Mathematician:John von Neumann

Mathematician

Hungarian-American mathematician who made major contributions to a vast range of fields, including set theory, functional analysis, quantum mechanics, ergodic theory, continuous geometry, economics, computer science, numerical analysis and statistics, to name but a few.

Founded the field of game theory in collaboration with Oskar Morgenstern.

Generally regarded as one of the foremost mathematicians in modern history.

Nationality

Hungarian/American

History

• Born: 28 Dec 1903 in Budapest, Austro-Hungarian Empire (now Hungary)
• Died: 8 Feb 1957 in Washington D.C., USA

Theorems and Definitions

• Von Neumann Algebra
• Von Neumann Architecture
• Von Neumann Boundedness
• Von Neumann Construction of Natural Numbers
• Von Neumann Entropy
• Von Neumann Hierarchy
• Von Neumann Programming Language
• Von Neumann Regular Ring
• Von Neumann Universal Constructor
• Von Neumann Universe

• Koopman-von Neumann Classical Mechanics (with Bernard Osgood Koopman)
• Von Neumann-Bernays-Gödel Set Theory (with Paul Isaac Bernays and Kurt Friedrich Gödel)

• Von Neumann Bicommutant Theorem
• Von Neumann Conjecture

• Birkhoff-von Neumann Theorem (with Garrett Birkhoff)
• Dirac-von Neumann Axioms (with Paul Adrien Maurice Dirac)
• Stone-von Neumann Uniqueness Theorem (with Marshall Harvey Stone)
• Von Neumann-Morgenstern Utility Theorem (with Oskar Morgenstern)

Results named for John von Neumann can be found here.

Definitions of concepts named for John von Neumann can be found here.

Axioms named for John von Neumann can be found here.

Publications

• 1928: Sur Theorie der Gesellschaftspiele (Math. Ann. Vol. 100: pp. 295 – 320)
• 1932: Mathematische Grundlagen der Quantenmechanik ("Mathematical Foundations of Quantum Mechanics")
• 1937: Über ein ökonomisches Gleichungssystem und eine Verallgemeinerung des Brouwerschen Fixpunktsatzes (Ergebnisse eines Mathematischen Kolloquiums Vol. 8: pp. 73 – 83)

• 1944: Theory of Games and Economic Behaviour (with Oskar Morgenstern)
  • 1947: Theory of Games and Economic Behaviour, 2nd ed. (with Oskar Morgenstern)

Notable Quotes

As a mathematical discipline travels far from its empirical source, or still more, if it is a second or third generation only indirectly inspired by ideas coming from "reality," it is beset with very grave dangers. It becomes more and more purely aestheticising, more and more purely l'art pour l'art. This need not be bad, if the field is surrounded by correlated subjects, which still have closer empirical connections, or if the discipline is under the influence of men with an exceptionally well-developed taste. But there is a grave danger that the subject will develop along the line of least resistance, that the stream, so far from its source, will separate into a multitude of insignificant branches, and that the discipline will become a disorganised mass of details and complexities. In other words, at a great distance from its empirical source, or after much "abstract" inbreeding, a mathematical subject is in danger of degeneration.

Quoted in 1972: George F. Simmons: Differential Equations.

In mathematics you don't understand things. You just get used to them.

Epigraph to 2008: David Joyner: Adventures in Group Theory (2nd ed.).

Also known as

Born Neumann János Lajos.

Some sources include an anglicised rendition of his middle name: John Louis von Neumann.

He can also be seen as Johann von Neumann.

Some sources capitalise the von, thus: John Von Neumann

Sources

• John J. O'Connor and Edmund F. Robertson: "John von Neumann": MacTutor History of Mathematics archive

• 1972: George F. Simmons: Differential Equations ... (previous) ... (next): Preface
• 1983: Morton D. Davis: Game Theory (revised ed.) ... (next): Author's Introduction
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Neumann, John Von (1903-57)
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): von Neumann, John (1903-57)
• 2008: David Joyner: Adventures in Group Theory (2nd ed.) ... (next): Epigraph
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): von Neumann, John (1903-57)
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Neumann, John Von
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Von Neumann, John (1903-57)