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| Vladimir Arnolʹd | |
|---|---|
| Name | Vladimir Arnolʹd |
| Birth date | 12 June 1937 |
| Birth place | Odessa |
| Death date | 29 June 2010 |
| Death place | Paris |
| Nationality | Soviet Union, Russia, France |
| Fields | Mathematics, Mathematical Physics |
| Alma mater | Moscow State University |
| Doctoral advisor | Iosif Shklover |
| Known for | KAM theory, Arnolʹd conjecture, Arnolʹd–Smale theorem, Arnolʹd diffusion, Arnolʹd tongues |
Vladimir Arnolʹd was a Soviet and Russian mathematician and physicist whose work reshaped dynamical systems, symplectic geometry, and singularity theory. He made foundational contributions linking Hamiltonian mechanics, celestial mechanics, and catastrophe theory and influenced generations at institutions including Moscow State University and Steklov Institute of Mathematics. His eclectic style bridged mathematicians and physicists such as Andrey Kolmogorov, Lev Landau, Aleksandr Lyapunov, Israel Gelfand, and John Milnor.
Arnolʹd was born in Odessa and educated in the Soviet system; he studied at Moscow State University where he encountered teachers and influences including Andrey Kolmogorov, Pavel Alexandrov, Israel Gelfand, and Sergey Smale. During his student years he engaged with problems related to Hamiltonian systems, Poincaré, Henri Poincaré, Jacques Hadamard, and Sofia Kovalevskaya. His doctoral work at the Steklov Institute of Mathematics placed him in the lineage of Nikolai Luzin and Dmitri Anosov while interacting with contemporaries such as Yakov Sinai and Lev Pontryagin.
Arnolʹd held positions at Moscow State University, the Steklov Institute of Mathematics, and later at institutions in France including Paris VI (Pierre and Marie Curie University). He supervised students who became prominent figures like Victor Ginzburg, Yuri Manin, Boris Khesin, and Alexei Varchenko. He lectured at venues such as the International Congress of Mathematicians, the Courant Institute, Institute for Advanced Study, and the École Normale Supérieure. His collaborations and exchanges connected him to researchers at Princeton University, Harvard University, Cambridge University, Oxford University, and ETH Zurich.
Arnolʹd formulated and advanced the KAM theory building on work by Andrey Kolmogorov and Jürgen Moser, impacting studies by V.I. Arnold, Michael Herman, Jean-Christophe Yoccoz, and Charles Fefferman. He proposed the Arnolʹd conjecture in symplectic topology that stimulated work by Clifford Taubes, Yasha Eliashberg, Paul Seidel, and Dusa McDuff. His classification of singularities influenced René Thom's catastrophe theory and tied to research by John Milnor, Vladimir Vassiliev, Mikhail Gromov, and Maxim Kontsevich. He discovered Arnolʹd diffusion and described Arnolʹd tongues in circle maps, connected to studies by Herman, Michael R. Herman, Jean-Baptiste Boussinesq, and Kolmogorov. Arnolʹd introduced geometric viewpoints linking Hamiltonian mechanics with Lagrangian submanifolds, Morse theory, Floer homology, and problems later addressed by Andreas Floer, Simon Donaldson, and Edward Witten. He contributed to caustics, wavefronts, and optics through singularity theory interacting with Vladimir Igorevich Arnold, Christopher Zeeman, and René Thom's circles. His name is attached to results such as the Arnolʹd–Smale theorem and concepts used by Pierre Deligne, Alexander Grothendieck, and Jean-Pierre Serre in broader mathematical contexts.
Arnolʹd authored influential texts including works on ordinary differential equations, symplectic geometry, singularity theory, and mathematical methods of classical mechanics. His books influenced readers alongside texts by V.I. Arnolʹd, Kolmogorov, Moser, Yakov Sinai, John Milnor, and Michael Atiyah. He published in journals associated with Russian Academy of Sciences, Acta Mathematica, Inventiones Mathematicae, Communications in Mathematical Physics, and proceedings of the International Congress of Mathematicians. His collected papers and lecture notes were disseminated through publishers such as Springer, Cambridge University Press, and Translations of the American Mathematical Society and are cited alongside works by Hermann Weyl, Sophus Lie, and Henri Poincaré.
Arnolʹd received recognitions including memberships in academies such as the Russian Academy of Sciences, the French Academy of Sciences (corresponding), and foreign memberships in organizations like the National Academy of Sciences and the Academia Europaea. He was awarded prizes comparable to those conferred by institutions such as the European Mathematical Society, International Mathematical Union, CNRS, and national honors from France and Russia. He gave plenary addresses at the International Congress of Mathematicians and held honorary doctorates from universities including Paris VI and other European institutions, joining lists with laureates like Grigori Perelman, Alexander Grothendieck, and Jean-Pierre Serre.
Arnolʹd's ideas shaped research programs in dynamical systems, symplectic topology, algebraic geometry, and mathematical physics, influencing figures such as Maxim Kontsevich, Yuri Manin, Mikhail Gromov, Dusa McDuff, Andreas Floer, Paul Seidel, Clifford Taubes, Edward Witten, and Simon Donaldson. His pedagogical style permeated curricula at Moscow State University, Steklov Institute of Mathematics, École Normale Supérieure, and Princeton University. Concepts bearing his name appear in research at institutions like Institute for Advanced Study, Courant Institute, ETH Zurich, Harvard University, and Cambridge University, and in applications to celestial mechanics, optics, quantum field theory, and topological quantum field theory. His collected lectures and problem books continue to train students alongside problem books by Paul Erdős, Terence Tao, and George Pólya.
Category:Mathematicians Category:1937 births Category:2010 deaths