# John von Neumann

*A separate article covers Saint John Neumann, the American priest.*

**John von Neumann (Neumann János)** (December 28, 1903 – February 8, 1957) was a Hungarian-born mathematician who made important contributions in quantum physics, functional analysis, set theory, computer science, economics and many other mathematical fields.

## Contents

## Biography

The oldest of three children, von Neumann was born **János Lajos Margittai Neumann** (two given names, two surnames respectively) in Budapest to *Neumann Miksa* (Max Neumann), a lawyer who worked in a bank, and *Kann Margit* (Margaret Kann). Growing up in a non-practising Jewish family, János, nicknamed "Jancsi", showed incredible memory at an early age, being able to divide eight-digit numbers in his head at the age of six. At the same age, when his mother once stared aimlessly in front of him, he asked, "What are you calculating?". János was already very interested in math, the nature of numbers and the logic of the world around him. He entered the Lutheran Gymnasium in 1911. In 1913, his father purchased a title, and János acquired the Austrian mark of nobility *von*, becoming János von Neumann—János was anglicised to John after he took up residence in the United States in the 1930s.

He received his Ph.D. in mathematics from the University of Budapest at the age of 23. He simultaneously learnt chemical engineering in Switzerland. Between 1926 and 1930 he was a private lecturer in Berlin, Germany.

Von Neumann was invited to Princeton University in 1930, and was one of four people selected for the first faculty of the Institute for Advanced Study, where he was a mathematics professor from its formation in 1933 until his death.

From 1936 to 1938 Alan Turing was a visitor at the Institute, where he completed a Ph.D. dissertation under the supervision of Alonzo Church. This visit occurred shortly after Turing's publication of his 1936 paper "On Computable Numbers with an Application to the Entscheidungsproblem" which involved the concepts of logical design and the universal machine. Von Neumann must have known of Turing's ideas but it is not clear whether he applied them to the design of the IAS machine ten years later.

In 1937, he became a naturalized citizen of the United States. In 1938 von Neumann was awarded the Bôcher Memorial Prize for his work in analysis.

Von Neumann was married twice. His first wife was Mariette Koevesi, whom he married in 1930. Von Neumann agreed to convert to Catholicism to placate her family. The couple divorced in 1937 and Von Neumann married his second wife, Klara Dan, in 1938. Von Neumann had one child, a daughter Marina, from his first marriage.

## Scientific contributions

Von Neumann was one of the initiators of game theory and published the classic book Theory of Games and Economic Behavior with Oskar Morgenstern in 1944. He worked in the Theory division at Los Alamos along with Hans Bethe and Victor Weisskopf during World War II as part of the Manhattan Project to develop the first atomic weapons.

One of von Neumann's signature achievements was his rigorous mathematical formulation of quantum mechanics in terms of linear operators on Hilbert spaces. He provided a rigorous foundation for quantum statistical mechanics. He also proposed a proof of the impossibility of hidden variables, showing that quantum mechanics was profoundly different from all previously known theories in physics. His proof contained a conceptual flaw, although subsequently correct proofs were provided by John Bell and others. He apparently held a belief in the role of the observer in creating the collapse of the quantum wave function, which reflects in his contributions to the development of the theory of quantum measurement.

Von Neumann gave his name to the von Neumann architecture used in most non-parallel-processing computers, because of his publication of the concept, though many feel that this naming ignores the contribution of J. Presper Eckert and John William Mauchly who worked on the concept during their work on ENIAC. Virtually every commercially available home computer, microcomputer and supercomputer is a von Neumann machine. He created the field of cellular automata without computers, constructing the first examples of self-replicating automata with pencil and graph paper. The concept of a universal constructor was fleshed out in his posthumous work *Theory of Self Reproducing Automata*. The term "von Neumann machine" also refers to self-replicating machines. Von Neumann proved that the most effective way large-scale mining operations such as mining an entire moon or asteroid belt can be accomplished is through the use of self-replicating machines, to take advantage of the exponential growth of such mechanisms.

In addition to his work on architecture, he is credited with at least one contribution to the study of algorithms. Donald Knuth cites von Neumann as the inventor, in 1945, of the well known merge sort algorithm, in which the first and second halves of an array are each sorted recursively and then merged together.

He also engaged in exploration of problems in the field of numerical hydrodynamics. With R. D. Richtmyer he developed an algorithm defining *artificial viscosity*, that proved essential to understanding many kinds of shock waves. It can fairly be said that we would not understand much of astrophysics, and might not even have highly developed jet and rocket engines, without that work. The problem to be solved was that when computers solve hydrodynamic or aerodynamic problems, they try to put too many computational gridpoints at regions of sharp discontinuity (shock waves). The *artificial viscosity* was a mathematical trick to slightly smooth the shock transition without sacrificing basic physics.

Von Neumann had a mind of great ingenuity and near total recall. He was an extrovert who loved drinking, dancing and having a good time. He had a fun-loving nature with a great love of jokes and humor. He died of cancer in Washington, D.C..

## Honors

The John von Neumann Theory Prize of the Institute for Operations Research and Management Science (INFORMS, previously TIMS-ORSA) is awarded annually to an individual (or sometimes group) who have made fundamental and sustained contributions to theory in operations research and the management sciences.

The IEEE John von Neumann Medal is awarded annually by the IEEE "for outstanding achievements in computer-related science and technology."

Von Neumann, a crater on Earth's Moon, is named after John von Neumann.

Along with American scientists Barbara McClintock, Josiah Willard Gibbs, and Richard Feynman, von Neumann was honored on a U.S. postage stamp in 2005. The set of self-adhesive 37-cent stamps was made available on May 4, 2005 in a pane of 20 stamps with five stamps for each.

## References

## Further reading

- von Neumann, John and Arthur W. Burks. 1966.
*Theory of Self-Reproducing Automata*, Univ. of Illinois Press, Urbana IL. - von Neumann, John. 1932. "Mathematical Foundations of Quantum Mechanics", Princeton U. Press, Princeton NJ. Transl. by R.T. Beyer from the original German.

## Students

- Donald B. Gillies, PhD student of John Von Neumann.
- John P. Mayberry, PhD student of John Von Neumann.

## External links

- O'Connor, John J., and Edmund F. Robertson. "John von Neumann".
*MacTutor History of Mathematics archive*. - John von Neumann's contribution to economic science – By Maria Joao Cardoso De Pina Cabral,
*International Social Science Review*, Fall-Winter 2003 - A Discussion of Artificial Viscosity
- Von Neuman's Universe, audio talk by George Dyson from ITConversations.com
- [1], article by Stephen Wolfram on Neumann's 100th birthday.

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