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© 2007

Kolmogorov’s Heritage in Mathematics

  • Éric Charpentier
  • Annick Lesne
  • Nikolaï K. Nikolski
Book

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Loïc Chaumont, Laurent Mazliak, Marc Yor
    Pages 41-66
  3. Giuseppe Da Prato
    Pages 67-96
  4. Mikhail Nikouline, Valentin Solev
    Pages 109-137
  5. Victor M. Buchstaber
    Pages 139-150
  6. Karl Sigmund
    Pages 177-186
  7. Étienne Ghys
    Pages 187-213
  8. John H. Hubbard
    Pages 215-238
  9. Bruno Durand, Alexander Zvonkin
    Pages 281-299

About this book

Introduction

A.N. Kolmogorov (b. Tambov 1903, d. Moscow 1987) was one of the most brilliant mathematicians that the world has ever known. Incredibly deep and creative, he was able to approach each subject with a completely new point of view: in a few magnificent pages, which are models of shrewdness and imagination, and which astounded his contemporaries, he changed drastically the landscape of the subject.

Most mathematicians prove what they can, Kolmogorov was of those who prove what they want. For this book several world experts were asked to present one part of the mathematical heritage left to us by Kolmogorov.

Each chapter treats one of Kolmogorov's research themes, or a subject that was invented as a consequence of his discoveries. His contributions are presented, his methods, the perspectives he opened to us, the way in which this research has evolved up to now, along with examples of recent applications and a presentation of the current prospects.

This book can be read by anyone with a master's (even a bachelor's) degree in mathematics, computer science or physics, or more generally by anyone who likes mathematical ideas. Rather than present detailed proofs, the main ideas are described. A bibliography is provided for those who wish to understand the technical details.

One can see that sometimes very simple reasoning (with the right interpretation and tools) can lead in a few lines to very substantial results.

The Kolmogorov Legacy in Physics was published by Springer in 2004 (ISBN 978-3-540-20307-0).

Keywords

Division Fourier series Kolmogorov equations Probability complexity dynamical systems proof

Editors and affiliations

  • Éric Charpentier
    • 1
  • Annick Lesne
    • 2
    • 3
  • Nikolaï K. Nikolski
    • 4
  1. 1.Institut de MathématiquesUniversité Bordeaux 1351 cours de la LibérationFrance
  2. 2.Laboratoire de Physique Théorique de la Matiére CondenséeUniversité Pierre et Marie Curie4 Place JussieuFrance
  3. 3.Institut des Hautes Études Scientifiques Le Bois-MarieFrance
  4. 4.Institut de MathématiquesUniversité Bordeaux 1351 cours de la LibréationFrance

Bibliographic information

Reviews

From the reviews:

"Andrei N. Kolmogorov (1903-1987) was one of the most prolific and influential mathematicians of the twentieth century. … this collection would be read by those who hold only a bachelor’s degree in mathematics, computer science or physics, and more generally, by those interested in mathematical ideas. … This impressive collection gives the reader an understanding of the depth and breadth of Kolmogorov’s contributions to mathematics. Each chapter includes a substantial list of references that invite further reading." (Elena Anne Marchisotto, MathDL, December, 2007)

"The object of Kolmogorov’s Heritage in Mathematics is to enable the general mathematical reader (educated to master’s level) to grasp something of Kolmogorov’s achievements. … I can judge, it is successful in its aim. … those mathematicians with a sense of history, who wish to place themselves within the general culture of mathematics, will find this book a worthy memorial to a great man." (T. W. Korner, SIAM reviews, Vol. 50 (4), December, 2008)