VI.91 John von Neumann

b. Budapest, 1903; d. Washington, District of Columbia, 1957

Axiomatic set theory;
quantum physics; measure theory; ergodic theory; operator theory; algebraic geometry;
theory of games; computer engineering; computer science

Raised as a Hungarian Jew in the Austrian Empire, Neumann János Lajos’s political outlook was strongly affected by the five-month reign of the communist Béla Kun’s regime after World War I. It formed his liberal and democratic political credo (although he did insist on retaining the title of nobility “margittai,” acquired by his father in 1913, which he later translated to the German “von”). He was a child prodigy, learning several languages and demonstrating an early enthusiasm for mathematics.

During the early 1920s von Neumann studied mathematics, physics, and chemistry in Berlin and Zürich, and was also enrolled to study mathematics in Budapest although he never attended any lectures there. He received a diploma in chemical engineering at the ETH Zürich and shortly afterward (in 1926) a doctorate in mathematics at the University of Budapest (his thesis was entitled “The axiomatic deduction of general set theory”). While engineering was considered a respectable profession for a brilliant young man with such wide-ranging interests, the theoretical challenges of mathematics and formal logic drove von Neumann to the more academic environment in Germany, where he immediately received attention from HILBERT [VI.63]. Although the sensible choice, academically speaking, would have been to stay with Hilbert at Göttingen—and he did spend six months there during 1926–27 on a Rockefeller Fellowship—he preferred the pulsating atmosphere of Berlin.

During the following years he published on the axiomatic foundations of set theory, on MEASURE THEORY [III.55], and on the mathematical foundations of quantum mechanics. He also wrote his first paper on game theory (“Zur Theorie der Gesellschaftsspiele,” published in Mathematische Annalen in 1928), proving the minimax theorem (the theorem that states that every two-person finite zero-sum game has optimal mixed strategies).

In 1927 von Neumann received his habilitation in mathematics from the Philosophical Faculty of Berlin University with a written thesis and a lecture on the foundations of set theory and mathematics, becoming one of the youngest Privatdozents in the history of the university. At this point he changed his name to the German Johann von Neumann. He gave lecture courses in Hamburg (1929–30) as well as in Berlin, but in 1933, with the Nazi seizure of power, he resigned from his appointment at Berlin. By that time he was already in Princeton, where his visiting status at the university, originally conferred in 1930, was transformed into a tenured position at the newly founded Institute for Advanced Study. He modified his name once again, this time to John von Neumann, receiving U.S. citizenship in 1937.

At Princeton he found a peaceful ivory tower. Much of his important mathematical work stems from that period in the mid 1930s: he published around six journal articles per year (a rate he maintained until his death), as well as several books. The Institute’s environment allowed him to expand his research scope, taking in, among other things, ERGODIC THEORY [V.9], Haar measure, certain spaces of operators on a HILBERT SPACE [III.37] (these spaces are now known as VON NEUMANN ALGEBRAS [IV.15 §2]), and “continuous geometry.”

Von Neumann was much too politically sensitive to ignore the European crisis that led to World War II. Having begun to investigate turbulent flow beyond the speed of sound in the mid 1930s, he was invited to the Ballistic Research Laboratory in 1937 as an expert on shock waves. Later he acted as a consultant to the Navy and the Air Force. Although he was not in the initial group of Los Alamos scientists, in 1943 he became an advisor to the Manhattan Project, where his mathematical treatment of shock waves became essential, leading to the “implosion lens,” an arrangement of explosives that started the uranium chain reaction.

In parallel with his war-related work, von Neumann pursued his interest in economics, which resulted in a collaboration with Oskar Morgenstern: their groundbreaking book The Theory of Games and Economic Behavior, partly based on his 1928 Mathematische Annalen paper, appeared in 1944.

In the 1940s von Neumann began to focus on computing as a result of two very different branches of his thinking: namely, the numerical approximation of solutions to otherwise unsolvable problems, and his proficiency in the foundations of mathematics. He had tried to enlist TURING [VI.94] as an assistant at Princeton and he was certainly aware of the importance of Turing’s seminal paper on computable numbers (1936). While Turing discussed an abstract machine in the form of a thought experiment, von Neumann also considered the problems arising from the actual construction of computers, such as those connected with the use of electronic hardware. His training as a mathematician allowed him to focus on the very essentials of computing machinery and avoid baroque designs like the Moore School’s ENIAC (Electronic Numerical Integrator And Computer). In 1945 he defined the essential components for the “Electronic Discrete Variable Computer.” His “First draft of a report on the EDVAC,” which summarized and focused ideas gathered from work on early electronic computers, provided a logical framework for the modern electronic computer, becoming a road map for computer architecture for the ensuing decades. While von Neumann probably did not consider this paper to have the same importance as his mathematical results, today it is considered the birth certificate of modern computers.

Von Neumann quickly recognized that programming computers (or “coding,” as he called it) was likely to be more demanding than building basic hardware. In essence he considered programming as a new branch of formal logic. In 1947 he coauthored (with Herman Goldstine) a three-part report, “Planning and coding of problems for an electronic computing instrument,” in which many insights on the novel and demanding art of software construction were collected together.

Von Neumann’s thinking went beyond the restrictions of calculating machines, and allowed him to venture into philosophical questions on the structure of the human brain and cellular automata and the idea of self-reproducing systems—questions that were forerunners to the disciplines now called “artificial intelligence” and “artificial life.” Consideration of these questions resulted in a series of lectures published as The Computer and the Brain (1958) and a book, Theory of Self-Reproducing Automata (1966), both of which appeared posthumously.

In 1954 von Neumann was appointed to the five-member U.S. Atomic Energy Commission and in 1956 he was awarded the Presidential Medal of Freedom by President Eisenhower.

Further Reading

Aspray, W. 1990. John von Neumann and the Origins of Modern Computing. Cambridge, MA: MIT Press.

Wolfgang Coy