# John von Neumann : biography

**John von Neumann** ( December 28, 1903 – February 8, 1957) was a Hungarian-born American pure and applied mathematician and polymath. He made major contributions to a vast number of fields, including mathematics (foundations of mathematics, functional analysis, ergodic theory, geometry, topology, and numerical analysis), physics (quantum mechanics, hydrodynamics, and fluid dynamics), economics (game theory), computer science (Von Neumann architecture, linear programming, self-replicating machines, stochastic computing), and statistics.Glimm, p. vii He was a pioneer of the application of operator theory to quantum mechanics, in the development of functional analysis, a principal member of the Manhattan Project and the Institute for Advanced Study in Princeton (as one of the few originally appointed), and a key figure in the development of game theory and the concepts of cellular automata, the universal constructor, and the digital computer.

Von Neumann’s mathematical analysis of the structure of self-replication preceded the discovery of the structure of DNA. In a short list of facts about his life he submitted to the National Academy of Sciences, he stated "The part of my work I consider most essential is that on quantum mechanics, which developed in Göttingen in 1926, and subsequently in Berlin in 1927–1929. Also, my work on various forms of operator theory, Berlin 1930 and Princeton 1935–1939; on the ergodic theorem, Princeton, 1931–1932." Along with Teller and Stanislaw Ulam, von Neumann worked out key steps in the nuclear physics involved in thermonuclear reactions and the hydrogen bomb.

Von Neumann wrote 150 published papers in his life; 60 in pure mathematics, 20 in physics, and 60 in applied mathematics. His last work, an unfinished manuscript written while in the hospital and later published in book form as *The Computer and the Brain*, gives an indication of the direction of his interests at the time of his death.

## Career and abilities

### Beginnings

Between 1926 and 1930, he taught as a *Privatdozent* at the University of Berlin, the youngest in its history. By the end of 1927, von Neumann had published twelve major papers in mathematics, and by the end of 1929, thirty-two papers, at a rate of nearly one major paper per month.MacRae, p. 145 Von Neumann’s powers of speedy, massive memorization and recall allowed him to recite volumes of information, and even entire directories, with ease.

In 1930, von Neumann was invited to Princeton University, New Jersey, and, subsequently, was one of the first four people selected for the faculty of the Institute for Advanced Study (two of the others being Albert Einstein and Kurt Gödel), where he remained a mathematics professor from its formation in 1933 until his death. His father, Max von Neumann had died in 1929. But his mother and his brothers followed John to the United States. He anglicized his first name to John, keeping the German-aristocratic surname of von Neumann. In 1937, von Neumann became a naturalized citizen of the U.S. In 1938, he was awarded the Bôcher Memorial Prize for his work in analysis.

### Set theory

The axiomatization of mathematics, on the model of Euclid’s *Elements*, had reached new levels of rigor and breadth at the end of the 19th century, particularly in arithmetic (thanks to the axiom schema of Richard Dedekind and Charles Sanders Peirce) and geometry (thanks to David Hilbert). At the beginning of the 20th century, efforts to base mathematics on naive set theory suffered a setback due to Russell’s paradox (on the set of all sets that do not belong to themselves).

The problem of an adequate axiomatization of set theory was resolved implicitly about twenty years later (by Ernst Zermelo and Abraham Fraenkel). Zermelo and Fraenkel provided Zermelo–Fraenkel set theory, a series of principles that allowed for the construction of the sets used in the everyday practice of mathematics. But they did not explicitly exclude the possibility of the existence of a set that belongs to itself. In his doctoral thesis of 1925, von Neumann demonstrated two techniques to exclude such sets: the *axiom of foundation* and the notion of *class.*