Vladimir Arnold

Biography

Vladimir Igorevich Arnold (12 June 1937 – 3 June 2010) was a Soviet and Russian mathematician known for his work in dynamical systems, classical mechanics, topology, and mathematical physics. Born in Odesa, he spent much of his career at Lomonosov Moscow State University in the Faculty of Mechanics and Mathematics, where he studied and later taught from 1961 to 1986. In 1986, he moved to the Steklov Mathematical Institute and began working at Paris Dauphine University in 1993, splitting his time between Moscow and Paris until his death in the 12th arrondissement of Paris on 3 June 2010.

Arnold's work was impressive in its variety and depth. At nineteen, he solved Hilbert's thirteenth problem, which asked if certain functions of several variables could be written as combinations of functions with fewer variables. He then helped develop the Kolmogorov–Arnold–Moser theorem, or KAM theory, focusing on the stability of quasi-periodic motions in Hamiltonian systems, which greatly impacted celestial mechanics and classical physics. He also helped create topological Galois theory with his student Askold Khovanskii and made significant contributions to symplectic topology.

In addition to these achievements, Arnold contributed to catastrophe theory, singularity theory, real algebraic geometry, hydrodynamics through differential geometry, and ordinary differential equations. His idea of Arnold diffusion explained how slight changes in some dynamical systems could lead to significant instability over time, affecting both mathematics and physics. The Arnold tongue, related to mode locking in oscillators, and the Arnold conjecture in symplectic geometry show his wide-ranging ideas.

Arnold was also a well-known teacher and popularizer of mathematics. He wrote influential textbooks like "Mathematical Methods of Classical Mechanics" and "Ordinary Differential Equations," which have been translated into many languages and are used worldwide. His seminars at Moscow State University influenced many students and guided Russian mathematics for years. He criticized overly abstract math education, opposing the Bourbaki school's approach and insisting on understanding the physical intuition behind math. His saying, 'Mathematics is the part of physics where experiments are cheap,' summed up his teaching philosophy.

Arnold received many awards, including the Lenin Prize in 1965, the first Crafoord Prize in Mathematics in 1982 (shared with Louis Nirenberg), the Lobachevsky Prize in 1992, the Harvey Prize in 1994, and the Wolf Prize in Mathematics in 2001. He was elected a Foreign Member of the Royal Society in 1988 and received honorary doctorates from Pierre and Marie Curie University, the University of Madrid Complutense, and others. He helped establish the Independent University of Moscow to maintain high standards in mathematical education during challenging times in Russia.