VON NEUMANN, JOHN

One of the most brilliant mathematicians of the twentieth century, John von Neumann (1903–1957) was born in Budapest, Hungary on December 28. He died February 8 in Washington, DC, having created the mathematical foundation for quantum mechanics, one of three competing theories of the physics of the universe, a theory of mathematical economics, the process for creating an implosion atomic bomb, and the theory of automation.

Von Neumann studied at the University of Budapest, the University of Berlin, and the prestigious Technische Hochschule in Zurich. While in Zurich, he worked with two outstanding mathematicians, Hermann (1885–1955) Weyl and George Polya (1887–1985). In 1926, von Neumann was awarded a Ph.D. in mathematics from the University of Budapest and a diploma in chemical engineering from the Zurich University.

Von Neumann lectured at the University of Berlin (1926–1929) and the University of Hamburg (1929–1930). During this later period he also held a Rockefeller fellowship that enabled him to do postdoctoral study with one of the mathematical giants of the time, David Hilbert (1862–1943), at the University at Göttingen. By 1927, von Neumann was acknowledged worldwide as a young mathematical genius, and in 1929, Oswald Veblen (1880–1960) invited him to Princeton University to lecture on quantum theory. In 1930 he became a visiting lecturer at Princeton and in 1931 was appointed a professor. In 1933, the Institute for Advanced Study was formed, and he became one of the first six full time members of the School of Mathematics. Von Neumann held this position for the remainder of his life.

Von Neumann published 130 articles and books during his career, evenly split between pure and applied mathematics, as well as twenty articles and books that made significant contributions to physics.

His 1932 book Mathematische Grundlagen der Quantenmechanik created a firm mathematical foundation for quantum mechanics. Quantum theory assumes that energy is not absorbed or radiated continuously, but rather discontinuously and only in multiples of definite invisible units called quanta. Quantum mechanics is a physical theory that describes the motion of objects using the principles of quantum theory. In this work, he also introduced a new form of algebra that he named rings of operators. In his monograph Algebras of Operators in Hilbert Space, von Neumann extended this algebra to group representation as well as to quantum mechanics. This part of mathematics is now called von Neumann algebras.

Von Neumann's 1937 paper "A Model of General Economic Equilibrium" has been repeatedly cited as the greatest paper in mathematical economics ever written. The paper provided a theory of capitol and economic growth based upon a mathematical foundation.

Von Neumann created the entire field of game theory. His 1944 book (written with Oskar Morgenstern), Theory of Games and Economic Behavior, not only completed the theory but also introduced several other sets of axioms in other fields of economics.

During the Second World War, von Neumann worked with the scientists and administrators at Los Alamos on the development of the atomic bomb. His two principal contributions to the Los Alamos project were the introduction of mathematical decision making and refinement of the implosion or plutonium bomb. He did not originate the idea of an implosion, but he did develop the correct density of explosives required to achieve the correct implosion.

Von Neumann's development of MANIC—an acronym for Mathematical Analyzer, Numerical Integrator, and Computer—enabled the United States to produce and test the world's first hydrogen bomb in 1952. Von Neumann spent much of his later life working in automata theory, a field that attempts to understand multiple automation applications working together to form a process or perform a task. He was also an early advocate of stored programs within a computer. His computer architecture is common to all personal computers and has come to be known as von Neumann architecture.

HENRY H. WALBESSER

SEE ALSO Decision Theory;Turing, Alan;Wiener, Norbert.

BIBLIOGRAPHY

Aspray, William. (1990). John von Neumann and the Origins of Modern Computing. Cambridge, MA: MIT Press. Describes the contributions of von Neumann to the development of von Neumann computer architecture.

Heims, Steve J. (1980). John von Neumann and Norbert Wiener: From Mathematics to the Technologies of Life and Death. Cambridge, MA: MIT Press. A dual biography, this is a work that traces the academic contributions of von Neumann and Norbert Wiener to the numerous areas of study each influenced as well as their relationship to one another.

Macrae, Norman. (1992). John von Neumann. New York: Pantheon. A general bibliography of the life, person, and contributions of the man.

von Neumann, John. (1937). "A Model of General Economic Equilibrium." In Ergebnisse eines mathematischen Kolloquiums [Reports of a mathematical colloquium], ed K. Menger. Notre Dame, IN: University Press of Notre Dame. Foretells what is to become the theory of games.

von Neumann, John, and Oskar Morgenstern. (1944). Theory of Games and Economic Behavior. Princeton, NJ: Princeton University Press. Offers a theory to explain certain classes of economic behavior.

von Neumann, John. (1958). The Computer and the Brain. New Haven, CT: Yale University Press. A work that stimulated the development of artificial intelligence as a field of study in computer science.

von Neumann, John. (1966). Theory of Self-Reproducing Automata. Urbana: University of Illinois Press. Published posthumously. A theory that explains the underlying structures needed to create automated systems capable of reproducing themselves.