Von Neumann, John

1903–1957

Mathematician

John von Neumann made key contributions in numerous fields of research during his relatively short life. His work in mathematics, particularly in set theory, was groundbreaking, and his definition of ordinal numbers, published at age 20, still sets the standard. In addition, he contributed significantly to quantum physics, computer science and meteorology, and game theory.

Born in Hungary, von Neumann studied chemistry at the University of Berlin while simultaneously completing doctoral work in mathematics at the University of Budapest. He received a Ph.D. in mathematics after completing a dissertation on set theory in 1926. In the same year, he earned a degree in chemical engineering from the Eidgennossische Technische Hochscule in Zurich. He lectured at the University of Berlin from 1926 to 1929, then accepted a position at Princeton University in 1930. In 1933, he was one of the original faculty at Princeton's newly founded Institute for Advanced Study (IAS); he held that position until his death from pancreatic cancer in 1957. During and after World War II, he held numerous research and governmental posts, contributing to the development of the hydrogen bomb. He received many awards, including the Medal of Freedom and the Enrico Fermi Award, both given in 1956 during his battle with cancer.

With the 1944 publication of Theory of Games and Economic Behavior, which he co-authored with Oskar Morgenstern, von Neumann applied mathematical analysis to economics and initiated the branch of economics and mathematics known as game theory. Game theory categorizes numerous types of “games,” in which interested parties compete or cooperate based on predefined rules. By analyzing such games, game theory determines the best strategies that rational, self-interested actors would take, providing economists with a rigorous, logical, mathematical framework to determine the actions of economic actors.

Von Neumann developed the minimax theorem, which applies to most two-person, zero-sum games, in which one player's losses are the other's gain. In such games, a value can be calculated that determines the best strategy, on average, for both players to follow. A simple example is the game of paper-rock-scissors: Each person must choose one of these three options without knowledge of what the other will choose. Von Neumann's minimax theorem proved mathematically that the best strategy for such a game is a mixed strategy of picking randomly. If one player follows this strategy, the best the other can do is to follow it as well, assuring 50/50 success. Von Neumann later applied the theorem to a simplified version of poker to devise a successful bidding strategy. Over the decades following the publication of Theory of Games and Economic Behavior, game theory grew and influenced other research in decision-making. By the 1950s, game theory was applied to military and political matters—most notably to the growing game of deterrence and brinksmanship that was the Cold War.

John von Neumann (right) poses with J. Robert Oppenheimer in front of the IAS Machine, 1952 (CORBIS).

Von Neumann's genius did not usually entail boldly developing new areas of research; instead, he had a striking ability to take the ideas of others and logically extend them in practical directions. His contributions to computer science were of this type. In 1944, while working on various military projects, including atomic-bomb research at Los Alamos, von Neumann became indirectly involved with the design and construction of ENIAC, the first electronic digital computer. Asked to write a report on improvements for ENIAC's successor, EDVAC, von Neumann circulated a first draft of the report, which others immediately copied and distributed. This report detailed proposed improvements on the logical structure of computers, including the use of central programming and memory to avoid having to reset the computer for every computation. Rethinking and extending the work of others, von Neumann envisioned the computer as a logical rather than a mechanical problem, allowing him to provide the model on which all future computers would be built. His report represents a crucial step in the history of computer science.

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