Vladimir Arnold
Vladimir Arnold  

Vladimir Arnold in 2008


Born  Odessa, Ukrainian SSR, Soviet Union 
12 June 1937
Died  3 June 2010 Paris, France 
(aged 72)
Nationality  Soviet Union, Russian 
Fields  Mathematics 
Alma mater  Moscow State University 
Doctoral advisor  Andrey Kolmogorov 
Doctoral students  
Known for  Arnold's cat map Arnold conjecture Arnold diffusion Arnold invariants Arnold's rouble problem Arnold's spectral sequence Arnold's stability theorem Arnold tongue Arnold web ABC flow Arnold–Givental conjecture Gömböc Gudkov's conjecture Hilbert's thirteenth problem KAM theorem Kolmogorov–Arnold theorem Liouville–Arnold theorem 
Notable awards  Shaw Prize (2008) State Prize of the Russian Federation (2007) Wolf Prize (2001) Dannie Heineman Prize for Mathematical Physics (2001) Harvey Prize (1994) RAS Lobachevsky Prize (1992) Crafoord Prize (1982) Lenin Prize (1965) 
Vladimir Igorevich Arnold (alternative spelling Arnol'd, Russian: Влади́мир И́горевич Арно́льд, 12 June 1937 – 3 June 2010)^{[1]}^{[2]} was a Soviet and Russian mathematician. While he is best known for the Kolmogorov–Arnold–Moser theorem regarding the stability of integrable systems, he made important contributions in several areas including dynamical systems theory, catastrophe theory, topology, algebraic geometry, symplectic geometry, differential equations, classical mechanics, hydrodynamics and singularity theory, including posing the ADE classification problem, since his first main result—the solution of Hilbert's thirteenth problem in 1957 at the age of 19.
Arnold was also known as a popularizer of mathematics. Through his lectures, seminars, and as the author of several popular mathematics books, he influenced many mathematicians and physicists.^{[3]}^{[4]} Many of his books were translated into English.
Contents
Biography
Vladimir Igorevich Arnold was born on 12 June 1937 in Odessa, Soviet Union. His father was Igor Vladimirovich Arnold (1900–1948), a mathematician. His mother was Nina Alexandrovna Arnold (1909–1986, née Isakovich), an art historian.^{[2]} When Arnold was thirteen, an uncle who was an engineer told him about calculus 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 and Charles Hermite.^{[5]}
While a student of Andrey Kolmogorov at Moscow State University and still a teenager, Arnold showed in 1957 that any continuous function of several variables can be constructed with a finite number of twovariable functions, thereby solving Hilbert's thirteenth problem.^{[6]}
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.^{[7]} Arnold can be said to have initiated the theory of symplectic topology as a distinct discipline. The Arnold conjecture on the number of fixed points of Hamiltonian symplectomorphisms and Lagrangian intersections were also a major motivation in the development of Floer homology.
In 1999 he suffered a serious bike accident in Paris, resulting in traumatic brain injury, and though he regained consciousness after a few weeks, he had amnesia and for some time could not even recognize his wife at the hospital,^{[8]} but he went on to make a good recovery.^{[9]}
Arnold worked at the Steklov Mathematical Institute in Moscow and at Paris Dauphine University up until his death. As of 2006^{[update]} he was reported to have the highest citation index among Russian scientists,^{[10]} and hindex of 40.
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:^{[11]}
There is a general principle that a stupid man can ask such questions to which one hundred wise men would not be able to answer. In accordance with this principle I shall formulate some problems.
Arnold died of acute pancreatitis^{[12]} on 3 June 2010 in Paris, nine days before his 73rd birthday.^{[13]} His students include Alexander Givental, Victor Goryunov, Sabir GuseinZade, Emil Horozov, Boris Khesin, Askold Khovanskii, Nikolay Nekhoroshev, Boris Shapiro, Alexander Varchenko, Victor Vassiliev and Vladimir Zakalyukin.^{[14]}
He was buried on June 15 in Moscow, at the Novodevichy Monastery.^{[15]}
In a telegram to Arnold's family, Russian President Dmitry Medvedev stated:
“The death of Vladimir Arnold, one of the greatest mathematicians of our time, is an irretrievable loss for world science. It is difficult to overestimate the contribution made by academician Arnold to modern mathematics and the prestige of Russian science.
Teaching had a special place in Vladimir Arnold's life and he had great influence as an enlightened mentor who taught several generations of talented scientists.
The memory of Vladimir Arnold will forever remain in the hearts of his colleagues, friends and students, as well as everyone who knew and admired this brilliant man.”^{[16]}
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. His writings present a fresh, often geometric approach to traditional mathematical topics like ordinary differential equations, 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 is that his books are meant to teach the subject to "those who truly wish to understand it" (Chicone, 2007).^{[17]}
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.^{[18]}^{[19]} Arnold was very interested in the history of mathematics.^{[20]} In an interview,^{[19]} he said he had learned much of what he knew about mathematics through the study of Felix Klein's book Development of Mathematics in the 19th Century —a book he often recommended to his students.^{[21]} He liked to study the classics, most notably the works of Huygens, Newton and Poincaré,^{[22]} and many times he reported to have found in their works ideas that had not been explored yet.^{[23]}
Work
This section requires expansion. (February 2015)

Arnold worked on dynamical systems theory, catastrophe theory, topology, algebraic geometry, symplectic geometry, differential equations, classical mechanics, hydrodynamics and singularity theory.^{[3]}
Dynamical systems
Moser and Arnold expanded the ideas of Kolmogorov (who was inspired by questions of Poincaré) and gave rise to what is now known as "KAM Theory", which concerns the persistence of some quasiperiodic 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.^{[24]}
Singularity theory
In 1965, Arnold attended René Thom's seminar on catastrophe theory. He later said of it: "I am deeply indebted to Thom, whose singularity seminar at the Institut des Hautes Etudes Scientifiques, which I frequented throughout the year 1965, profoundly changed my mathematical universe."^{[25]} After this event, singularity theory became one of the major interests of Arnold and his students.^{[26]} 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".^{[27]}^{[28]}^{[29]}
Fluid dynamics
In 1966, Arnold published "Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits", 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.^{[30]}^{[31]}^{[32]}
Real algebraic geometry
In 1971, Arnold published "On the arrangement of ovals of real plane algebraic curves, involutions of fourdimensional smooth manifolds, and the arithmetic of integral quadratic forms",^{[33]} which gave new animus to real algebraic geometry. In it, he made major advances in the direction of a solution to Gudkov's conjecture, by finding a connection between it and fourdimensional topology.^{[34]} The conjecture was to be later fully solved by V. A. Rokhlin building on Arnold's work.^{[35]}^{[36]}
Honours and awards
 Lenin Prize (1965, with Andrey Kolmogorov),^{[37]} "for work on celestial mechanics."
 Crafoord Prize (1982, with Louis Nirenberg),^{[38]} "for contributions to the theory of nonlinear differential equations."
 Foreign Honorary Member of the American Academy of Arts and Sciences (1987)^{[39]}
 Lobachevsky Prize of the Russian Academy of Sciences (1992)^{[40]}
 Harvey Prize (1994), "for basic contribution to the stability theory of dynamical systems, his pioneering work on singularity theory and seminal contributions to analysis and geometry."
 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, astrophysics, statistical mechanics, hydrodynamics and optics."^{[41]}
 Wolf Prize in Mathematics (2001), "for his deep and influential work in a multitude of areas of mathematics, including dynamical systems, differential equations, and singularity theory."^{[42]}
 State Prize of the Russian Federation (2007),^{[43]} "for outstanding success in mathematics."
 Shaw Prize in mathematical sciences (2008, with Ludwig Faddeev), "for their contributions to mathematical physics."
The minor planet 10031 Vladarnolda was named after him in 1981 by Lyudmila Georgievna Karachkina.^{[44]}
The Arnold Mathematical Journal, published for the first time in 2015, is named after him.^{[45]}
He was a plenary speaker at both the 1974 and 1983 International Congress of Mathematicians in Vancouver and Warsaw, respectively.^{[46]}
Fields Medal omission
Even though Arnold was nominated for being awarded the 1974 Fields Medal, 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 dissidents had led him into direct conflict with influential Soviet officials, and he suffered persecution himself – even though not a dissident – including not being allowed to leave the Soviet Union during most of the 1970s and 1980s.^{[47]}^{[48]}
Selected bibliography
 V. I. Arnold, Mathematical Methods of Classical Mechanics, SpringerVerlag (1989), ISBN 0387968903.^{[49]}^{[50]}
 V. I. Arnold, Geometrical Methods In The Theory Of Ordinary Differential Equations, SpringerVerlag (1988), ISBN 0387966498.
 V. I. Arnold, Ordinary Differential Equations, The MIT Press (1978), ISBN 0262510189.
 V. I. Arnold, A. Avez, Ergodic Problems of Classical Mechanics, AddisonWesley (1989), ISBN 0201094061.
 V.I. Arnold, Huygens and Barrow, Newton and Hooke: Pioneers in mathematical analysis and catastrophe theory from evolvents to quasicrystals, Eric J.F. Primrose translator, Birkhäuser Verlag (1990) ISBN 3764323833 .
 V. I. Arnold, Teoriya Katastrof (Catastrophe Theory, in Russian), 4th ed. Moscow, EditorialURSS (2004), ISBN 5354006740.
 V. I. Arnold, "Tsepniye Drobi" (Continued Fractions, in Russian), Moscow (2001).
 V. I. Arnold, Yesterday and Long Ago, Springer (2007), ISBN 9783540287346.
 Arnold, V. I.; V. S. Afraimovich (1999). Bifurcation Theory And Catastrophe Theory. Springer. ISBN 3540653791.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
 Arnolʹd, V. I.: On the teaching of mathematics. (Russian) Uspekhi Mat. Nauk 53 (1998), no. 1(319), 229–234; translation in Russian Math. Surveys 53 (1998), no. 1, 229–236.
 Vladimir I. Arnold, ed. (2004). Arnold's Problems (2nd ed.). SpringerVerlag. ISBN 3540207481.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
 V. I. Arnold (2014). Mathematical Understanding of Nature: Essays on Amazing Physical Phenomena and Their Understanding by Mathematicians. American Mathematical Society. ISBN 9781470417017.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
 V. I. Arnolʹd; S. M. GuseinZade; A. N. Varchenko. Singularities of Differentiable Maps, Volume I: The Classification of Critical Points, Caustics and Wave Fronts. Birkhäuser (1985).
 V. I. Arnolʹd; S. M. GuseinZade; A. N. Varchenko. Singularities of Differentiable Maps, Volume II: Monodromy and Asymptotics of Integrals. Monographs in Mathematics. Birkhäuser (1988).
 Vladimir I. Arnold. Real Algebraic Geometry.
 Vladimir I. Arnold. Lectures on Partial Differential Equations.
 Vladimir I. Arnold. 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 (2009).
 Vladimir I. Arnold. 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 (2013).
 Vladimir I. Arnold. Experimental Mathematics. American Mathematical Society.
 Lectures and Problems: A Gift to Young Mathematicians, American Math Society, (2015)
See also
 Arnold's cat map
 Arnold conjecture
 Arnold's rouble problem
 KAM theorem
 Gömböc
 Arnold–Givental conjecture
 Arnold tongue
 Arnold diffusion
 Arnold–Liouville theorem
 Independent University of Moscow
References
 ↑ Mort d'un grand mathématicien russe, AFP (Le Figaro)
 ↑ ^{2.0} ^{2.1} GuseinZade, S. M.; Varchenko, A. N. . "Obituary: Vladimir Arnold (12 June 1937–3 June 2010)", Newsletter of the European Mathematical Society, Issue 78 (December 2010), pp. 28–29.
 ↑ ^{3.0} ^{3.1} O'Connor, John J.; Robertson, Edmund F., "Vladimir Arnold", MacTutor History of Mathematics archive, University of St Andrews<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>.
 ↑ Bartocci, Claudio; Betti, Renato; Guerraggio, Angelo; Lucchetti, Roberto; Williams, Kim (2010). Mathematical Lives: Protagonists of the Twentieth Century From Hilbert to Wiles. Springer. p. 211. ISBN 9783642136061.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
 ↑ Табачников, С. Л. . "Интервью с В.И.Арнольдом", Квант, 1990, Nº 7, pp. 2–7. (in Russian)
 ↑ Daniel Robertz (13 October 2014). Formal Algorithmic Elimination for PDEs. Springer. p. 192. ISBN 9783319114453.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
 ↑ Great Russian Encyclopedia (2005), Moscow: Bol'shaya Rossiyskaya Enciklopediya Publisher, vol. 2.
 ↑ Arnold: Yesterday and Long Ago (2010)
 ↑ Polterovich and Scherbak (2011)
 ↑ List of Russian Scientists with High Citation Index
 ↑ "Vladimir Arnold". The Daily Telegraph. London. 12 July 2010.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
 ↑ Kenneth Chang (June 11, 2010). "Vladimir Arnold Dies at 72; Pioneering Mathematician". The New York Times. Retrieved 12 June 2013.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
 ↑ "Number's up as top mathematician Vladimir Arnold dies". Herald Sun. 4 June 2010. Retrieved 20100606.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
 ↑ Vladimir Arnold at the Mathematics Genealogy Project
 ↑ "From V. I. Arnold's web page". Retrieved 12 June 2013.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
 ↑ "Condolences to the family of Vladimir Arnold". Presidential Press and Information Office. 15 June 2010. Retrieved 1 September 2011.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
 ↑ Carmen Chicone (2007), Book review of "Ordinary Differential Equations", by Vladimir I. Arnold. SpringerVerlag, Berlin, 2006. SIAM Review 49(2):335–336. (Chicone mentions the criticism but does not agree with it.)
 ↑ See [1] and other essays in [2].
 ↑ ^{19.0} ^{19.1} An Interview with Vladimir Arnol'd, by S. H. Lui, AMS Notices, 1991.
 ↑ Oleg Karpenkov. "Vladimir Igorevich Arnold"
 ↑ B. Khesin and S. Tabachnikov, Tribute to Vladimir Arnold, Notices of the AMS, 59:3 (2012) 378–399.
 ↑ Goryunov, V.; Zakalyukin, V. (2011), "Vladimir I. Arnold", Moscow Mathematical Journal, 11 (3)<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>.
 ↑ See for example: Arnold, V. I.; Vasilev, V. A. (1989), "Newton's Principia read 300 years later" and Arnold, V. I. (2006); "Forgotten and neglected theories of Poincaré".
 ↑ Szpiro, George G. (20080729). Poincare's Prize: The HundredYear Quest to Solve One of Math's Greatest Puzzles. Penguin. ISBN 9781440634284.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
 ↑ http://www.math.upenn.edu/Arnold/Arnoldinterview1997.pdf
 ↑ http://www.ias.ac.in/resonance/Volumes/19/09/07870796.pdf
 ↑ Note: It also appears in another article by him, but in English: Local Normal Forms of Functions, http://www.maths.ed.ac.uk/~aar/papers/arnold15.pdf
 ↑ Dirk Siersma; Charles Wall; V. Zakalyukin (30 June 2001). New Developments in Singularity Theory. Springer Science & Business Media. p. 29. ISBN 9780792369967.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
 ↑ http://arxiv.org/pdf/math/0203260.pdf
 ↑ Terence Tao (22 March 2013). Compactness and Contradiction. American Mathematical Soc. pp. 205–206. ISBN 9780821894927.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
 ↑ http://www.theguardian.com/science/2010/aug/19/viarnoldobituary
 ↑ IAMP News Bulletin, July 2010, pp. 25–26
 ↑ Note: The paper also appears with other names, as in http://perso.univrennes1.fr/mariefrancoise.roy/cirm07/arnold.pdf
 ↑ A. G. Khovanskii; Aleksandr Nikolaevich Varchenko; V. A. Vasiliev (1997). Topics in Singularity Theory: V. I. Arnold's 60th Anniversary Collection (preface). American Mathematical Soc. p. 10. ISBN 9780821808078.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
 ↑ Arnold: Swimming Against the Tide. p. 159.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
 ↑ http://arxiv.org/pdf/math/0004134.pdf
 ↑ O. Karpenkov, "Vladimir Igorevich Arnold", Internat. Math. Nachrichten, no. 214, pp. 49–57, 2010. (link to arXiv preprint)
 ↑ Harold M. Schmeck Jr. (June 27, 1982). "American and Russian Share Prize in Mathematics". New York Times.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
 ↑ "Book of Members, 17802010: Chapter A" (PDF). American Academy of Arts and Sciences. Retrieved 25 April 2011.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
 ↑ D. B. Anosov, A. A. Bolibrukh, Lyudvig D. Faddeev, A. A. Gonchar, M. L. Gromov, S. M. GuseinZade, Yu. S. Il'yashenko, B. A. Khesin, A. G. Khovanskii, M. L. Kontsevich, V. V. Kozlov, Yu. I. Manin, A. I. Neishtadt, S. P. Novikov, Yu. S. Osipov, M. B. Sevryuk, Yakov G. Sinai, A. N. Tyurin, A. N. Varchenko, V. A. Vasil'ev, V. M. Vershik and V. M. Zakalyukin (1997) . "Vladimir Igorevich Arnol'd (on his sixtieth birthday)". Russian Mathematical Surveys, Volume 52, Number 5. (translated from the Russian by R. F. Wheeler)
 ↑ American Physical Society – 2001 Dannie Heineman Prize for Mathematical Physics Recipient
 ↑ The Wolf Foundation – Vladimir I. Arnold Winner of Wolf Prize in Mathematics
 ↑ Названы лауреаты Государственной премии РФ Kommersant 20 May 2008.
 ↑ Lutz D. Schmadel. Dictionary of Minor Planet Names. Springer Science & Business Media. p. 717. ISBN 9783642297182.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
 ↑ Editorial (2015), "Journal Description Arnold Mathematical Journal", Arnold Mathematical Journal, 1 (1): 1–3, doi:10.1007/s4059801500066<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>.
 ↑ http://www.mathunion.org/db/ICM/Speakers/SortedByLastname.php
 ↑ Martin L. White (2015). "Vladimir Igorevich Arnold". Encyclopædia Britannica.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
 ↑ Thomas H. Maugh II (June 23, 2010). "Vladimir Arnold, noted Russian mathematician, dies at 72". The Washington Post. Retrieved March 18, 2015.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
 ↑ Review by Ian N. Sneddon (Bulletin of the American Mathematical Society, Vol. 2): http://www.ams.org/journals/bull/19800202/S027309791980147552/S027309791980147552.pdf
 ↑ Review by R. Broucke (Celestial Mechanics, Vol. 28): http://adsabs.harvard.edu/full/1982CeMec..28..345A
Further reading
 Khesin, Boris; Tabachnikov, Serge (Coordinating Editors). "Tribute to Vladimir Arnold", Notices of the American Mathematical Society, March 2012, Volume 59, Number 3, pp. 378–399.
 Khesin, Boris; Tabachnikov, Serge (Coordinating Editors). "Memories of Vladimir Arnold", Notices of the American Mathematical Society, April 2012, Volume 59, Number 4, pp. 482–502.
 Boris A. Khesin; Serge L. Tabachnikov (2014). Arnold: Swimming Against the Tide. American Mathematical Society. ISBN 9781470416997.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
 Leonid Polterovich; Inna Scherbak (7 September 2011). "V.I. Arnold (1937–2010)". Jahresbericht der Deutschen MathematikerVereinigung. 113 (4): 185–219. doi:10.1365/s1329101100276.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
 "Features: "Knotted Vortex Lines and Vortex Tubes in Stationary Fluid Flows"; "On Delusive Nodal Sets of Free Oscillations"" (PDF). EMS Newsletter (96): 26–48. June 2015. ISSN 1027488X.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
External links
Wikimedia Commons has media related to [[commons:Lua error in Module:WikidataIB at line 506: attempt to index field 'wikibase' (a nil value).Lua error in Module:WikidataIB at line 506: attempt to index field 'wikibase' (a nil value).]]. 
Wikiquote has quotations related to: Vladimir Arnold 
 V. I. Arnold's web page
 Personal web page
 V. I. Arnold lecturing on Continued Fractions
 A short curriculum vitae
 On Teaching Mathematics, text of a talk espousing Arnold's opinions on mathematical instruction
 Problems from 5 to 15, a text by Arnold for school students, available at the IMAGINARY platform
 Vladimir Arnold at the Mathematics Genealogy Project
 S. Kutateladze, Arnold Is Gone
 В.Б.Демидовичем (2009), МЕХМАТЯНЕ ВСПОМИНАЮТ 2: В.И.Арнольд, pp. 25–58
 Author profile in the database zbMATH
 Articles containing Russianlanguage text
 Articles to be expanded from February 2015
 Articles using small message boxes
 Articles containing Frenchlanguage text
 Commons category link from Wikidata
 1937 births
 2010 deaths
 20thcentury mathematicians
 21stcentury mathematicians
 Russian mathematicians
 Russian Jews
 Deaths from peritonitis
 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
 Members of the United States National Academy of Sciences
 Moscow State University alumni
 Moscow State University faculty
 People from Odessa
 Soviet mathematicians
 State Prize of the Russian Federation laureates
 Topologists
 University of Paris faculty
 Wolf Prize in Mathematics laureates
 Mathematical physicists
 Textbook writers
 Geometers
 Algebraic geometers
 Differential geometers
 Dynamical systems theorists
 Newton scholars