Mathematical Events of the Twentieth Century

• 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.

"... 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