The World as a Mathematical Game (eBook)

Contents 6
Abbreviations 8
Introduction 9
Janos Neumann’s Early Years 13
1.1 A Jewish family in early twentieth century Budapest 13
1.2 A young talent in Hungarian mathematics belle epoque 14
1.3 Lights and shadows. The von Neumann generation 19
1.4 Student years in Germany 25
Von Neumann and the Mathematics of Göttingen 30
2.1 The Göttingen mathematicians 30
2.2 Hilbert’s mathematical optimism 33
2.3 The problems of the foundations of mathematics and the axiomatic approach 36
2.4 The axiomatization of quantum mechanics and functional spaces 42
2.5 A crucial contribution to game theory 50
A Mathematician Between Past and Future 60
3.1 Continuity and evolution in von Neumann’s thought 60
3.2 Axiomatics and the twentieth century renewal of mathematical practice 64
3.3 Von Neumann’s conception of mathematics 68
3.4 The language of mathematics and determinism 71
3.5 The world as a strategic game: a mathematical idea of rationality 78
Von Neumann in the United States 86
4.1 Princeton and the American mathematical community in the 1930s 86
4.2 A lucky migrant 90
4.3 Scientific commitment during World War II 93
4.4 From the Manhattan Project to the Atomic Energy Commission 98
4.5 Scientific research and national security during the Cold War 102
4.6 Freedom and limitations in the development of science and technology 107
4.7 Systems, information, control 115
4.8 Von Neumann’s final years: a very engaged expert and the time stealthily borrowed for the scientist’s projects 126
Beyond Mathematics: von Neumann’s Scientific Activity in the 1940s and 1950s 131
5.1 From rational economy to the axiomatization of economic behaviour 131
5.2 The theory of games: a new mathematics for the social sciences 138
5.3 Decisions, organization, operations research 143
5.4 Engineering and mathematics: the project of an electronic calculator 148
5.5 The use of computer in scientific research 157
5.6 The brain-computer analogy 164
Concluding Remarks: von Neumann and Twentieth Century Science 176
Chronology 182
Bibliography 184
Sources and scholarship on John von Neumann 184
John von Neumann’s published works and archived papers 185
Works by von Neumann mentioned in the book 186
General bibliography 190
Index of Names 209