked on

and

Michèle Audin Michèle Audin (Algiers, 3 January, 1954) is a French mathematician, writer, and a former professor. She has worked as a professor at the University of Geneva, the University of Paris-Saclay and most recently at the University of Strasbourg, wher ...

described him as "a geometer in the widest possible sense of the word" and said that "he was very fast to make connections between different fields".

Hilbert's thirteenth problem

The problem is the following question: can every continuous function of three variables be expressed as a composition of finitely many continuous functions of two variables? The affirmative answer to this general question was given in 1957 by Vladimir Arnold, then only nineteen years old and a student of

. Kolmogorov had shown in the previous year that any function of several variables can be constructed with a finite number of three-variable functions. Arnold then expanded on this work to show that only two-variable functions were in fact required, thus answering the Hilbert's question when posed for the class of continuous functions.

Dynamical systems

Moser and Arnold expanded the ideas of

Kolmogorov Andrey Nikolaevich Kolmogorov ( rus, Андре́й Никола́евич Колмого́ров, p=ɐnˈdrʲej nʲɪkɐˈlajɪvʲɪtɕ kəlmɐˈɡorəf, a=Ru-Andrey Nikolaevich Kolmogorov.ogg, 25 April 1903 – 20 October 1987) was a Sovi ...

(who was inspired by questions of Poincaré) and gave rise to what is now known as Kolmogorov–Arnold–Moser theorem (or "KAM theory"), which concerns the persistence of some quasi-periodic motions (nearly integrable Hamiltonian systems) when they are perturbed. KAM theory shows that, despite the perturbations, such systems can be stable over an infinite period of time, and specifies what the conditions for this are. In 1964, Arnold introduced the Arnold web, the first example of a stochastic web.

Singularity theory

In 1965, Arnold attended

René Thom René Frédéric Thom (; 2 September 1923 – 25 October 2002) was a French mathematician, who received the Fields Medal in 1958. He made his reputation as a topologist, moving on to aspects of what would be called singularity theory; he becam ...

's seminar on

. He later said of it: "I am deeply indebted to Thom, whose singularity seminar at the

Institut des Hautes Etudes Scientifiques An institute is an organisational body created for a certain purpose. They are often research organisations (research institutes) created to do research on specific topics, or can also be a professional body. In some countries, institutes can ...

, which I frequented throughout the year 1965, profoundly changed my mathematical universe." After this event,

became one of the major interests of Arnold and his students. Among his most famous results in this area is his classification of simple singularities, contained in his paper "Normal forms of functions near degenerate critical points, the Weyl groups of A_k,D_k,E_k and Lagrangian singularities".

Fluid dynamics

In 1966, Arnold published "", in which he presented a common geometric interpretation for both the Euler's equations for rotating rigid bodies and the Euler's equations of fluid dynamics, this effectively linked topics previously thought to be unrelated, and enabled mathematical solutions to many questions related to fluid flows and their turbulence.

Real algebraic geometry

In the year 1971, Arnold published "On the arrangement of ovals of real plane algebraic curves, involutions of four-dimensional smooth

manifold In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n-dimensional manifold, or ''n-manifold'' for short, is a topological space with the property that each point has a n ...

s, and the arithmetic of integral quadratic forms", which gave new life to real algebraic geometry. In it, he made major advances in the direction of a solution to

Gudkov's conjecture In real algebraic geometry, Gudkov's conjecture, also called Gudkov’s congruence, (named after Dmitry Gudkov) was a conjecture, and is now a theorem, which states that an M-curve of even degree 2d obeys the congruence : p - n \equiv d^2\, (\! ...

, by finding a connection between it and four-dimensional topology. The conjecture was to be later fully solved by V. A. Rokhlin building on Arnold's work.

Symplectic geometry

The

, linking the number of fixed points of Hamiltonian symplectomorphisms and the topology of the subjacent manifolds, was the motivating source of many of the pioneer studies in symplectic topology.

Topology

According to Victor Vassiliev, Arnold "worked comparatively little on topology for topology's sake." And he was rather motivated by problems on other areas of mathematics where topology could be of use. His contributions include the invention of a topological form of the Abel–Ruffini theorem and the initial development of some of the consequent ideas, a work which resulted in the creation of the field of topological Galois theory in the 1960s.

Theory of plane curves

According to Marcel Berger, Arnold revolutionized plane curves theory. Among his contributions are the Arnold invariants of plane curves.

Other

Arnold conjectured the existence of the gömböc.

Honours and awards

* Lenin Prize (1965, with

), "for work on

celestial mechanics Celestial mechanics is the branch of astronomy that deals with the motions of objects in outer space. Historically, celestial mechanics applies principles of physics (classical mechanics) to astronomical objects, such as stars and planets, ...

." *

Crafoord Prize The Crafoord Prize is an annual science prize established in 1980 by Holger Crafoord, a Swedish industrialist, and his wife Anna-Greta Crafoord. The Prize is awarded in partnership between the Royal Swedish Academy of Sciences and the Crafoord Foun ...

(1982, with Louis Nirenberg), "for contributions to the theory of non-linear differential equations." * Elected member of the United States

National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, 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 Nat ...

in 1983). * Foreign Honorary Member of the

American Academy of Arts and Sciences The American Academy of Arts and Sciences (abbreviation: AAA&S) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, a ...

(1987) * Elected a

Foreign Member of the Royal Society Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the judges of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural knowledge, including mathematic ...

(ForMemRS) of London in 1988. * Elected member of the

American Philosophical Society The American Philosophical Society (APS), founded in 1743 in Philadelphia, is a scholarly organization that promotes knowledge in the sciences and humanities through research, professional meetings, publications, library resources, and communit ...

in 1990. * Lobachevsky Prize of the Russian Academy of Sciences (1992) * Harvey Prize (1994), "for basic contribution to the stability theory of

dynamical system In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water i ...

s, his pioneering work on

and seminal contributions to

analysis Analysis ( : analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (3 ...

and

geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

." * Dannie Heineman Prize for Mathematical Physics (2001), "for his fundamental contributions to our understanding of dynamics and of singularities of maps with profound consequences for

mechanics Mechanics (from Ancient Greek: μηχανική, ''mēkhanikḗ'', "of machines") is the area of mathematics and physics concerned with the relationships between force, matter, and motion among physical objects. Forces applied to objec ...

astrophysics Astrophysics is a science that employs the methods and principles of physics and chemistry in the study of astronomical objects and phenomena. As one of the founders of the discipline said, Astrophysics "seeks to ascertain the nature of the h ...

statistical mechanics In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic b ...

and

optics Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultrav ...

." *

Wolf Prize in Mathematics The Wolf Prize in Mathematics is awarded almost annually by the Wolf Foundation in Israel. It is one of the six Wolf Prizes established by the Foundation and awarded since 1978; the others are in Agriculture, Chemistry, Medicine, Physics and Arts ...

(2001), "for his deep and influential work in a multitude of areas of mathematics, including dynamical systems, differential equations, and singularity theory." *

State Prize of the Russian Federation The State Prize of the Russian Federation, officially translated in Russia as Russian Federation National Award, is a state honorary prize established in 1992 following the breakup of the Soviet Union. In 2004 the rules for selection of laureates ...

(2007),Названы лауреаты Государственной премии РФ

Kommersant ''Kommersant'' (russian: Коммерсантъ, , ''The Businessman'' or Commerce Man, often shortened to Ъ) is a nationally distributed daily newspaper published in Russia mostly devoted to politics and business. The TNS Media and NRS Russia ...

20 May 2008. "for outstanding success in mathematics." *

Shaw Prize The Shaw Prize is an annual award presented by the Shaw Prize Foundation. Established in 2002 in Hong Kong, it honours "individuals who are currently active in their respective fields and who have recently achieved distinguished and signifi ...

in mathematical sciences (2008, with

Ludwig Faddeev Ludvig Dmitrievich Faddeev (also ''Ludwig Dmitriyevich''; russian: Лю́двиг Дми́триевич Фадде́ев; 23 March 1934 – 26 February 2017) was a Soviet and Russian mathematical physicist. He is known for the discovery of the ...

), "for their contributions to

mathematical physics Mathematical physics refers to the development of 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 developm ...

." The

minor planet According to the International Astronomical Union (IAU), a minor planet is an astronomical object in direct orbit around the Sun that is exclusively classified as neither a planet nor a comet. Before 2006, the IAU officially used the term ''minor ...

10031 Vladarnolda was named after him in 1981 by

Lyudmila Georgievna Karachkina Lyudmila Georgievna Karachkina (russian: Людмила Георгиевна Карачкина, born 3 September 1948, Rostov-on-Don) is an astronomer and discoverer of minor planets. In 1978 she began as a staff astronomer of the Institute for ...

. The '' Arnold Mathematical Journal'', published for the first time in 2015, is named after him. The Arnold Fellowships, of the London Institute are named after him. He was a plenary speaker at both the 1974 and 1983

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 Nevanlinna Prize (to be rena ...

in Vancouver and

Warsaw Warsaw ( pl, Warszawa, ), officially the Capital City of Warsaw,, abbreviation: ''m.st. Warszawa'' is the capital and largest city of Poland. The metropolis stands on the River Vistula in east-central Poland, and its population is officiall ...

, respectively.

Fields Medal omission

Even though Arnold was nominated for the 1974

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 the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award h ...

, which was then viewed as the highest honour a mathematician could receive, interference from the Soviet government led to it being withdrawn. Arnold's public opposition to the persecution of

dissident A dissident is a person who actively challenges an established political or religious system, doctrine, belief, policy, or institution. In a religious context, the word has been used since the 18th century, and in the political sense since the 20th ...

s had led him into direct conflict with influential Soviet officials, and he suffered persecution himself, including not being allowed to leave the Soviet Union during most of the 1970s and 1980s.

Selected bibliography

* 1966: * 1978: ''Ordinary Differential Equations'', The MIT Press . * 1985: * 1988: * 1988: * 1989: * 1989 * 1989: (with A. Avez) ''Ergodic Problems of Classical Mechanics'', Addison-Wesley . * 1990: ''Huygens and Barrow, Newton and Hooke: Pioneers in mathematical analysis and catastrophe theory from evolvents to quasicrystals'', Eric J.F. Primrose translator,

Birkhäuser Verlag Birkhäuser was a Swiss publisher founded in 1879 by Emil Birkhäuser. It was acquired by Springer Science+Business Media in 1985. Today it is an imprint used by two companies in unrelated fields: * Springer continues to publish science (particu ...

(1990) . * 1991: * 1995:''Topological Invariants of Plane Curves and Caustics'', American Mathematical Society (1994) * 1998: "On the teaching of mathematics" (Russian) Uspekhi Mat. Nauk 53 (1998), no. 1(319), 229–234; translation in '' Russian Math. Surveys'' 53(1): 229–236. * 1999: (with Valentin Afraimovich) ''Bifurcation Theory And Catastrophe Theory'' Springer * 2001: "Tsepniye Drobi" (Continued Fractions, in Russian), Moscow (2001). * 2004: ''Teoriya Katastrof'' (Catastrophe Theory, in Russian), 4th ed. Moscow, Editorial-URSS (2004), . * 2004: * 2004: * 2007: ''Yesterday and Long Ago'', Springer (2007), . * 2013: Review by Fernando Q. Gouvêa of ''Real Algebraic Geometry'' by Arnold https://www.maa.org/press/maa-reviews/real-algebraic-geometry * 2014: * 2015: ''Experimental Mathematics''. American Mathematical Society (translated from Russian, 2015). * 2015: ''Lectures and Problems: A Gift to Young Mathematicians'', American Math Society, (translated from Russian, 2015)

Collected works

* 2010: A. B. Givental; B. A. Khesin; J. E. Marsden; A. N. Varchenko; V. A. Vassilev; O. Ya. Viro; V. M. Zakalyukin (editors). ''Collected Works, Volume I: Representations of Functions, Celestial Mechanics, and KAM Theory (1957–1965)''.

Springer Springer or springers may refer to: Publishers * Springer Science+Business Media, aka Springer International Publishing, a worldwide publishing group founded in 1842 in Germany formerly known as Springer-Verlag. ** Springer Nature, a multinationa ...

* 2013: A. B. Givental; B. A. Khesin; A. N. Varchenko; V. A. Vassilev; O. Ya. Viro; (editors). ''Collected Works, Volume II: Hydrodynamics, Bifurcation Theory, and Algebraic Geometry (1965–1972)''. Springer. * 2016: Givental, A.B., Khesin, B., Sevryuk, M.B., Vassiliev, V.A., Viro, O.Y. (Eds.). ''Collected Works, Volume III: Singularity Theory 1972–1979. Springer. * 2018: Givental, A.B., Khesin, B., Sevryuk, M.B., Vassiliev, V.A., Viro, O.Y. (Eds.). ''Collected Works, Volume IV: Singularities in Symplectic and Contact Geometry 1980–1985''. Springer. * 2022 (To be published, September 2022): Alexander B. Givental, Boris A. Khesin, Mikhail B. Sevryuk, Victor A. Vassiliev, Oleg Ya. Viro (Eds.). ''Collected Works, Volume VI: Dynamics, Combinatorics, and Invariants of Knots, Curves, and Wave Fronts 1992–1995''. Springer.

References

External links

V. I. Arnold's web page

Personal web page

V. I. Arnold lecturing on Continued Fractions

A short curriculum vitae

text of a talk espousing Arnold's opinions on mathematical instruction

* ttp://imaginary.org/sites/default/files/taskbook_arnold_en_0.pdf Problems from 5 to 15 a text by Arnold for school students, available at th
IMAGINARY platform
*

В.Б.Демидовичем (2009), МЕХМАТЯНЕ ВСПОМИНАЮТ 2: В.И.Арнольд, pp. 25–58

Author profile
in the database zbMATH {{DEFAULTSORT:Arnold, Vladimir 1937 births 2010 deaths Scientists from Odesa 20th-century Russian mathematicians 21st-century Russian mathematicians Fellows of the American Academy of Arts and Sciences Foreign Members of the Royal Society Lenin Prize winners Mathematical analysts Full Members of the USSR Academy of Sciences Full Members of the Russian Academy of Sciences Members of the French Academy of Sciences Foreign associates of the National Academy of Sciences Moscow State University alumni Soviet mathematicians State Prize of the Russian Federation laureates Topologists Fluid dynamicists University of Paris faculty Wolf Prize in Mathematics laureates Mathematical physicists Textbook writers Geometers Algebraic geometers Differential geometers Dynamical systems theorists Newton scholars Deaths from pancreatitis Moscow State University faculty Steklov Institute of Mathematics faculty Independent University of Moscow faculty Members of the American Philosophical Society Members of the German Academy of Sciences at Berlin Algebraists Odesa Jews