# John von Neumann

### From Wikipedia, the free encyclopedia

John von Neumann in the 1940s | |

Born | December 28, 1903(1903-12-28) Budapest, Austria-Hungary |
---|---|

Died | February 8, 1957
(aged 53) Washington DC, USA |

Residence | United States |

Nationality | American |

Field | Mathematics |

Institutions | Los Alamos University of Berlin Princeton University |

Alma mater | University
of Pázmány Péter ETH Zurich |

Academic advisor | Leopold Fejer |

Notable students | Donald B. Gillies |

Known for | Game theory von Neumann algebra von Neumann architecture Cellular automata |

Notable prizes | Enrico Fermi Award 1956 |

Religion | Converted Roman Catholic; previously Agnostic; born to a non-practicing Jewish family |

**John von Neumann** (Hungarian **Margittai Neumann János Lajos**; born
December
28, 1903 in Budapest, Austria-Hungary; died February
8, 1957 in Washington D.C., United
States) was an Austria-Hungary-born American mathematician who made
contributions to quantum physics, functional analysis,
set
theory, topology, economics, computer science, numerical analysis,
hydrodynamics (of
explosions), statistics and many other
mathematical fields as one of history's outstanding mathematicians.^{[1]} Most
notably, von Neumann was a pioneer of the application of operator theory to quantum mechanics
(*see* von Neumann
algebra), a member of the Manhattan Project and
the Institute for
Advanced Study at Princeton (as one
of the few originally appointed — a group collectively referred to as the
"demi-gods"), and the co-creator of game theory and the concepts
of cellular automata and
the universal
constructor. Along with Edward Teller and Stanislaw Ulam, von
Neumann worked out key steps in the nuclear physics involved
in thermonuclear reactions
and the hydrogen bomb.

## Contents |

## [edit] Biography

The eldest of three brothers, von Neumann was born **Neumann János Lajos**
(Hungarian names have the family name first) in Budapest, Hungary, to a Jewish family. His father was
Neumann Miksa (Max Neumann), a lawyer who worked in a bank. His mother was Kann Margit
(Margaret Kann). János, nicknamed "Jancsi" (Johnny), was an extraordinary prodigy. At the age of
six, he could divide two 8-digit numbers in his head.

He entered the German speaking Lutheran Gymnasium in
Budapest in 1911. In 1913 his father was rewarded with ennoblement for his
service to the Austro-Hungarian empire, the Neumann family acquiring the
Hungarian mark of *Margittai*, or the Austrian equivalent *von*. Neumann János therefore
became János von Neumann, a name that he later changed to the German Johann von
Neumann. After teaching as history's youngest Privatdozent of the University of
Berlin from 1926 to 1930, he, his mother, and his brothers emigrated to the
United States; this in the early 1930s, after Hitler's rise to power in Germany. He anglicized
Johann to John, he kept the Austrian-aristocratic surname of von Neumann,
whereas his brothers adopted surnames Vonneumann and Neumann (using the *de
Neumann* form briefly when first in the US).

Although von Neumann unfailingly dressed formally, he enjoyed throwing
extravagant parties and driving hazardously (frequently while reading a book,
and sometimes crashing into a tree or getting arrested). He once reported one of
his many car accidents in this way: "I was proceeding down the road. The trees
on the right were passing me in orderly fashion at 60 miles per hour. Suddenly
one of them stepped in my path."^{[2]} He
was a profoundly committed hedonist who liked to eat and
drink heavily (it was said that he knew how to count everything except
calories), tell dirty stories and very insensitive jokes (for example: "bodily
violence is a displeasure done with the intention of giving pleasure"), and
persistently gaze at the legs of young women (so much so that female secretaries
at Los Alamos often covered up the exposed undersides of their desks with
cardboard.)

He received his Ph.D. in mathematics (with minors in experimental physics and chemistry) from the University of Budapest at the age of 23. He simultaneously earned his diploma in chemical engineering from the ETH Zurich in Switzerland at the behest of his father, who wanted his son to invest his time in a more financially viable endeavour than mathematics. Between 1926 and 1930 he was a private lecturer in Berlin, Germany.

By age 25 he had published 10 major papers, and by 30, nearly 36.^{[citation
needed]}

Von Neumann was invited to Princeton, New Jersey in 1930, and was one of four people selected for the first faculty of the Institute for Advanced Study (two of the others were Albert Einstein and Kurt Gödel), 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 at Princeton. 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 US. In 1938 von Neumann was awarded the Bôcher Memorial Prize for his work in analysis.

Von Neumann married twice. He married Mariette Kövesi in 1930. When he
proposed to her, he was incapable of expressing anything beyond "You and I might
be able to have some fun together, seeing as how we both like to drink."^{[citation
needed]} Von Neumann agreed to convert to Catholicism in
order to marry and remained a Catholic until his death. The couple divorced in
1937. He then married Klara Dan in 1938. Von Neumann had one child, by his first
marriage, a daughter named Marina. She
is a distinguished professor of international trade and public policy at the University of
Michigan.

Von Neumann was diagnosed with bone cancer or pancreatic cancer in
1957, possibly caused by exposure to radioactivity while
observing A-bomb
tests in the Pacific or in later work on nuclear weapons at Los
Alamos, New Mexico. (Fellow nuclear
pioneer Enrico Fermi had died of stomach cancer in 1954.)
Von Neumann died within a few months of the initial diagnosis, in excruciating
pain. The cancer had spread to his brain, inhibiting mental ability. When at Walter Reed
Hospital in Washington, D.C., he
invited Roman Catholic priest
(Father Anselm Strittmatter), who administered him the last Sacraments.^{[3]} He
died under military security lest he reveal military secrets while heavily
medicated. John Von Neumann was buried at Princeton Cemetery in
Princeton, Mercer
County, New Jersey.

He wrote 150 published papers in his life; 60 in pure mathematics, 20 in physics, and 60 in applied mathematics. He was developing a theory of the structure of the human brain before he died.

Von Neumann entertained notions which would now trouble many. His love for
meteorological prediction led him to dream of manipulating the environment by
spreading colorants on the polar ice caps in order to enhance absorption of
solar radiation (by reducing the albedo) and thereby raise global
temperatures. He also favored a preemptive nuclear attack on the USSR, believing that doing so could
prevent it from obtaining the atomic bomb.^{[4]}

## [edit] Logic

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 Richard Dedekind and Giuseppe Peano) and geometry (thanks to David Hilbert). At the beginning of the twentieth century, set theory, the new branch of mathematics invented by Georg Cantor, and thrown into crisis by Bertrand Russell with the discovery of his famous paradox (on the set of all sets which do not belong to themselves), had not yet been formalized.

The problem of an adequate axiomatization of set theory was resolved
implicitly about twenty years later (by Ernst Zermelo and Abraham Frankel) by way
of a series of principles which allowed for the construction of all sets used in
the actual practice of mathematics, but which did not explicitly exclude the
possibility of the existence of sets which belong to themselves. In his doctoral
thesis of 1925, von Neumann demonstrated how it was possible to exclude this
possibility in two complementary ways: the *axiom of
foundation* and the notion of *class.*

The axiom of foundation established that every set can be constructed from
the bottom up in an ordered succession of steps by way of the principles of
Zermelo and Frankel, in such a manner that if one set belongs to another then
the first must necessarily come before the second in the succession (hence
excluding the possibility of a set belonging to itself.) In order to demonstrate
that the addition of this new axiom to the others did not produce
contradictions, von Neumann introduced a method of demonstration (called the
*method of inner models*) which
later became an essential instrument in set theory.

The second approach to the problem took as its base the notion of class, and
defines a set as a class which belongs to other classes, while a *proper
class* is defined as a class which does not belong to other classes. Under
the Zermelo/Frankel approach, the axioms impede the construction of a set of all
sets which do not belong to themselves. In contrast, under the von Neumann
approach, the class of all sets which do not belong to themselves can be
constructed, but it is a *proper class* and not a set.

With this contribution of von Neumann, the axiomatic system of the theory of
sets became fully satisfactory, and the next question was whether or not it was
also definitive, and not subject to improvement. A strongly negative answer
arrived in September of 1930 at the historical mathematical Congress of Königsberg, in which Kurt
Gödel announced his first
theorem of incompleteness: the usual axiomatic systems are incomplete, in
the sense that they cannot prove every truth which is expressible in their
language. This result was sufficiently innovative as to confound the majority of
mathematicians of the time. But von Neumann, who had participated at the
Congress, confirmed his fame as an instantaneous thinker, and in less than a
month was able to communicate to Gödel himself an interesting consequence of his
theorem: the usual axiomatic systems are unable to demonstrate their own
consistency. It is precisely this consequence which has attracted the most
attention, even if Gödel originally considered it only a curiosity, and had
derived it independently anyway (it is for this reason that the result is called
*Gödel's second theorem*, without mention of von Neumann.)

## [edit] Quantum mechanics

At the International
Congress of Mathematicians of 1900, David Hilbert presented
his famous list of twenty-three problems considered central for the development
of the mathematics of the new century. The sixth of these was *the axiomatization
of physical theories.* Among the new physical theories of the century the
only one which had yet to receive such a treatment by the end of the 1930s was
quantum mechanics. QM found itself in a condition of foundational crisis similar
to that of set theory at the beginning of the century, facing problems of both
philosophical and technical natures. On the one hand, its apparent
non-determinism had not been reduced to an explanation of a deterministic form.
On the other, there still existed two independent but equivalent heuristic
formulations, the so-called *matrix mechanical* formulation due to Werner Heisenberg and
the *wave mechanical* formulation due to Erwin Schrödinger,
but there was not yet a single, unified satisfactory theoretical
formulation.

After having completed the axiomatization of set theory, von Neumann began to
confront the axiomatization of QM. He immediately realized, in 1926, that a
quantum system could be considered as a point in a so-called Hilbert
space, analogous to the 6N dimension (N is the number of particles, 3
general coordinate and 3 canonical momentum for each) phase space of classical
mechanics but with infinitely many dimensions (corresponding to the infinitely
many possible states of the system) instead: the traditional physical quantities
(e.g. position and momentum) could therefore be represented as particular linear operators
operating in these spaces. The *physics* of quantum mechanics was thereby
reduced to the *mathematics* of the linear Hermitian operators on Hilbert
spaces. For example, the famous uncertainty
principle of Heisenberg, according to which the determination of the
position of a particle prevents the determination of its momentum and vice
versa, is translated into the *non-commutativity* of the two corresponding
operators. This new mathematical formulation included as special cases the
formulations of both Heisenberg and Schrödinger, and culminated in the 1932
classic *The
Mathematical Foundations of Quantum Mechanics.* However, physicists
generally ended up preferring another approach to that of von Neumann (which was
considered elegant and satisfactory by mathematicians). This approach was
formulated in 1930 by Paul Dirac.

In any case, von Neumann's abstract treatment permitted him also to confront
the foundational issue of determinism vs. non-determinism and in the book he
demonstrated a theorem according to which quantum mechanics could not possibly
be derived by statistical approximation from a deterministic theory of the type
used in classical mechanics. This demonstration contained a conceptual error,
but it helped to inaugurate a line of research which, through the work of John Stuart Bell in
1964 on Bell's Theorem and the
experiments of Alain Aspect in 1982,
demonstrated that quantum physics requires a *notion of reality*
substantially different from that of classical physics.

In a complementary work of 1936, von Neumann proved (along with Garrett Birkhoff) that
quantum mechanics also requires a *logic* substantially different from the
classical one. For example, light (photons) cannot pass through two successive
filters which are polarized perpendicularly (e.g. one horizontally and the other
vertically), and therefore, a fortiori, it cannot pass if
a third filter polarized diagonally is added to the other two, either before or
after them in the succession. But if the third filter is added *in between*
the other two, the photons will indeed pass through. And this experimental fact
is translatable into logic as the *non-commutativity* of conjunction .
It was also demonstrated that the laws of distribution of classical logic,
and ,
are not valid for quantum theory. The reason for this is that a quantum
disjunction, unlike the case for classical disjunction, can be true even when
both of the disjuncts are false and this is, in turn, attributable to the fact
that it is frequently the case, in quantum mechanics, that a pair of
alternatives are semantically determinate, while each of its members are
necessarily indeterminate. This latter property can be illustrated by a simple
example. Suppose we are dealing with particles (such as electrons) of
semi-integral spin (angular momentum) for which there are only two possible
values: positive or negative. Then, a principle of indetermination establishes
that the spin, relative to two different directions (e.g. *x* and *y*)
results in a pair of incompatible quantities. Suppose that the state **ɸ** of
a certain electron verifies the proposition "the spin of the electron in the
*x* direction is positive." By the principle of indeterminacy, the value of
the spin in the direction *y* will be completely indeterminate for
**ɸ**. Hence, **ɸ** can verify neither the proposition "the spin in the
direction of *y* is positive" nor the proposition "the spin in the
direction of *y* is negative." Nevertheless, the disjunction of the
propositions "the spin in the direction of *y* is positive or the spin in
the direction of *y* is negative" must be true for **ɸ**. In the case of
distribution, it is therefore possible to have a situation in which ,
while .

## [edit] Economics

Up until the 1930s economics involved a great deal of mathematics and
numbers, but almost all of this was either superficial or irrelevant. It was
used, for the most part, to provide uselessly precise formulations and solutions
to problems which were intrinsically *vague.* Economics found itself in a
state similar to that of physics of the 17th century: still waiting for the
development of an appropriate language in which to express and resolve its
problems. While physics had found its language in the infinitesimal
calculus, von Neumann proposed the language of game theory and a general
equilibrium theory for economics.

His first significant contribution was the minimax theorem of 1928. This theorem establishes that in certain zero sum games involving perfect information (in which players know a priori the strategies of their opponents as well as their consequences), there exists one strategy which allows both players to minimize their maximum losses (hence the name minimax). When examining every possible strategy, a player must consider all the possible responses of the player's adversary and the maximum loss. The player then plays out the strategy which will result in the minimization of this maximum loss. Such a strategy, which minimizes the maximum loss, is called optimal for both players just in case their minimaxes are equal (in absolute value) and contrary (in sign). If the common value is zero, the game becomes pointless.

Von Neumann eventually improved and extended the minimax theorem to include
games involving imperfect information and games with more than two players. This
work culminated in the 1944 classic *Theory
of Games and Economic Behavior* (written with Oskar Morgenstern).
This resulted in such public attention that The New York Times
did a front page story, the likes of which only Einstein had previously
earned.

Von Neumann's second important contribution in this area was the solution, in 1937, of a problem first described by Leon Walras in 1874, the existence of situations of equilibrium in mathematical models of market development based on supply and demand. He first recognized that such a model should be expressed through disequations and not equations, and then he found a solution to Walras problem by applying a fixed-point theorem derived from the work of Luitzen Brouwer. The lasting importance of the work on general equilibria and the methodology of fixed point theorems is underscored by the awarding of Nobel prizes in 1972 to Kenneth Arrow and, in 1983, to Gerard Debreu.

Von Neumann was also the inventor of the method of proof, used in game
theory, known as backward induction
(which he first published in 1944 in the book co-authored with Morgenstern,
Theory of Games and Economic Behaviour).^{[5]}

## [edit] Armaments

After obtaining US citizenship, von Neumann took an interest in 1937 in
*applied* mathematics, and then developed an expertise in explosives. This
led him to a large number of military consultancies, primarily for the Navy,
which in turn led to his involvement in the Manhattan Project.

Von Neumann took part in the design of the explosive lenses needed to compress the plutonium core of the Trinity test device and the "Fat Man" weapon that was later dropped on Nagasaki. Upon his appointment to the committee to select potential targets for the USA's arsenal of atomic weapons, he had proposed the city of Kyoto as his first choice, but this was dismissed by Secretary of War Henry Stimson.

One of his discoveries was that large bombs are more devastating when detonated above the ground because of the force of shock waves. The most notable application of this occurred in August 1945, when the first atomic weapons were detonated over Hiroshima and Nagasaki at the very altitude calculated by him to produce the most damage. After the war, Robert Oppenheimer remarked that the physicists involved in the Manhattan project had "known sin". Von Neumann's rather arch response was that "sometimes someone confesses a sin in order to take credit for it".

Von Neumann continued unperturbed in his work and became, along with Edward Teller, one of the sustainers of the hydrogen bomb project. He then collaborated with spy Klaus Fuchs on further development of the bomb, and in 1946 the two filed a secret patent on "Improvement in Methods and Means for Utilizing Nuclear Energy", which outlined a scheme for using a fission bomb to compress fusion fuel to initiate a thermonuclear reaction. (Herken, pp. 171, 374). Though this was not the key to the hydrogen bomb — the Teller-Ulam design — it was judged to be a move in the right direction.

## [edit] Computer science

Von Neumann's hydrogen bomb work was also played out in the realm of computing, where he and Stanislaw Ulam developed simulations on von Neumann's digital computers for the hydrodynamic computations. During this time he contributed to the development of the Monte Carlo method, which allowed complicated problems to be approximated using random numbers. Because using lists of "truly" random numbers was extremely slow for the ENIAC, von Neumann developed a form of making pseudorandom numbers, using the middle-square method. Though this method has been criticized as crude, von Neumann was aware of this: he justified it as being faster than any other method at his disposal, and also noted that when it went awry it did so obviously, unlike methods which could be subtly incorrect.

While consulting for the Moore
School of Electrical Engineering on the EDVAC project, von Neumann wrote
an incomplete set of notes titled the *First
Draft of a Report on the EDVAC*. The paper, which was widely distributed,
described a computer architecture in which
data and program memory are mapped into the same address space. This
architecture became the de facto standard and can be contrasted with a so-called
Harvard
architecture, which has separate program and data memories on a separate
bus. Although the single-memory architecture became commonly known by the name
von Neumann
architecture as a result of von Neumann's paper, the architecture's
conception involved the contributions of others, including J. Presper Eckert and
John William
Mauchly, inventors of the ENIAC at the University of
Pennsylvania.^{[6]} With
very few exceptions, all present-day home computers, microcomputers, minicomputers and mainframe computers
use this single-memory computer architecture.

Von Neumann also created the field of cellular automata
without the aid of computers, constructing the first 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*. Von Neumann proved that the most effective way of
performing large-scale mining operations such as mining an entire moon or asteroid
belt would be by using self-replicating machines, taking advantage of their
exponential
growth.

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 merge sort algorithm, in which the first and second halves of an array are each sorted recursively and then merged together. His algorithm for simulating a fair coin with a biased coin [1] is used in the "software whitening" stage of some hardware random number generators.

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

## [edit] Politics and social affairs

Von Neumann obtained at the age of 29 one of the first five professorships at the new Institute for Advanced Study in Princeton, New Jersey (another had gone to Albert Einstein). He was a frequent consultant for the Central Intelligence Agency, the United States Army, the RAND Corporation, Standard Oil, IBM, and others.

During a Senate committee hearing he described his political ideology as "violently anti-communist, and much more militaristic than the norm". As President of the Von Neumann Committee for Missiles at first, and later as a member of the United States Atomic Energy Commission, starting from 1953 up until his death in 1957, he was influential in setting U.S. scientific and military policy. Through his committee, he developed various scenarios of nuclear proliferation, the development of intercontinental and submarine missiles with atomic warheads, and the controversial strategic equilibrium called mutual assured destruction (aka the M.A.D. doctrine).

## [edit] Honors

The John von Neumann Theory Prize of the Institute for Operations Research and the Management Sciences (INFORMS, previously TIMS-ORSA) is awarded annually to an individual (or 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."

The John von Neumann Lecture is given annually at the Society for Industrial and Applied Mathematics (SIAM) by a researcher who has contributed to applied mathematics, and the chosen lecturer is also awarded a monetary prize.

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

The John von Neumann Computing Center in Princeton, New Jersey was named in his honour. [2]

The professional society of Hungarian computer scientists, Neumann János Számítógéptudományi Társaság, is named after John von Neumann.

On May 4, 2005 the United States
Postal Service issued the *American Scientists* commemorative postage
stamp series, a set of four 37-cent self-adhesive stamps in several
configurations. The scientists depicted were John von Neumann, Barbara McClintock,
Josiah Willard
Gibbs, and Richard Feynman.

The John von Neumann Award of the Rajk László College for Advanced Studies was named in his honour, and is given every year from 1995 to professors, who had on outstanding contribution at the field of exact social sciences, and through their work they had a heavy influence to the professional development and thinking of the members of the college.

## [edit] See also

- Von Neumann algebra
- Von Neumann conjecture
- Von Neumann entropy
- Stone–von Neumann theorem
- Von Neumann–Bernays–Gödel set theory
- Von Neumann universe
- Von Neumann bicommutant theorem
- Von Neumann regular ring
- Von Neumann architecture
- Von Neumann universal constructor
- Self-replicating spacecraft

### [edit] Students

- Donald B. Gillies, PhD student.
- Israel Halperin, PhD
student.
^{[7]} - Jim
Mayberry, PhD student.
^{[citation needed]}

## [edit] Notes

**^**John von Neumann. MSN Encarta.**^**http://scidiv.bcc.ctc.edu/Math/vonNeumann.html**^**Halmos, P.R. The Legend of Von Neumann, The American Mathematical Monthly, Vol. 80, No. 4. (Apr., 1973), pp. 382-394**^**John Von Neumann: The Scientific Genius Who Pioneered the Modern Computer, Game Theory, Nuclear Deterrence, and Much More**^**John MacQuarrie. Mathematics and Chess. School of Mathematics and Statistics, University of St Andrews, Scotland.**^**The mistaken name for the architecture is discussed in John W. Mauchly and the Development of the ENIAC Computer, part of the online ENIAC museum, and in Robert Slater's computer history book,*Portraits in Silicon*.**^**While Israel Halperin's thesis advisor is often listed as Salomon Bochner, this may be because "Professors at the university direct doctoral theses but those at the Institute do not. Unaware of this, in 1934 I asked von Neumann if he would direct my doctoral thesis. He replied Yes." (Israel Halperin, "The Extraodrinary Inspiration of John von Neumann", Proceedings of Symposia in Pure Mathematics, vol. 50 (1990), pp 15--17)

## [edit] References

*This article was originally based on
material from the Free
On-line Dictionary of Computing, which is licensed under
the GFDL.*

- Steve
J. Heims, 1980.
*John von Neumann and Norbert Wiener, from Mathematics to the technologies of life and death.*MIT Press. - Gregg
Herken, 2002.
*Brotherhood of the Bomb: The Tangled Lives and Loyalties of Robert Oppenheimer, Ernest Lawrence, and Edward Teller*. - Israel, Giorgio, and Gasca, Ana Millan, 1995.
*The World as a Mathematical Game: John von Neumann, Twentieth Century Scientist*. - Norman Macrae, 1992.
*John von Neumann: The Scientific Genius Who Pioneered the Modern Computer, Game Theory, Nuclear Deterrence, and Much More*. Pantheon Press. ISBN 0-679-41308-1. - Robert Slater.
*Portraits in Silicon*, pp 23-33. ISBN 0-262-69131-0.

## [edit] Further reading

- Jean van
Heijenoort, 1967.
*A Source Book in Mathematical Logic, 1879-1931*. Harvard Univ. Press.- 1923. "On the introduction of transfinite numbers," 346-54.
- 1925. "An axiomatization of set theory," 393-413.

- 1932.
*Mathematical Foundations of Quantum Mechanics*, Beyer, R. T., trans., Princeton U. Press 1996 edition: ISBN ISBN 0-691-02893-1 - 1944. (with Oskar Morgenstern)
*Theory of Games and Economic Behavior*. Princeton Univ. Press. - 1966. (with Arthur W. Burks)
*Theory of Self-Reproducing Automata*. Univ. of Illinois Press.

Secondary:

- Norman Macrae, 1999. "John von Neumann: The Scientific Genius Who Pioneered the Modern Computer, Game Theory, Nuclear Deterrence, and Much More". Reprinted by the American Mathematical Society.
- Aspray,
William, 1990.
*John von Neumann and the Origins of Modern Computing*. - Dalla
Chiara, Maria Luisa and Giuntini, Roberto 1997,
*La Logica Quantistica*in Boniolo, Giovani, ed.,*Filosofia della Fisica*(Philosophy of Physics). Bruno Mondadori. - Goldstine,
Herman, 1980.
*The Computer from Pascal to von Neumann*. - Hashagen, Ulf:, 2006: Johann Ludwig Neumann von Margitta (1903-1957). Teil 1: Lehrjahre eines jüdischen Mathematikers während der Zeit der Weimarer Republik. In: Informatik-Spektrum 29 (2), S. 133-141.
- Hashagen, Ulf:, 2006: Johann Ludwig Neumann von Margitta (1903-1957). Teil 2: Ein Privatdozent auf dem Weg von Berlin nach Princeton. In: Informatik-Spektrum 29 (3), S. 227-236.
- Poundstone,
William.
*Prisoner's Dilemma: John von Neumann, Game Theory and the Puzzle of the Bomb*. 1992. - 1958,
*Bulletin of the American Mathemetical Society 64*. - 1990.
*Proceedings of the American Mathematical Society Symposia in Pure Mathematics 50*.

## [edit] External links

- O'Connor, John J; 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 - Von Neumann vs.
Dirac — from
*Stanford Encyclopedia of Philosophy.* - Edward Teller talking about von Neumann on Peoples Archive.
- A Discussion of Artificial Viscosity
- Von Neumann's Universe, audio talk by George Dyson from ITConversations.com
- John von Neumann's 100th Birthday, article by Stephen Wolfram on Neumann's 100th birthday.
- John von Neumann at the Mathematics Genealogy Project
- His biography at Hungary.hu
- Bibliography of von Neumann's works
- Annotated bibliography for John von Neumann from the Alsos Digital Library for Nuclear Issues
- Budapest Tech Polytechnical Institution - John von Neumann Faculty of Informatics

Persondata | |
---|---|

NAME | Neumann, John von |

ALTERNATIVE NAMES | Neumann János Lajos Margittai (Hungarian) |

SHORT DESCRIPTION | Mathematician and polymath |

DATE OF BIRTH | December 28, 1903(1903-12-28) |

PLACE OF BIRTH | Budapest, Austria-Hungary |

DATE OF DEATH | February 8, 1957 |

PLACE OF DEATH | Washington DC, USA |

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