Vladimir Igorevich Arnold

Abstract

The list of fields of mathematics in which Vladimir Igorevich Arnold (born in 1937 in Odessa, passed away in 2010 in Paris) made fundamental contributions is very long. If, without any attempt at being exhaustive, we limit ourselves to geometry and mathematical physics, we have algebraic geometry (real and complex), symplectic topology and the geometry of contact varieties on the one hand, and on the other hydrodynamics, classical mechanics, celestial mechanics, integrable systems and the theory of dynamical systems. His name is tied to many key concepts in twentieth-century mathematics and mechanics, such as the Kolmogorov–Arnold–Moser (KAM) theory, Arnold diffusion, Arnold-stability (or A-stability, in hydrodynamics), and the characteristic classes of Arnold–Maslov, to name only a few. This belies what he himself calls “Arnold’s law”, according to which only a very small number of discoveries are attributed to the right person.