On-line papers of V.I.Arnold

Mathematical papers and talks

On the representability of functions of two variables in the form $\chi(\phi(x)+\psi(y))$. Uspehy Math. Nauk 1957, 12:2, 119-121.

Russian text.

On the functions of three variables. Doklady AN USSR, 1957, 114:4, 679-681.

Russian text.

On the representation of continuous functions of three variables by the superpositions of continuous functions of two variables. Matem. Sbornik, 1959, 48:1, 3-74 and 1962, 56:3, 392. (Scan of some pages.)

Russian text.

The cohomology ring of the group of colored [meaning: pure] braids. Mat.Zametki (Math. Notes), 1969, 5:2, 227-231.

English text.

Nekotorye zadachi teorii differencialnyh uravnenij. Tezisy lekcii, 9 pages. 1974.

scan, pdf, 5Mb (in Russian).

A-graded Algebras and Continued Fractions (1989).

Russian text (translated from the English original by S.V.Chmutov).

The Vassiliev Theory of Discriminants and Knots. Notes of the talk at European Congress of 1992, published in 1994 (?).

part 1 (pdf), part 2 (pdf).

On topological properties of Legendre projections in contact geometry of wave fronts (1993).

English version.

Plane Curves, Their Invariants, Perestroikas and Classificatoins. Forschungsinstitut fuer Mathematik ETH Zuerich, 1993.

scanned pdf file (58 pages)

Problems, solvable and non-solvable geometrically and analytically (1994).

Russian text (translated from the French original by S.V.Duzhin).

Toronto lectures, June 1997 (last updated August, 1998).

• Lecture 1: From Hilbert's Superposition Problem to Dynamical Systems. Postscript, TeX source.
• Lecture 2: Symplectization, Complexification and Mathematical Trinities. Postscript, TeX source.
• Lecture 3: Topological Problems in Wave Propagation Theory and Topological Economy Principle in Algebraic Geometry. Postscript, TeX source.

Remarks on the Parabolic Curves on Surfaces and on the Many-Dimensional M\"obius--Sturm Theory. 26-Aug-97.

Abstract. AMSTeX file. PostScript file.

Towards the Legendrian Sturm Theory of Space Curves (Dec-97; Web edition 30-Mar-98).

AMSTeX source file, PostScript.

On the problem of realization of a given Gaussian curvature function. 12-Feb-98.

TeX file. DVI file.

Singularities of Fractions and Behaviour of Polynomials at Infinity (17-Mar-98).

LaTeX source file, PostScript.

Topological problems of the theory of asymptotic curves (14-May-98).

LaTeX source file (12 Kb), PostScript (42 Kb).

Relatives of the quotient of the complex projective plane by the complex conjugation. 26-May-98.

Abstract.
LaTeX source file (12 Kb).
PostScript (51 Kb).
Russian LaTeX (13 Kb).
Russian PostScript (61 Kb).

Higher dimensional continued fractions. 02-Sep-98.

Abstract.
PostScript file (84 Kb).

Simple singularities of curves. (Russian version: 20-Nov-98, English version: 17-Mar-99).

Abstract (Russian).
Abstract (English).
LaTeX (Russian).(10 Kb)
PostScript (Russian) (47 Kb).
LaTeX (English).(9 Kb)
PostScript (Engslish) (65 Kb).

First steps of local symplectic algebra. First version 12-Jan-99, updated 22-Jan-99.

Abstract.
TeX source file (22-Jan-99).(8 Kb)
PostScript file (22-Jan-99) (39 Kb).

Polymathematics: is mathematics a single science or a set of arts?. On the server since 10-Mar-99.

Abstract.
LaTeX source file.(16 Kb)
PostScript file (78 Kb).

First steps of local contact algebra. 17-Mar-99.

Abstract.
TeX source file.(12 Kb)
PostScript file (48 Kb).

Complexity of finite sequences of 0 and 1 and geometry of finite functional spaces. (In Russian). 14 pages. 21-Dec-05.

TeX source file (UNIX).(12 Kb)
TeX source file (DOS).(12 Kb)
PostScript file (115 Kb).

Smooth functions statistics. Funct. Anal. Other Math. 1 (2006), no. 2, pp. 111-118.

Pdf file, 9 pages.

Problem lists

Mathematical Trivium (in French).

LaTeX source file.
PostScript file.

Problem List (February 1998).

LaTeX source file.
PostScript file.

Problem List (September 1998).

LaTeX source file.
PostScript file (gzipped).

Arnold's problems, Mar-99 (in Russian).

TeX file.
PostScript file.

Several problems about semigroups of natural numbers. Feb-99.

Text file (Russian in transliteration)..

Two problems (September 2001).

PostScript file (gzipped).

Problem List (January 2002).

PostScript file (gzipped).

Essays and talks on mathematics in society

O prepodavanii matematiki ("Sur l'enseignment mathematique"). Published in Uspehi Mat. Nauk, 1998.

Russian TeX file. Russian PostScript file. French TeX file. French PostScript file.

Innumeracy and the Fires of the Inquisition (Article in the newspaper "Izvestiya" 17-Jan-98). Web edition 22-May-98.

English translation (LaTeX file).
English translation (postscript).

The antiscientifical revolution and mathematics. (Talk at the meeting of the Pontifical Academy at Vatican, 26 October 1998, "Changing concepts of nature at the turn of the millennium".)

LaTeX source file (6 Kb).
PostScript (19 Kb).

Polymathematics: is mathematics a set of arts or a single science? (talk to be given at the conference "Mathematics towards the third millennium" (Rome, May 27-29, 1999) at the Accademia dei Lincei). 29-Sep-98.

abstract.

Pobednoe shestvie antinauchnoi revolucii ("Triumphant pace of antiscientific revolution") (Article in the newspaper "Izvestiya", February 1999). Posted on this site on 16-Sep-00.

text file (Cyrillic).
text file (transliteration).
LaTeX file.
postscript file.

Kalifornijskie voiny v Dubne ("Californian wars in Dubna") (Article in the newspaper "Obschaya gazeta", September 2000). Posted on this site on 23-Sep-00.

text file (Cyrillic).
text file (transliteration).
postscript file.
See also a related report by S.Chmutov and S.Duzhin.

On-line papers of V.I.Arnold are also available at the Web site of the Parisian seminar.