John von Neumann (December
28, 1903 – February 8, 1957) was an Austro-Hungarian-born American mathematician who made
major contributions to a vast range of fields, including set theory, functional analysis, quantum mechanics, ergodic theory, continuous geometry, economics and game
theory, computer science,
numerical analysis, hydrodynamics (of explosions), and statistics, as well as many other mathematical
fields. He is generally regarded as one of the foremost
mathematicians of the 20th century. The mathematician
Jean Dieudonné called von Neumann "the
last of the great mathematicians."
Even in Budapest, in the time
that produced geniuses like Szilárd (1898), Wigner (1902), and Teller (1908), his brilliance stood
out.Most notably, von Neumann was a pioneer of
the application of operator theory
to quantum mechanics, 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 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.
Biography
The eldest
of three brothers, von Neumann was born Neumann János
Lajos (in Hungarian the family name comes first) on
December 28, 1903 in Budapest, Austro-Hungarian Empire, to a
wealthy Jewish family. His father was
Neumann Miksa (Max Neumann), a lawyer who worked in a
bank. His mother was Kann Margit (Margaret Kann). Von
Neumann's ancestors had originally immigrated to Hungary from
Russia.
János, nicknamed "Jancsi" (Johnny), was a
child prodigy who showed an aptitude for
languages, memorization, and mathematics. He entered the
German-speaking Lutheran
Fasori
Gimnázium in Budapest in 1911. Although he attended school at
the grade level appropriate to his age, his father hired private
tutors to give him advanced instruction in those areas in which he
had displayed an aptitude. In 1913, his father was rewarded with
ennoblement for his service to the
Austro-Hungarian empire. (After becoming
semi-autonomous in
1867, Hungary had found itself in need of a vibrant mercantile
class.) The Neumann family thus acquiring the title
margittai, Neumann János became margittai Neumann János
(John Neumann of Margitta), which he later changed to the German
Johann von Neumann. He received his
Ph.D. in
mathematics (with minors in
experimental physics and
chemistry) from
Pázmány Péter
University in Budapest at the age of 22.
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 taught as a
privatdozent at the University of
Berlin, the youngest in its history. By age 25, he
had published ten major papers, and by 30, nearly 36.
Max von Neumann died in 1929. In 1930, von Neumann, his mother, and
his brothers emigrated to the United States. He
anglicized his first name to John, keeping 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 U.S.).
Von
Neumann was invited to Princeton University, New Jersey in 1930, 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.
In 1937, von Neumann 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, just
prior to emigrating to the United States.
They had one daughter
(von Neumann's only child), Marina, who is now a
distinguished professor of international trade and public policy at
the University of
Michigan. The couple divorced in 1937. In 1938, von
Neumann married Klari Dan, whom he had met during his last trips
back to Budapest prior to the outbreak of World War II. The von
Neumanns were very active socially within the Princeton academic
community, and it is from this aspect of his life that many of the
anecdotes which surround von Neumann's legend originate.
Gravestone of John von Neumann
In 1955, von Neumann was diagnosed with what was either
bone or
pancreatic
cancer.While he was in the hospital he wrote a short monograph,
The Computer and the Brain, observing that the basic computing
hardware of the brain indicated a different methodology than the
one used in developing the computer. Von Neumann died a year and a
half later, in great pain.
While at Walter Reed Hospital in Washington, D.C., he invited a Roman
Catholic priest, Father Anselm Strittmatter, O.S.B., to visit him for consultation (a move
which shocked some of von Neumann's friends). The priest
then administered to him the last
Sacraments. 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.
Von Neumann wrote 150 published papers in his life; 60 in pure
mathematics, 20 in physics, and 60 in applied mathematics. His last
work, 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.
Logic and 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
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 discovered 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 Fraenkel) 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 Fraenkel, 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/Fraenkel 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 1930 at the historic 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: namely that 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.)
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.
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.
Economics and game theory
Von Neumann's first significant contribution to economics was the
minimax theorem of 1928. This
theorem establishes that in certain
zero sum
games with
perfect
information (i.e., in which players know at each time all moves
that have taken place so far), there exists a strategy for each
player 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). The public interest in
this work was such that
The New York
Times ran a front page story, something which only
Einstein had previously elicited.
Von Neumann's second important contribution in this area was the
solution, in 1937, of a problem first described by
Léon 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
L. E. J.
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, in 1983 to
Gerard Debreu, and in 1994 to
John Nash who had improved von Neumann's theory in
his Princeton Ph.D thesis.
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).
Nuclear weapons
Beginning in the late 1930s, von Neumann began to take more of an
interest in applied (as opposed to pure) mathematics. In
particular, he developed an expertise in explosions—phenomena which
are difficult to model mathematically. 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.
The involvement
included frequent trips by train to the project's secret research
facilities in Los Alamos, New Mexico.
Von
Neumann's principal contribution to the atomic bomb itself was in
the concept and 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. While von Neumann did
not originate the "implosion" concept, he was one of its most
persistent proponents, encouraging its continued development
against the instincts of many of his colleagues, who felt such a
design to be unworkable. The lens shape design work was completed
by July 1944.
In a visit to Los Alamos in September 1944, von Neumann showed that
the pressure increase from explosion shock wave reflection from
solid objects was greater than previously believed if the angle of
incidence of the shock wave was between 90° and some limiting
angle. As a result, it was determined that the effectiveness of an
atomic bomb would be enhanced with detonation some kilometers above
the target, rather than at ground level.
Beginning
in the spring of 1945, along with four other scientists and various
military personnel, von Neumann was included in the target
selection committee responsible for choosing the Japanese cities of Hiroshima and
Nagasaki as the first targets of the
atomic bomb. Von Neumann oversaw computations related to
the expected size of the bomb blasts, estimated death tolls, and
the distance above the ground at which the bombs should be
detonated for optimum shock wave propagation and thus maximum
effect.
The cultural capital Kyoto, which had been spared the firebombing inflicted
upon militarily significant target cities like Tokyo in World War
II, was von Neumann's first choice, a selection seconded by
Manhattan Project leader General Leslie
Groves. However, this target was dismissed by
Secretary of War Henry Stimson.
On July
16, 1945, with numerous other Los Alamos personnel, von Neumann was
an eyewitness to the first
atomic bomb blast, conducted
as a test of the implosion method device, 35 miles (56 km)
southeast of Socorro, New
Mexico. Based on his observation alone, von Neumann
estimated the test had resulted in a blast equivalent to 5
kilotons of
TNT, but
Enrico Fermi produced a more accurate
estimate of 10 kilotons by dropping scraps of torn-up paper as the
shock wave passed his location and watching how far they scattered.
The actual power of the explosion had been between 20 and 22
kilotons.
After the war,
Robert Oppenheimer
remarked that the physicists involved in the Manhattan project had
"known sin". Von Neumann's 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 those who
sustained the hydrogen bomb project. He then collaborated with
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.
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 the data and the program are both stored in
the computer's memory in the same address space. This architecture
became the de facto standard until technology enabled more advanced
architectures. The earliest computers were 'programmed' by altering
the electronic circuitry. Although the single-memory, stored
program architecture became commonly known by the name
von Neumann architecture as a
result of von Neumann's paper, the architecture's description was
based on the work of
J.
Presper Eckert and John William Mauchly, inventors of the
ENIAC at the University of Pennsylvania.
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 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.
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.
Throughout his life von Neumann had a respect and admiration for
business and government leaders; something which was often at
variance with the inclinations of his scientific colleagues. He
enjoyed associating with persons in positions of power, and this
led him into government service.
As President of the Von Neumann Committee for Missiles, and later
as a member of the
United States Atomic
Energy Commission, from 1953 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). During a Senate
committee hearing he described his political ideology as "violently
anti-communist, and much more militaristic than the norm".
Von Neumann's interest in meteorological prediction led him to
propose manipulating the environment by spreading colorants on the
polar ice caps in order to enhance absorption of solar radiation
(by reducing the
albedo), thereby raising
global temperatures.
He also favored a preemptive nuclear attack
on the USSR, believing
that doing so could prevent it from obtaining the atomic
bomb.
Personality
Von Neumann invariably wore a conservative grey flannel business
suit - he was even known to play tennis wearing his business suit -
and he enjoyed throwing large parties at his home in Princeton,
occasionally twice a week. Despite being a notoriously bad driver,
he nonetheless enjoyed driving (frequently while reading a book) -
occasioning numerous arrests as well as accidents. He reported one
of his 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." (The von
Neumanns would return to Princeton at the beginning of each
academic year with a new car.) It was said of him at Princeton
that, while he was indeed a demigod, he had made a detailed study
of humans and could imitate them perfectly.
Von Neumann liked to eat and drink heavily; his wife, Klara, said
that he could count everything except calories. He enjoyed
Yiddish and
"off-color" humor (especially
limericks).
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.
The
crater Von
Neumann on the Moon is named after
him.
The John von Neumann Computing Center in Princeton, New Jersey ( )
was named in his honour.
The professional society of Hungarian computer scientists,
John von Neumann Computer
Society, is named after John von Neumann
On February 15, 1956, Neumann was presented with the
Presidential Medal of Freedom
by President
Dwight
Eisenhower
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.
Selected works
See also
- PhD Students
Biographical material
- Aspray, William, 1990. John von Neumann and the Origins of
Modern Computing.
- Chiara, Dalla, 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.
- Halmos, Paul R., 1985. I Want To Be A Mathematician
Springer-Verlag
- 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.
- Heim, Steve J., 1980. John von Neumann and Norbert Weiner:
From Mathematics to the Technologies of Life and Death
MIT Press
- Macrae, Norman, 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.
- Poundstone, William.
Prisoner's Dilemma: John von Neumann, Game Theory and the
Puzzle of the Bomb. 1992.
- Redei, Miklos (ed.), 2005 John von Neumann: Selected
Letters American Mathematical Society
- Ulam, Stanisław, 1983.
Adventures of a Mathematician Scribner's
- Vonneuman, Nicholas A. John von Neumann as Seen by His
Brother ISBN 0-9619681-0-9
- 1958, Bulletin of the American Mathematical Society
64.
- 1990. Proceedings of the American Mathematical Society
Symposia in Pure Mathematics 50.
- John von Neumann 1903-1957, biographical memoir
by S. Bochner, National Academy of Sciences, 1958
- Popular periodicals
- Video
Notes
- Dictionary of Scientific Bibliography, ed. C. C. Gillispie,
Scibners, 1981
- Doran, p. 2
- Doran, p. 1
- While there is a general agreement that the initially
discovered bone tumor was a secondary growth, sources differ as to
the location of the primary cancer. While Macrae gives it as
pancreatic, the Life magazine article says it was
prostate.
- The question of whether or not von Neumann had formally
converted to Catholicism upon his marriage to Mariette Kövesi (who
was Catholic) is addressed by Halmos (ref. 5). He was baptised
Roman Catholic but he certainly was not a practicing member of that
religion after his divorce.
- Halmos, P.R. The Legend of Von Neumann, The American
Mathematical Monthly, Vol. 80, No. 4. (Apr., 1973), pp.
382-394
- John von Neumann at Find a Grave[1]
- 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, in Robert Slater's computer history book, Portraits
in Silicon, and in Nancy Stern's book From ENIAC to
UNIVAC .
- see MAA documentary, especially comments by Morgenstern
regarding this aspect of von Neumann's personality
- See, e.g., Macrae page 332 and Heims, pages 236 -
247.
- See Macrae pp. 170 -171
- 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 Extraordinary
Inspiration of John von Neumann", Proceedings of Symposia in Pure
Mathematics, vol. 50 (1990), pp. 15-17).
References
External links
- von Neumann's contribution to economics —
International Social Science Review
- von Neumann biography — University of St.
Andrews, Scotland
- Oral history interview with Alice R. Burks and Arthur W. Burks, Charles
Babbage Institute, University of Minnesota, Minneapolis.
Alice Burks and Arthur
Burks describe ENIAC, EDVAC, and IAS computers,
and John von Neumann's contribution to the development of
computers.
- Oral history interview with Eugene P. Wigner, Charles
Babbage Institute, University of Minnesota, Minneapolis. Wigner
talks about his association with John von Neumann during their
school years in Hungary, their graduate studies in Berlin, and
their appointments to Princeton in 1930. Wigner discusses von
Neumann's contributions to the theory of quantum mechanics, and von
Neumann's interest in the application of theory to the atomic bomb
project.
- Oral history interview with Nicholas C. Metropolis, Charles Babbage Institute,
University of Minnesota. Metropolis, the first director of computing
services at Los Alamos National
Laboratory, discusses John von Neumann's work in
computing. Most of the interview concerns activity at Los
Alamos: how von Neumann came to consult at the laboratory; his
scientific contacts there, including Metropolis; von Neumann's
first hands-on experience with punched card equipment; his
contributions to shock-fitting and the implosion problem;
interactions between, and comparisons of von Neumann and Enrico Fermi; and the development of Monte Carlo techniques. Other topics include:
the relationship between Alan Turing and
von Neumann; work on numerical methods for non-linear problems; and
the ENIAC calculations
done for Los Alamos.
- Von Neumann vs. Dirac — from Stanford Encyclopedia
of Philosophy.
- Edward Teller talking about von Neumann on Peoples Archive.
- A Discussion of Artificial Viscosity
- John von Neumann Postdoctoral Fellowship - Sandia
National Laboratories
- Von Neumann's Universe, audio talk by George Dyson
- John von Neumann's 100th Birthday, article by
Stephen Wolfram on Neumann's 100th
birthday.
- His biography at Hungary.hu
- Annotated bibliography for John von Neumann from
the Alsos Digital Library for Nuclear Issues
- Budapest Tech
Polytechnical Institution - John von Neumann Faculty of
Informatics
- The American Presidency Project
- John Von Neumann Memorial at Find A Grave