Israel G., Gasca A.M. The World as a Mathematical Game: John von Neumann and Twentieth Century Science

Birkhauser Basel, 2009. — 207 p.Galileo and Newton’s work towards the mathematisation of the physical world; Leibniz’s universal logical calculus; the Enlightenment’s mathématique sociale. John von Neumann inherited all these aims and philosophical intuitions, together with an idea that grew up around the Vienna Circle of an ethics in the form of an exact science capable of guiding individuals to make correct decisions. With the help of his boundless mathematical capacity, von Neumann developed a conception of the world as a mathematical game, a world globally governed by a universal logic in which individual consciousness moved following different strategies: his vision guided him from set theory to quantum mechanics, to economics and to his theory of automata (anticipating artificial intelligence and cognitive science). This book provides the first comprehensive scientific and intellectual biography of John von Neumann, a man who perhaps more than any other is representative of twentieth century science.AbbreviationsJános Neumann's Early Years
A Jewish family in early twentieth century Budapest
A young talent in Hungarian mathematics belle époque
Lights and shadows. The von Neumann generation
Student years in Germany
Von Neumann and the Mathematics of Göttingen
The Göttingen mathematicians
Hilbert's mathematical optimism
The problems of the foundations of mathematics and the axiomatic approach
The axiomatization of quantum mechanics and functional spaces
A crucial contribution to game theory
A Mathematician Between Past and Future
Continuity and evolution in von Neumann's thought
Axiomatics and the twentieth century renewal of mathematical practice
Von Neumann's conception of mathematics
The language of mathematics and determinism
The world as a strategic game: a mathematical idea of rationality
Von Neumann in the United States
Princeton and the American mathematical community in the 1930s
A lucky migrant
Scientific commitment during World War II
From the Manhattan Project to the Atomic Energy Commission
Scientific research and national security during the Cold War
Freedom and limitations in the development of science and technology
Systems, information,control
Von Neumann's final years: a very engaged expert and the time stealthily borrowed for the scientist's projects
Beyond Mathematics: von Neumann's Scientific Activity in the 1940s and 1950s
From rational economy to the axiomatization of economic behaviour
The theory of games: a new mathematics for the social sciences
Decisions, organization, operations research
Engineering and mathematics: the project of an electronic calculator
The use of computer in scientific research
The brain-computer analogy
Concluding Remarks: von Neumann and Twentieth Century Science
ChronologySources and scholarship on John von Neumann
John von Neumann's published works and archived papers
Works by von Neumann mentioned in the book
General bibliography
Index of Names