Max von Neumann died in 1929. In 1930 von
Neumann, his mother, and his brothers emigrated to the United States. He
anglicized Johann to John, keeping the Austrianaristocratic 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 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.
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.
In 1955 von Neumann was diagnosed with what was either bone or
pancreatic cancer[4], possibly caused by exposure to radiation during
his witnessing of atomic bomb tests. Von Neumann died a year and a half
following the initial diagnosis, 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)[5]. The priest then administered
to him the last Sacraments.[6] 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.[7]
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 of 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 twentythree 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
nondeterminism had not been reduced to an explanation of a
deterministic form. On the other, there still existed two independent
but equivalent heuristic formulations, the socalled 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
socalled 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 noncommutativity 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. nondeterminism 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
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). 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
fixedpoint 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 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 coauthored with Morgenstern, Theory of Games and Economic
Behaviour).[8]
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[1].
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.[9]
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.[10] 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,
who had been impressed with the city during a visit while Governor
General of the Philippines.[11]
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 tornup 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.[9]
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 TellerUlam 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 middlesquare 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 socalled Harvard
architecture, which has separate program and data memories on a separate
bus. Although the singlememory 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.[12] With very few exceptions,
all presentday home computers, microcomputers, minicomputers and
mainframe computers use this singlememory computer architecture.
Von Neumann also created the field of cellular automata without the aid
of computers, constructing the first selfreplicating automata with
pencil and graph paper. The concept of a universal constructor was
fleshed out in his posthumous work Theory of Self Reproducing
Automata.[13] Von Neumann proved that the most effective way of
performing largescale mining operations such as mining an entire moon
or asteroid belt would be by using selfreplicating 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.[14] His
algorithm for simulating a fair coin with a biased coin[15] 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.[16]
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 anticommunist, 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.[17]
Personality
Although von Neumann invariably wore a conservative grey flannel
business suit, he enjoyed throwing large parties at his home in
Princeton, occasionally twice a week.[18] Despite being a notoriously
bad driver, he nonetheless enjoyed driving (frequently while reading a
book)  occasioning numerous arrests as well as accidents. He once
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."[19] (The
von Neumanns would return to Princeton at the beginning of each academic
year with a new car.)
A committed hedonist, von Neumann liked to eat and drink heavily; his
wife, Klara, said that he could count everything except calories. He
enjoyed yiddish and "offcolor" humor (especially limericks) and could
make very insensitive jokes (for example: "bodily violence is a
displeasure done with the intention of giving pleasure").[citation
needed] Von Neumann persistently gazed 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).[20]
Honors
The John von Neumann Theory Prize of the Institute for Operations
Research and the Management Sciences (INFORMS, previously TIMSORSA) 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 computerrelated 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
(40°20′55″N 74°35′32″W / 40.348695, 74.592251 (John von Neumann
Computing Center)) was named in his honor.
The professional society of Hungarian computer scientists, John von
Neumann Computer Society, is named after John von Neumann[21].
On May 4, 2005 the United States Postal Service issued the American
Scientists commemorative postage stamp series, a set of four 37cent
selfadhesive 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 honor, 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.
See also
Stone–von Neumann theorem
Von Neumann–Bernays–Gödel set theory
Von Neumann algebra
Von Neumann architecture
Von Neumann bicommutant theorem
Von Neumann conjecture
Von Neumann entropy
Von Neumann programming languages
Von Neumann regular ring
Von Neumann universal constructor
Von Neumann universe
Selfreplicating spacecraft 
Aharon's Jewish Books and Judaica
600 South Holly Street Suite 103
Denver, Colorado 80246
3033227345
8008308660
Map to Aharon's Jewish Books and Judaica
Store Hours
Monday through Thursday 9 AM to 6 PM
Friday 9 AM to 2 PM
Sunday 9 AM to 4 PM 
