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Mathematical Events of the Twentieth Century

  • Book
  • Feb 2007

Overview

Editors:
  1. † A. A. Bolibruch
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  2. Yu. S. Osipov

    1. Academy of Sciences, Moscow, Russia

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  3. Ya. G. Sinai

    1. Department of Mathematics, University of Princeton, Princeton, USA

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  4. V. I. Arnold
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  5. A. A. Bolibruch
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  6. A. M. Vershik
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  7. Yu. I. Manin
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  8. Yu. S. Osipov
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  9. Ya.G. Sinai
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  10. V.M. Tikhomirov
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  11. L.D. Faddeev
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  12. V. B. Philippov
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  • During the 20th century the Soviet Union/Russia became a world leader for mathematics

  • This book documents the highlights of this development

  • Includes supplementary material: sn.pub/extras

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Table of contents (24 chapters)

  1. Front Matter

    Pages I-VIII
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  2. Dynamical Systems in the 1960s: The Hyperbolic Revolution

    • D. V. Anosov
    Pages 1-17

  3. From Hilbert’s Superposition Problem to Dynamical Systems

    • V. I. Arnold
    Pages 19-47

  4. Inverse Monodromy Problems of the Analytic Theory of Differential Equations

    • A. A. Bolibruch
    Pages 49-74

  5. What Modern Mathematical Physics Is Supposed to Be

    • L. D. Faddeev
    Pages 75-84

  6. Discovery of the Maximum Principle

    • R. V. Gamkrelidze
    Pages 85-99

  7. The Qualitative Theory of Differential Equations in the Plane

    • Yu. S. Il’yashenko
    Pages 101-132

  8. Computerization… Let’s Be Careful

    • P. S. Krasnoshchekov
    Pages 133-143

  9. The Generalized Shift, Transformation Operators, and Inverse Problems

    • V. A. Marchenko
    Pages 145-162

  10. Mathematics and the Trajectories of Typhoons

    • V. P. Maslov
    Pages 163-183

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

    • Yu. V. Matiyasevich
    Pages 185-213

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

    • V. D. Milman
    Pages 215-241

  13. About Aleksandrov, Pontryagin and Their Scientific Schools

    • E. F. Mishchenko
    Pages 243-268

  14. Hilbert’s Seventh Problem

    • Yu. V. Nesterenko
    Pages 269-282

  15. The Great Kolmogorov

    • S. M. Nikol’skii
    Pages 283-296

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

    • A. N. Parshin
    Pages 297-329

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

    • A. A. Razborov
    Pages 331-346

  18. Homoclinic Trajectories: From Poincaré to the Present

    • L. P. Shil’nikov
    Pages 347-370

  19. From “Disorder” to Nonlinear Filtering and Martingale Theory

    • A. N. Shiryaev
    Pages 371-397

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

    • Ya. G. Sinai
    Pages 399-407
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Keywords

About this book

Russian mathematics (later Soviet mathematics, and Russian mathematics once again) occupies a special place in twentieth-century mathematics. In addition to its well-known achievements, Russian mathematics established a unique style of research based on the existence of prominent mathematical schools. These schools were headed by recognized leaders, who became famous due to their talents and outstanding contributions to science. The present collection is intended primarily to gather in one book the t- timonies of the participants in the development of mathematics over the past century. In their articles the authors have expressed their own points of view on the events that took place. The editors have not felt that they had a right to make any changes, other than stylistic ones, or to add any of their own commentary to the text. Naturally, the points of view of the authors should not be construed as those of the editors. The list of mathematicians invited to participate in the present edition was quite long. Unfortunately, some of the authors for various reasons did not accept our invitation, and regretfully a number of areas of research are not fully represented here. Nevertheless, the material that has been assembled is of great value not only in the scientific sense, but also in its historical context. We wish to express our gratitude to all the authors who contributed.

Reviews

"... 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

Editors and Affiliations

  • Academy of Sciences, Moscow, Russia

    Yu. S. Osipov

  • Department of Mathematics, University of Princeton, Princeton, USA

    Ya. G. Sinai

Bibliographic Information

  • Book Title: Mathematical Events of the Twentieth Century

  • Editors: † A. A. Bolibruch, Yu. S. Osipov, Ya. G. Sinai, V. I. Arnold, A. A. Bolibruch, A. M. Vershik, Yu. I. Manin, Yu. S. Osipov, Ya.G. Sinai, V.M. Tikhomirov, L.D. Faddeev, … V. B. Philippov

  • DOI: https://doi.org/10.1007/3-540-29462-7

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2006

  • Hardcover ISBN: 978-3-540-23235-3Published: 20 September 2005

  • Edition Number: 1

  • Number of Pages: VIII, 545

  • Number of Illustrations: 96 b/w illustrations

  • Additional Information: Original Russian edition published by PHASIS, Moscow, Russia, 2003. English edition published jointly with PHASIS, Moscow.

  • Topics: History of Mathematical Sciences, Mathematics, general, Physics, general

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