1 The Applicability of Mathematics. - 2 Physics for Mathematicians. - 3 Ideas of Space and Space-Time. - 4 Philosophical Implications of Some Recent Scientific Discoveries. - 5 A First Look at Computing: A Personal Retrospective. - 6 Computers in Mathematics. - 7 Experiments in Chess on Electronic Computing Machines: Some Early Efforts. - 8 Computations in Parallel. - 9 Patterns of Growth of Figures. - 10 More on Patterns of Growth. - 11 How to Formulate Mathematically the Problems of the Rate of Evolution. - 12 Some Further Ideas and Prospects in Biomathematics. - 13 Further Applications of Mathematics in the Natural Sciences. - 14 Thermonuclear Devices. - 15 The Orion Project. - 16 John von Neumann 19031957. - 17 Von Neumann: The Interaction of Mathematics and Computing. - 18 John von Neumann on Computers and the Brain. - 19 Gamow and Mathematics: Personal Reminiscences. - 20 Marian Smoluchowski and the Theory of Probabilities in Physics. - 21 Kazimierz Kuratowski. - 22 Stefan Banach. - 23 A Concluding Paean. Language: English