Vladimir Arnold
Soviet and Russian mathematician (source does not provide details about Arnold).
Vladimir Igorevich Arnold was a Soviet and Russian mathematician whose work spanned numerous fields, including dynamical systems, algebra, catastrophe theory, topology, real algebraic geometry, symplectic geometry, differential equations, classical mechanics, hydrodynamics, geometric analysis, and singularity theory. He is most famous for the Kolmogorov–Arnold–Moser theorem, which addresses the stability of integrable systems. Arnold achieved his first major result at age nineteen in 1957 by solving Hilbert’s thirteenth problem, demonstrating that any continuous function of several variables could be constructed using a finite number of functions of just two variables. He co-founded three new branches of mathematics: topological Galois theory with his student Askold Khovanskii, KAM theory with Andrey Kolmogorov and Jürgen Moser, and symplectic topology. Arnold was also a prolific popularizer of mathematics through his lectures, seminars, and textbooks, including *Mathematical Methods of Classical Mechanics* and *Ordinary Differential Equations*, many of which were translated into English. His educational philosophy opposed the Bourbaki approach. He is known for the dictum that mathematics is the part of physics where experiments are cheap, and the Arnold principle states that discoveries are rarely attributed to the correct person. Arnold worked at Moscow State University from 1961 to 1986, at the Steklov Mathematical Institute from 1986 onward, and at Paris Dauphine University from 1993. He was a founder of the Independent University of Moscow and received the inaugural Crafoord Prize in 1982, the Wolf Prize in Mathematics in 2001, and the Shaw Prize in 2008.
- born
- 12 June 1937, Odessa, Ukrainian SSR, Soviet Union
- died
- 3 June 2010
- field
- Mathematics
- nationality
- Soviet and Russian
- known_for
- Kolmogorov–Arnold–Moser theorem, Hilbert's thirteenth problem, Arnold tongues, Arnold web, Liouville–Arnold theorem, classification of simple singularities, Arnold conjecture
Quick Facts
- Native Name Lang
- ru
- Birth Date
- df=y · 1937 · 06 · 12
- Birth Place
- Odessa, Ukrainian SSR, Soviet Union
- Death Date
- df=y · 2010 · 06 · 03 · 1937 · 06 · 12
- Death Place
- Paris, France
- Citizenship
- Soviet Union · Russia
- Fields
- Mathematics
- Workplaces
- Paris Dauphine University / Steklov Institute of Mathematics / Independent University of Moscow / Moscow State University
- Education
- Moscow State University
- Thesis Title
- On The Representation of Continuous Functions of 3 Variables By The Superpositions of Continuous Functions of 2 Variables
- Thesis Year
- 1961
- Doctoral Advisor
- Andrey Kolmogorov
Facts from the source article.
Lore & Background
Vladimir Igorevich Arnold (1937–2010) was a Soviet and Russian mathematician whose work spanned dynamical systems, algebra, topology, geometry, and classical mechanics. He is best known for the Kolmogorov–Arnold–Moser theorem on the stability of integrable systems, and he co-founded three mathematical branches: topological Galois theory, KAM theory, and symplectic topology. At age 19, while a student of Andrey Kolmogorov, he solved Hilbert’s thirteenth problem by showing that any continuous function of several variables can be constructed from a finite number of two-variable functions. Arnold also contributed to catastrophe theory, real algebraic geometry, singularity theory, and hydrodynamics, and later shifted focus to discrete mathematics. He authored influential textbooks and popular mathematics books, many translated into English, and was a noted populariser of mathematics. His views on education opposed those of the Bourbaki group. He is remembered for the dictum “Mathematics is the part of physics where experiments are cheap” and the Arnold principle that discoveries are rarely attributed to the correct person. Born in Odessa to a mathematician father and an art historian mother, he studied at Moscow State University, where his teachers included Kolmogorov, Gelfand, and Pontriagin. He worked at Moscow State University, the Steklov Mathematical Institute, and Paris Dauphine University, and helped found the Independent University of Moscow. He supervised 46 PhD students and received the inaugural Crafoord Prize, the Wolf Prize, and the Shaw Prize.
Reader's Guide
Vladimir Arnold’s mathematical work was deeply rooted in the interplay between geometry and physics, a perspective he championed throughout his career. He is most famous for co-founding KAM theory, which explains the stability of many quasi-periodic motions in perturbed Hamiltonian systems, and for solving Hilbert’s thirteenth problem as a teenager by proving that any continuous function of several variables can be built from a finite number of functions of just two variables. Beyond these achievements, he helped establish three entirely new branches of mathematics: topological Galois theory, KAM theory, and symplectic topology. His influence extended across dynamical systems, catastrophe theory, algebra, topology, real algebraic geometry, differential equations, classical mechanics, hydrodynamics, and singularity theory, where he posed the ADE classification problem. Arnold was also a prolific educator and popularizer, authoring widely used textbooks and popular books that shaped generations of mathematicians and physicists. His teaching philosophy explicitly opposed the formal, axiomatic approach of the Bourbaki group. He is remembered for his dictum that mathematics is the part of physics where experiments are cheap, and for the Arnold principle, which wryly observes that discoveries are rarely attributed to the correct person. His later years saw a shift in focus toward discrete mathematics.
Did You Know?
- Vladimir Arnold only once, as the person who reported that Alexander Gelfond was the Chief Cryptographer of the Soviet Navy during World War II.
Frequently Asked Questions
Who is Vladimir Arnold?
Vladimir Igorevich Arnold (1937–2010) was a Soviet and Russian mathematician born in Odessa whose work spanned dynamical systems, singularity theory, and symplectic geometry. He is widely regarded as one of the most versatile and influential mathematicians of the twentieth century.
What is the KAM theorem and what did Arnold contribute?
The Kolmogorov–Arnold–Moser theorem states that most invariant tori in a near-integrable Hamiltonian system survive under small perturbations. Arnold co-developed the rigorous proof of this result, establishing the stability framework that underpins much of modern celestial mechanics and nonlinear dynamics.
What did Arnold solve at age 19?
In 1956, at nineteen, he produced a negative solution to Hilbert's thirteenth problem, demonstrating that a general algebraic function of three or more variables cannot be written as a finite composition of continuous functions of just two variables. The result closed a question David Hilbert had posed in 1900.
What is the Arnold conjecture?
The Arnold conjecture, formulated in the 1980s, asserts that the number of fixed points of a Hamiltonian diffeomorphism on a compact symplectic manifold is bounded below by the sum of its Betti numbers. It became a central driving problem in symplectic topology and Floer theory.
Why is Vladimir Arnold considered so important to mathematics?
Arnold uniquely bridged pure and applied mathematics, producing foundational results in dynamical systems (KAM theory, Arnold tongues, Arnold web), the classification of simple singularities, and the geometric foundations of mechanics (Liouville–Arnold theorem). His ability to connect topology, algebra, and physics made him a unifying figure whose ideas still shape research across multiple fields.
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