VON NEUMANN, JOHN

born Dec. 3, 1903, Budapest, Hung. died Feb. 8, 1957, Washington, D.C., U.S. original name Johann Von Neumann Hungarian-American mathematician who made important contributions in quantum physics, logic, meteorology, and computer science. His theory of games had a significant influence upon economics. Von Neumann studied chemistry at the University of Berlin and, at Technische Hochschule in Zrich, received the diploma in chemical engineering in 1926. The same year, he received the Ph.D. in mathematics from the University of Budapest, with a dissertation about set theory. His axiomatization has left a permanent mark on the subject; and his definition of ordinal numbers, published when he was 20, has been universally adopted. Von Neumann was privatdocent (lecturer) at Berlin in 1926-29 and at the University of Hamburg in 1929-30. During this time he worked mainly on quantum physics and operator theory. Largely because of his work, quantum physics and operator theory can be viewed as two aspects of the same subject. In 1930 von Neumann was visiting lecturer at Princeton University; he was appointed professor in 1931. In 1932 he gave a precise formulation and proof of the "ergodic hypothesis" of statistical mathematics. His book on quantum mechanics, The Mathematical Foundations of Quantum Mechanics, published in 1932, remains a standard treatment of the subject. In 1933 he became a professor at the newly founded Institute for Advanced Study, Princeton, keeping that position for the rest of his life. Meanwhile, he turned his attention to the challenge made in 1900 by a German mathematician, David Hilbert (q.v.), who proposed 23 basic theoretical problems for 20th-century mathematical research. Von Neumann solved a special case of Hilbert's fifth problem, the case of compact groups. In the second half of the 1930s the main part of von Neumann's publications, written partly in collaboration with F.J. Murray, was on "rings of operators" (now called Neumann algebras). Of all his work, these concepts will quite probably be remembered the longest. Currently it is one of the most powerful tools in the study of quantum physics. An important outgrowth of rings of operators is "continuous geometry." Von Neumann saw that what really determines the character of the dimensional structure of a space is the group of rotations that the structure allows. The groups of rotations associated with rings of operators make possible the description of space with continuously varying dimensions. About 20 of von Neumann's 150 papers are in physics; the rest are distributed more or less evenly among pure mathematics (mainly set theory, logic, topological group, measure theory, ergodic theory, operator theory, and continuous geometry) and applied mathematics (statistics, numerical analysis, shock waves, flow problems, hydrodynamics, aerodynamics, ballistics, problems of detonation, meteorology, and two nonclassical aspects of applied mathematics, games and computers). His publications show a break from pure to applied research around 1940. During World War II, he was much in demand as a consultant to the armed forces and to civilian agencies. His two main contributions were his espousal of the implosion method for bringing nuclear fuel to explosion and his participation in the development of the hydrogen bomb. The mathematical cornerstone of von Neumann's theory of games is the "minimax theorem," which he stated in 1928; its elaboration and applications are in the book he wrote jointly with Oskar Morgenstern in 1944, Theory of Games and Economic Behavior. The minimax theorem says that for a large class of two-person games, there is no point in playing. Either player may consider, for each possible strategy of play, the maximum loss that he can expect to sustain with that strategy and then choose as his "optimal" strategy the one that minimizes the maximum loss. If a player follows this reasoning, then he can be statistically sure of not losing more than that value called the minimax value. Since (this is the assertion of the theorem) that minimax value is the negative of the one, similarly defined, that his opponent can guarantee for himself, the long-run outcome is completely determined by the rules. In computer theory, von Neumann did much of the pioneering work in logical design, in the problem of obtaining reliable answers from a machine with unreliable components, the function of "memory," machine imitation of "randomness," and the problem of constructing automata that can reproduce their own kind. One of the most striking ideas, to the study of which he proposed to apply computer techniques, was to dye the polar ice caps so as to decrease the amount of energy they would reflect-the result could warm the Earth enough to make the climate of Iceland approximate that of Hawaii. The "axiomatic method" is sometimes mentioned as the secret of von Neumann's success. In his hands it was not pedantry but perception; he got to the root of the matter by concentrating on the basic properties (axioms) from which all else follows. His insights were illuminating and his statements precise.