The book is a collection of 23 essays written by Stanislaw Ulam from 1946 to 1982. The author, a native of Poland, came to the United States in 1935 at the invitation of John von Neumann. Ulam was elected member of the (American) National Academy of Sciences, the American Academy of Arts and Sciences, and the American Philosophical Society, and the author of more than 150 technical papers, essays and reports, several scientific books, and an autobiography. His influence on the development of mathematics and, in particular, the application of mathematics in unconventional areas can hardly be overestimated. For the first time, his insight into the origins and trends of twentieth century mathematics and its applications are compiled this fascinating volume. The topics are widespread: physics for mathematicians, space and time, the philosophical implications of some recent scientific discoveries, chess on computers, parallel computing (cellular automata), patterns of growth (the game of life), a mathematical formulation of the rate of evolution, biomathematics, thermonuclear devices, and nuclear pulse propulsion (the origin project for sending very large vehicles to other planets). Some further essays are dedicated to other famous persons: first, John von Neumann, his friend, the Soviet physicist Gamow, and the Polish scientists Marian Smoluchowski, Kazimierz Kuratowski, and Stefan Banach. Ulam’s ability to see the inner core of a problem enabled him to open many mathematical doors. This collection offers a view of many of those areas.