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The Legacy of John von Neumann
Edited by: John Impagliazzo, Hofstra University, Hempstead, NY, James G. Glimm, State University of New York at Stony Brook, NY, and Isadore Singer, Massachusetts Institute of Technology, Cambridge, MA
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Proceedings of Symposia in Pure Mathematics
1990; 334 pp; softcover
Volume: 50
ISBN-10: 0-8218-4219-6
ISBN-13: 978-0-8218-4219-5
List Price: US$45
Member Price: US$36
Order Code: PSPUM/50.S
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The ideas of John von Neumann have had a profound influence on modern mathematics and science. One of the great thinkers of our century, von Neumann initiated major branches of mathematics--from operator algebras to game theory to scientific computing--and had a fundamental impact on such areas as self-adjoint operators, ergodic theory and the foundations of quantum mechanics, and numerical analysis and the design of the modern computer.

This volume contains the proceedings of an AMS Symposium in Pure Mathematics, held at Hofstra University, in May 1988. The symposium brought together some of the foremost researchers in the wide range of areas in which von Neumann worked. These articles illustrate the sweep of von Neumann's ideas and thinking and document their influence on contemporary mathematics. In addition, some of those who knew von Neumann when he was alive have presented here personal reminiscences about him. This book is directed to those interested in operator theory, game theory, ergodic theory, and scientific computing, as well as to historians of mathematics and others having an interest in the contemporary history of the mathematical sciences. This book will give readers an appreciation for the workings of the mind of one of the mathematical giants of our time.

Table of Contents

  • M. v. N. Whitman -- John von Neumann: A personal view
  • P. D. Lax -- Remembering John von Neumann
  • F. Ulam -- Nonmathematical reminiscences about Johnny von Neumann
  • I. Halperin -- The extraordinary inspiration of John von Neumann
  • N. A. Vonneuman -- The philosophical legacy of John von Neumann, in light of its inception and evolution in his formative years
  • G. W. Mackey -- Von Neumann and the early days of ergodic theory
  • D. S. Ornstein -- Von Neumann and ergodic theory
  • H. Furstenberg -- Nonconventional ergodic averages
  • F. J. Murray -- The rings of operators papers
  • R. V. Kadison -- Operator algebras-An overview
  • A. Connes -- Introduction à la géométrie non-commutative
  • H. Araki -- Some of the legacy of John von Neumann in physics: Theory of measurement, quantum logic, and von Neumann algebras in physics
  • A. M. Jaffe -- Mathematics motivated by physics
  • I. E. Segal -- The mathematical implications of fundamental physical principles
  • H. H. Goldstine and J. v. Neumann -- On the principles of large scale computing machines
  • J. Glimm -- Scientific computing: Von Neumann's vision, today's realities, and the promise of the future
  • Z.-S. She, E. Jackson, and S. A. Orszag -- Intermittency of turbulence
  • E. Clementi, S. Chin, G. Corongiu, J. Given, G. C. Lie, M. Migliore, and P. Procacci -- Supercomputer simulations of the interaction of biomolecules in solution
  • J. D. Cowan -- Von Neumann and neural networks
  • E. R. Berlekamp -- Two-person, perfect-information games
  • W. Aspray -- The origins of John von Neumann's theory of automata
  • N. Pippenger -- Developments in "the synthesis of reliable organisms from unreliable components"
  • Photographs
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