Mathematical Events of the Twentieth Century

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 presentedition 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.

Table of Contents:
Dynamical Systems in the 1960s: The Hyperbolic Revolution.- From Hilbert’s Superposition Problem to Dynamical Systems.- Inverse Monodromy Problems of the Analytic Theory of Differential Equations.- What Modern Mathematical Physics Is Supposed to Be.- Discovery of the Maximum Principle.- The Qualitative Theory of Differential Equations in the Plane.- Computerization… Let’s Be Careful.- The Generalized Shift, Transformation Operators, and Inverse Problems.- Mathematics and the Trajectories of Typhoons.- Hilbert’s Tenth Problem: Diophantine Equations in the Twentieth Century.- Observations on the Movement of People and Ideas in Twentieth-Century Mathematics.- About Aleksandrov, Pontryagin and Their Scientific Schools.- Hilbert’s Seventh Problem.- The Great Kolmogorov.- Numbers as Functions: The Development of an Idea in the Moscow School of Algebraic Geometry.- The P NP-Problem: A View from the 1990s.- Homoclinic Trajectories: From Poincaré to the Present.- From “Disorder” to Nonlinear Filtering and Martingale Theory.- How Mathematicians and Physicists Found Each Other in the Theory of Dynamical Systems and in Statistical Mechanics.- Approximation Theory in the Twentieth Century.- The Life and Fate of Functional Analysis in the Twentieth Century.- Half a Century As One Day.- Nikolai Nikolaevich Bogolyubov — Mathematician by the Grace of God.- Global Solvability Versus Collapse in the Dynamics of an Incompressible Fluid.