2006

Mathematical Events of the Twentieth Century

ISBN: 978-3-540-23235-3 (Print) 978-3-540-29462-7 (Online)

Table of contents (24 chapters)

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  1. Front Matter

    Pages I-VIII

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    Book Chapter

    Pages 1-17

    Dynamical Systems in the 1960s: The Hyperbolic Revolution

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    Book Chapter

    Pages 19-47

    From Hilbert’s Superposition Problem to Dynamical Systems

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    Pages 49-74

    Inverse Monodromy Problems of the Analytic Theory of Differential Equations

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    Pages 75-84

    What Modern Mathematical Physics Is Supposed to Be

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    Pages 85-99

    Discovery of the Maximum Principle

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    Pages 101-132

    The Qualitative Theory of Differential Equations in the Plane

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    Pages 133-143

    Computerization… Let’s Be Careful

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    Pages 145-162

    The Generalized Shift, Transformation Operators, and Inverse Problems

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    Book Chapter

    Pages 163-183

    Mathematics and the Trajectories of Typhoons

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    Book Chapter

    Pages 185-213

    Hilbert’s Tenth Problem: Diophantine Equations in the Twentieth Century

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    Book Chapter

    Pages 215-241

    Observations on the Movement of People and Ideas in Twentieth-Century Mathematics

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    Book Chapter

    Pages 243-268

    About Aleksandrov, Pontryagin and Their Scientific Schools

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    Pages 269-282

    Hilbert’s Seventh Problem

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    Pages 283-296

    The Great Kolmogorov

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    Book Chapter

    Pages 297-329

    Numbers as Functions: The Development of an Idea in the Moscow School of Algebraic Geometry

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    Book Chapter

    Pages 331-346

    The P \(\mathop = \limits^? \) NP-Problem: A View from the 1990s

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    Book Chapter

    Pages 347-370

    Homoclinic Trajectories: From Poincaré to the Present

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    Book Chapter

    Pages 371-397

    From “Disorder” to Nonlinear Filtering and Martingale Theory

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    Book Chapter

    Pages 399-407

    How Mathematicians and Physicists Found Each Other in the Theory of Dynamical Systems and in Statistical Mechanics

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    Book Chapter

    Pages 409-436

    Approximation Theory in the Twentieth Century

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