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Description
(Text)
This book contains several contributions on the most outstanding events in the development of twentieth century mathematics, representing a wide variety of specialities in which Russian and Soviet mathematicians played a considerable role. The articles are written in an informal style, from mathematical philosophy to the description of the development of ideas, personal memories and give a unique account of personal meetings with famous representatives of twentieth century mathematics who exerted great influence in its development.
This book will be of great interest to mathematicians, who will enjoy seeing their own specialities described with some historical perspective. Historians will read it with the same motive, and perhaps also to select topics for future investigation.
(Table of content)
D.V.Anosov: Dynamical Systems in the 1960s: The Hyperbolic Revolution.- V.I.Arnold: From Hilbert's Superposition Problem to Dynamical Systems.- A.A.Bolibruch: Inverse Monodromy Problems of the Analytic Theory of Differential Equations.- L.D.Faddeev: What Modern Mathematical Physics is Supposed to be.- R.V.Gamkrelidze: Discovery of the Maximum Principle.- Yu.S.Il'yashenko: The Qualitative Theory of Diferential Equations in the Plane.- P.S.Krasnoshchekov: Computerization... Let's be Careful.- V.A.Marchenko: The Generalized Shift, Transformation Operators, and Inverse Problems.- V.P.Maslov: Mathematics and the Trajectories of Typhoons.- Yu.V.Matiyasevich: Hilbert's Tenth Problem: Diophantine Equations in the Twentieth Century.- V.D.Milman: Observations on the Movement of People and Ideas in Twentieth-Century Mathematics.- E.F.Mishchenko: About Aleksandrov, Pontryagin and Their Scientific Schools.- Yu.V.Nesterenko: Hilbert's Seventh Problem.- S.M.Nikol'skii: The Great Kolmogorov.- A.N.Parshin: Numbers as Functions: The Development of an Idea in the Moscow School of Algebraic Geometry.- A.A.Razborov: The P=NP-Problem: A View from the 1990s.- L.P.Shil'nikov: Homoclinic Trajectories: From Poincaré to the Present.- A.N.Shiryaev: From 'Disorder' to Nonlinear Filtering and Martingale Theory.- Ya.G.Sinai: How Mathematicians and Physicists Found Each Other in the Theory of Dynamical Systems and in Statistical Mechanics.- V.M.Tikhomirov: Approximation Theory in the Twentieth Century.- A.M.Vershik: The Life and Fate of Functional Analysis in the Twentieth Century.- A.G.Vitushkin: Half a Century as one day.- V.S.Vladimirov: Nikolai Nikolaevich Bogolyubov - Mathematician by the Grace of God.- V.I.Yudovich: Global Solvability Versus Collapse in the Dynamics of an Incompressible Fluid.- Name Index
(Review)
"... This is, obviously, a very cursory look at a collection with a great deal of information and many fascinating features, mathematical and nonmathematical, that often make one wish for more. ..."
Richard Beals, SIAM Review Vol. 48, Issue 3, p. 596-600, 2006
