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John von Neumann was a Hungarian and later American pure and applied mathematician, physicist, inventor, polymath, and polyglot. He made major contributions to a number of fields, including mathematics (foundations of mathematics, functional analysis, ergodic theory, geometry, topology, and numerical analysis), physics (quantum mechanics, hydrodynamics, and fluid dynamics), economics (game theory), computing (Von Neumann architecture, linear programming, self-replicating machines, stochastic computing), and statistics. He was a pioneer of the application of operator theory to quantum mechanics, in the development of functional analysis, 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, the universal constructor, and the digital computer.

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John von Neumann (From Wikipedia)

Born: December 28, 1903, Budapest, Austria-Hungary

Died: February 8, 1957 (aged 53) Washington, D.C., United States

Residence: United States Nationality: Hungarian and American Fields: Mathematics and computer science Institutions: University of Berlin, Princeton University, Institute for Advanced Study, Site Y, Los Alamos Alma mater University of Pázmány Péter, ETH Zürich

Known for: von Neumann Equation, Game theory von Neumann algebras von Neumann architecture Von Neumann bicommutant theorem Von Neumann cellular automaton Von Neumann universal constructor Von Neumann entropy Von Neumann regular ring Von Neumann–Bernays–Gödel set theory Von Neumann universe Von Neumann conjecture Von Neumann's inequality Stone–von Neumann theorem Von Neumann stability analysis Minimax theorem Von Neumann extractor Von Neumann ergodic theorem Direct integral

Notable awards: Enrico Fermi Award (1956)

John von Neumann (December 28, 1903 – February 8, 1957) was a 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 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 greatest mathematicians in modern history. The mathematician Jean Dieudonné called von Neumann "the last of the great mathematicians", while Peter Lax described him as possessing the most "fearsome technical prowess" and "scintillating intellect" of the century. Even in Budapest, in the time that produced geniuses like Theodore von Kármán (b. 1881), Leó Szilárd (b. 1898), Eugene Wigner (b. 1902), and Edward Teller (b. 1908), his brilliance stood out.

Von Neumann was a pioneer of the application of operator theory to quantum mechanics, in the development of functional analysis, 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 Teller and Stanisław 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 somewhat wealthy Jewish parents.[7][8][9] 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 a child prodigy who showed an aptitude for languages, memorization, and mathematics. By the age of six, he could exchange jokes in Classical Greek, memorize telephone directories, and displayed prodigious mental calculation abilities. He entered the Hungarian-speaking Lutheran high school Fasori Evangelikus 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. Recognized as a mathematical prodigy, at the age of 15 he began to study under Gábor Szegő. On their first meeting, Szegő was so impressed with the boy's mathematical talent that he was brought to tears. 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[1] 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 Klara 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. 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, written while in the hospital and later 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.) 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. Quantum mechanics 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 quantum mechanics. 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[clarification needed], 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 Gérard 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.[18] 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. The Fuchs-von Neumann patent used radiation implosion, but not in the same way as is used in what became the final hydrogen bomb design, the Teller-Ulam design. Their work was, however, incorporated into the "George" shot of Operation Greenhouse, which was instructive in testing out concepts that went into the final design. The Fuchs-von Neumann work was passed on, by Fuchs, to the USSR as part of his nuclear espionage, but it was not used in the Soviet's own, independent development of the Teller-Ulam design. The historian Jeremy Bernstein has pointed out that ironically, "John von Neumann and Klaus Fuchs, produced a brilliant invention in 1946 that could have changed the whole course of the development of the hydrogen bomb, but was not fully understood until after the bomb had been successfully made."

Computer science

Von Neumann's hydrogen bomb work was also played out in the realm of computing, where he and Stanisław 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, 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 at the University of Pennsylvania on the EDVAC project, von Neumann wrote an incomplete 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 was commonly called 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.[24] His algorithm for simulating a fair coin with a biased coin[25] 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.

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. 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 to enhance absorption of solar radiation (by reducing the albedo), thereby raising global temperatures. He also favored a preemptive nuclear attack on the Soviet Union, 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.[28] His white clapboard house at 26 Westcott Road was one of the largest in Princeton. Despite being a notoriously bad driver, he nonetheless enjoyed driving (frequently while reading a book) - occasioning numerous arrests as well as accidents. When Cuthbert Hurd hired him as a consultant to IBM, Hurd often quietly paid the fines for his traffic tickets.

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 has been given every year since 1995 to professors who have made an outstanding contribution to the exact social sciences and through their work have strongly influenced the professional development and thinking of the members of the college. _____________________________________________

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John von Neumann was a mathematical genius who did seminal work on quantum mechanics, set theory, game theory, logic and operator theory, the hydrodynamics of explosions and the theory of shocks, ballistics, statistics, the concepts and theory of automata, etc.

John von Neumann was born Janos Lajos Margittai Neumann on December 28, 1903, in Budapest, Hungary. Raised in a non-practicing Jewish family, he had an incredible memory at an early age, being able to divide eight-digit numbers in his head at the age of six.

Von Neumann received his Ph.D. in mathematics from the University of Budapest at the age of 23. He simultaneously learned chemistry in Switzerland. Between 1926 and 1930, he was a private lecturer in Berlin, Germany. In 1930, the same year he married Mariette Koevesi.

Princeton University invited him to lecture on mathematical physics. While at Princeton, the founders of the newly created Institute for Advanced Study asked him to accept a chair in mathematics. Dr. von Neumann became one of the original members of the prestigious institute, where he remained for the rest of his life.

In 1937, the same year von Neumann divorced his first wife, he became a naturalized citizen of the U.S. In 1938, he married Klara Dan, and he was awarded the Bocher Memorial Prize for his work in analysis.

In 1943, von Neumann began working on the Manhattan Project, where he tackled the immense calculations required for construction of an atomic bomb. Faced with that daunting task, he became interested in using machines for the calculation of numbers and the resolution of specific mathematical problems. During and after the war, his interest in computers grew, and he contributed extensively to the construction of the first modern computers. This work established principles on which today's computers are based. His primary area of interest, however, centered on game theory: the study of the conflict between two opponents seeking to arrive at two different goals, each wishing to beat the other.

One of von Neumann's signature achievements was his rigorous mathematical formulation of quantum mechanics in terms of linear operators on Hilbert spaces. He provided a rigorous foundation for quantum statistical mechanics and proposed a proof of the impossibility of hidden variables, showing that quantum mechanics was profoundly different from all previously known theories in physics.

He is also credited with at least one contribution to the study of algorithms. Donald Knuth cites von Neumann as the inventor, in 1945, of the well-known merge sort algorithm, in which the first and second halves of an array are each sorted recursively and then merged together. He also engaged in exploration of problems in the field of numerical hydrodynamics.

In 1955, President Eisenhower appointed von Neumann to the Atomic Energy Commission, and in 1956 he received its Enrico Fermi Award. He died from cancer on February 8, 1957, in Washington, D.C.

http://www.atomicarchive.com/Bios/vonNeumann.shtml

Von Neumann was a pioneer of the application of operator theory to quantum mechanics, in the development of functional analysis, a principal member of the Manhattan Project and the Institute for Advanced Study in Princeton and a key figure in the development of Game Theory. Along with Teller and Stanisław Ulam, von Neumann worked out key steps in the nuclear physics involved in thermonuclear reactions and the hydrogen bom.

John von Neumann was born János von Neumann. He was called Jancsi as a child, a diminutive form of János. His father, Max Neumann, was a top banker and he was brought up in a extended family, living in Budapest where as a child he learnt languages from the German and French governesses that were employed. Although the family were Jewish, Max Neumann did not observe the strict practices of that religion and the household seemed to mix Jewish and Christian traditions.

As a child von Neumann showed he had an incredible memory. Poundstone, in, writes:-

At the age of six, he was able to exchange jokes with his father in classical Greek. The Neumann family sometimes entertained guests with demonstrations of Johnny's ability to memorise phone books. A guest would select a page and column of the phone book at random. Young Johnny read the column over a few times, then handed the book back to the guest. He could answer any question put to him (who has number such and such?) or recite names, addresses, and numbers in order.

In 1911 von Neumann entered the Lutheran Gymnasium. The school had a strong academic tradition which seemed to count for more than the religious affiliation both in the Neumann's eyes and in those of the school. His mathematics teacher quickly recognised von Neumann's genius and special tuition was put on for him. The school had another outstanding mathematician one year ahead of von Neumann, namely Eugene Wigner.

World War I had relatively little effect on von Neumann's education but, after the war ended, Béla Kun controlled Hungary for five months in 1919 with a Communist government. The Neumann family fled to Austria as the affluent came under attack. However, after a month, they returned to face the problems of Budapest. When Kun's government failed, the fact that it had been largely composed of Jews meant that Jewish people were blamed. Such situations are devoid of logic and the fact that the Neumann's were opposed to Kun's government did not save them from persecution.

It is also worth explaining how Max Neumann's son acquired the "von" to become János von Neumann. In 1913 Max Neumann purchased a title but did not change his name. His son, however, used the German form von Neumann where the "von" indicated the title.

In 1921 von Neumann completed his education at the Lutheran Gymnasium. His first mathematics paper, written jointly with Fekete the assistant at the University of Budapest who had been tutoring him, was published in 1922. However Max Neumann did not want his son to take up a subject that would not bring him wealth. Max Neumann asked Theodore von Kármán to speak to his son and persuade him to follow a career in business. Perhaps von Kármán was the wrong person to ask to undertake such a task but in the end all agreed on the compromise subject of chemistry for von Neumann's university studies.

Hungary was not an easy country for those of Jewish descent for many reasons and there was a strict limit on the number of Jewish students who could enter the University of Budapest. Of course, even with a strict quota, von Neumann's record easily won him a place to study mathematics in 1921 but he did not attend lectures. Instead he also entered the University of Berlin in 1921 to study chemistry.

Von Neumann studied chemistry at the University of Berlin until 1923 when he went to Zurich. He achieved outstanding results in the mathematics examinations at the University of Budapest despite not attending any courses. Von Neumann received his diploma in chemical engineering from the Technische Hochschule in Zürich in 1926. While in Zurich he continued his interest in mathematics, despite studying chemistry, and interacted with Weyl and Pólya who were both at Zurich. He even took over one of Weyl's courses when he was absent from Zurich for a time. Pólya said [18]:-

Johnny was the only student I was ever afraid of. If in the course of a lecture I stated an unsolved problem, the chances were he'd come to me as soon as the lecture was over, with the complete solution in a few scribbles on a slip of paper.

Von Neumann received his doctorate in mathematics from the University of Budapest, also in 1926, with a thesis on set theory. He published a definition of ordinal numbers when he was 20, the definition is the one used today.

Von Neumann lectured at Berlin from 1926 to 1929 and at Hamburg from 1929 to 1930. However he also held a Rockefeller Fellowship to enable him to undertake postdoctoral studies at the University of Göttingen. He studied under Hilbert at Göttingen during 1926-27. By this time von Neumann had achieved celebrity status [8]:-

By his mid-twenties, von Neumann's fame had spread worldwide in the mathematical community. At academic conferences, he would find himself pointed out as a young genius.

Veblen invited von Neumann to Princeton to lecture on quantum theory in 1929. Replying to Veblen that he would come after attending to some personal matters, von Neumann went to Budapest where he married his fiancée Marietta Kovesi before setting out for the United States. In 1930 von Neumann became a visiting lecturer at Princeton University, being appointed professor there in 1931.

Between 1930 and 1933 von Neumann taught at Princeton but this was not one of his strong points:-

His fluid line of thought was difficult for those less gifted to follow. He was notorious for dashing out equations on a small portion of the available blackboard and erasing expressions before students could copy them.

In contrast, however, he had an ability to explain complicated ideas in physics:-

For a man to whom complicated mathematics presented no difficulty, he could explain his conclusions to the uninitiated with amazing lucidity. After a talk with him one always came away with a feeling that the problem was really simple and transparent.

He became one of the original six mathematics professors (J W Alexander, A Einstein, M Morse, O Veblen, J von Neumann and H Weyl) in 1933 at the newly founded Institute for Advanced Study in Princeton, a position he kept for the remainder of his life.

During the first years that he was in the United States, von Neumann continued to return to Europe during the summers. Until 1933 he still held academic posts in Germany but resigned these when the Nazis came to power. Unlike many others, von Neumann was not a political refugee but rather he went to the United States mainly because he thought that the prospect of academic positions there was better than in Germany.

In 1933 von Neumann became co-editor of the Annals of Mathematics and, two years later, he became co-editor of Compositio Mathematica. He held both these editorships until his death.

Von Neumann and Marietta had a daughter Marina in 1936 but their marriage ended in divorce in 1937. The following year he married Klára Dán, also from Budapest, whom he met on one of his European visits. After marrying, they sailed to the United States and made their home in Princeton. There von Neumann lived a rather unusual lifestyle for a top mathematician. He had always enjoyed parties]:-

Parties and nightlife held a special appeal for von Neumann. While teaching in Germany, von Neumann had been a denizen of the Cabaret-era Berlin nightlife circuit.

Now married to Klára the parties continued:-

The parties at the von Neumann's house were frequent, and famous, and long.

Ulam summarises von Neumann's work in [35]. He writes:-

In his youthful work, he was concerned not only with mathematical logic and the axiomatics of set theory, but, simultaneously, with the substance of set theory itself, obtaining interesting results in measure theory and the theory of real variables. It was in this period also that he began his classical work on quantum theory, the mathematical foundation of the theory of measurement in quantum theory and the new statistical mechanics.

His text Mathematische Grundlagen der Quantenmechanik (1932) built a solid framework for the new quantum mechanics. Van Hove writes in:-

Quantum mechanics was very fortunate indeed to attract, in the very first years after its discovery in 1925, the interest of a mathematical genius of von Neumann's stature. As a result, the mathematical framework of the theory was developed and the formal aspects of its entirely novel rules of interpretation were analysed by one single man in two years (1927-1929).

Self-adjoint algebras of bounded linear operators on a Hilbert space, closed in the weak operator topology, were introduced in 1929 by von Neumann in a paper in Mathematische Annalen . Kadison explains in [22]:-

His interest in ergodic theory, group representations and quantum mechanics contributed significantly to von Neumann's realisation that a theory of operator algebras was the next important stage in the development of this area of mathematics.

Such operator algebras were called "rings of operators" by von Neumann and later they were called W*-algebras by some other mathematicians. J Dixmier, in 1957, called them "von Neumann algebras" in his monograph Algebras of operators in Hilbert space (von Neumann algebras). In the second half of the 1930's and the early 1940s von Neumann, working with his collaborator F J Murray, laid the foundations for the study of von Neumann algebras in a fundamental series of papers.

However von Neumann is know for the wide variety of different scientific studies. Ulam explains how he was led towards game theory:-

Von Neumann's awareness of results obtained by other mathematicians and the inherent possibilities which they offer is astonishing. Early in his work, a paper by Borel on the minimax property led him to develop ... ideas which culminated later in one of his most original creations, the theory of games.

In game theory von Neumann proved the minimax theorem. He gradually expanded his work in game theory, and with co-author Oskar Morgenstern, he wrote the classic text Theory of Games and Economic Behaviour (1944).

Ulam continues in [35]:-

An idea of Koopman on the possibilities of treating problems of classical mechanics by means of operators on a function space stimulated him to give the first mathematically rigorous proof of an ergodic theorem. Haar's construction of measure in groups provided the inspiration for his wonderful partial solution of Hilbert's fifth problem, in which he proved the possibility of introducing analytical parameters in compact groups.

In 1938 the American Mathematical Society awarded the Bôcher Prize to John von Neumann for his memoir Almost periodic functions and groups. This was published in two parts in the Transactions of the American Mathematical Society, the first part in 1934 and the second part in the following year. Around this time von Neumann turned to applied mathematics [35]:-

In the middle 30's, Johnny was fascinated by the problem of hydrodynamical turbulence. It was then that he became aware of the mysteries underlying the subject of non-linear partial differential equations. His work, from the beginnings of the Second World War, concerns a study of the equations of hydrodynamics and the theory of shocks. The phenomena described by these non-linear equations are baffling analytically and defy even qualitative insight by present methods. Numerical work seemed to him the most promising way to obtain a feeling for the behaviour of such systems. This impelled him to study new possibilities of computation on electronic machines ...

Von Neumann was one of the pioneers of computer science making significant contributions to the development of logical design. Shannon writes in [29]:-

Von Neumann spent a considerable part of the last few years of his life working in [automata theory]. It represented for him a synthesis of his early interest in logic and proof theory and his later work, during World War II and after, on large scale electronic computers. Involving a mixture of pure and applied mathematics as well as other sciences, automata theory was an ideal field for von Neumann's wide-ranging intellect. He brought to it many new insights and opened up at least two new directions of research.

He advanced the theory of cellular automata, advocated the adoption of the bit as a measurement of computer memory, and solved problems in obtaining reliable answers from unreliable computer components.

During and after World War II, von Neumann served as a consultant to the armed forces. His valuable contributions included a proposal of the implosion method for bringing nuclear fuel to explosion and his participation in the development of the hydrogen bomb. From 1940 he was a member of the Scientific Advisory Committee at the Ballistic Research Laboratories at the Aberdeen Proving Ground in Maryland. He was a member of the Navy Bureau of Ordnance from 1941 to 1955, and a consultant to the Los Alamos Scientific Laboratory from 1943 to 1955. From 1950 to 1955 he was a member of the Armed Forces Special Weapons Project in Washington, D.C. In 1955 President Eisenhower appointed him to the Atomic Energy Commission, and in 1956 he received its Enrico Fermi Award, knowing that he was incurably ill with cancer.

Eugene Wigner wrote of von Neumann's death [18]:-

When von Neumann realised he was incurably ill, his logic forced him to realise that he would cease to exist, and hence cease to have thoughts ... It was heartbreaking to watch the frustration of his mind, when all hope was gone, in its struggle with the fate which appeared to him unavoidable but unacceptable.

Von Neumann's death is described in these terms:-

... his mind, the amulet on which he had always been able to rely, was becoming less dependable. Then came complete psychological breakdown; panic, screams of uncontrollable terror every night. His friend Edward Teller said, "I think that von Neumann suffered more when his mind would no longer function, than I have ever seen any human being suffer."

Von Neumann's sense of invulnerability, or simply the desire to live, was struggling with unalterable facts. He seemed to have a great fear of death until the last... No achievements and no amount of influence could save him now, as they always had in the past. Johnny von Neumann, who knew how to live so fully, did not know how to die.

It would be almost impossible to give even an idea of the range of honours which were given to von Neumann. He was Colloquium Lecturer of the American Mathematical Society in 1937 and received the its Bôcher Prize as mentioned above. He held the Gibbs Lectureship of the American Mathematical Society in 1947 and was President of the Society in 1951-53.

He was elected to many academies including the Academia Nacional de Ciencias Exactas (Lima, Peru), Academia Nazionale dei Lincei (Rome, Italy), American Academy of Arts and Sciences (USA), American Philosophical Society (USA), Instituto Lombardo di Scienze e Lettere (Milan, Italy), National Academy of Sciences (USA) and Royal Netherlands Academy of Sciences and Letters (Amsterdam, The Netherlands).

Von Neumann received two Presidential Awards, the Medal for Merit in 1947 and the Medal for Freedom in 1956. Also in 1956 he received the Albert Einstein Commemorative Award and the Enrico Fermi Award mentioned above.

http://ei.cs.vt.edu/%7Ehistory/VonNeumann.html

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http://www.google.com/search?client=safari&rls=en&q=von+Neumann&ie=...
Books for von Neumann

http://www.amazon.com/s/ref=nb_sb_noss?url=search-alias%3Daps&field...

http://www.pasz.com/gathering/attendees.html

http://www.siam.org/news/news.php?id=318

http://videoactive.wordpress.com/the-consortium/neumann/

Good Housekeeping Magazine, September 1956 "Married to a Man Who Believes the Mind Can Move the World"

 Life Magazine, February 25, 1957 "Passing of a Great Mind"

Video

• "John von Neumann, A Documentary" (60 min.), Mathematical Association of America

http://www.stephenwolfram.com/publications/recent/neumann/

http://www.forbes.com/2006/12/10/business-game-theory-tech-cx_th_ga...

LIFE magazine, Feb 25, 1957 - page 89 - 104

Neumann biography Írta: Horváth Ilona    2009. március 25. szerda 15:08  
János Neumann was born on 28 th December 1903, the eldest of three brothers. His father, Miksa, was a lawyer who worked in a bank. Both he and his wife provided not only creature comforts but also an intellectual background for the children. With his exceptional intelligence he created such an atmosphere at home that helped the firstborn son's talent develop. It was recorded that Miksa spoke Old Greek so well that he jested with his six-year-old son, Janos in this language. He also ensured that his sons spoke quite a few foreign languages. János, besides Old Greek, spoke German fluently, learnt Latin and later English. Miksa Neumann died at the age of 59 in 1926. A typical example for the intellectual atmosphere: János and his brother Miklós read Goethe's Faust both the original German drama and its Hungarian translation many times so that they could discuss the reading of it. According to Miklós's reminiscence János was interested in nature. He believed to recognise such cohesive force in it that he thought the human intelligence was not enough to understand it. However, he believed that we have to try to explain the mystery of nature with all the available tools. He tried to explain the nervous system with the analogy of logic of the computer, the secrets of genetics with the theory of self reproducing automata, the structure of atoms with the means of quantum mechanics, and phenomena of weather and weather forecast with the numerical meteorology. János Neumann was ten years old when his father was rewarded with ennoblement for his service to the Austro-Hungarian Empire. Thus the family acquired the name margittai, and Neumann János became John von Neumann of Margitta. János Neumann used the name John von Neumann in America and he is known by this name in the world of science. János, nicknamed "Jancsi" (Johnny), was a prodigy who showed aptitudes for languages, memorization, and mathematics. He entered the German-speaking Lutheran Fasori Gimnázium ( Secondary Grammar School ) in Budapest in the year 1911. Although he attended school at the grade level appropriate to his age, his father hired private tutors to give him advanced instruction in the areas in which he had displayed an aptitude. 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 10 major papers (on set theory, algebra and quantum mechanics), and by 30, nearly 36. In September 1930 at the historic mathematical Congress of Königsberg , 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.) Neumann was invited to Princeton University , New Jersey in 1930. One year later he became a professor. For three years he held lectures both in Europe and in the USA . When Hitler rose to power he emigrated to the States for good, where he gained citizenship in 1937. 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 Klára Dán, 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. 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 . 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 description was based on the work of J. Presper Eckert and John William Mauchly , inventors of the ENIAC at the University of Pennsylvania . With very few exceptions, all present-day home computers, microcomputers , minicomputers and mainframe computers use this single-memory computer architecture. US President Eisenhower presented Neumann with the Medal of Freedom at a ceremony at the White House on February 15, 1956. This was his last appearance in public. John von Neumann died in February 1957 of cancer that was a result of irradiation in the atomic bomb tests. Today more and more schools and institutes take von Neumann's name. Also the Institute of Electrical and Electronics Engineers (IEEE) has been presenting medals named after Neumann for outstanding achievements in computer-related science and technology since 1990 . Adapted from Wikipedia Free Encyclopedia  

© 2010 Neumann János Számítástechnikai Szakközépiskola

http://wiki.geni.com/index.php/Jewish_Dynasties

http://genealogy.math.ndsu.nodak.edu/id.php?id=53213

Mathematics Genealogy Project

John (Janos) von Neumann

Biography MathSciNet

--------------------------------------------------------------------------------

Ph.D. Eötvös Loránd University 1926
Dissertation: Advisor: Leopold (Lipót) Fejér

Students: Click here to see the students listed in chronological order.

Name School Year Descendants

1. Donald Gillies Princeton University 1953 54
2. Israel Halperin Princeton University 1936 39
3. John Mayberry Princeton University 1956

According to our current on-line database, John (Janos) von Neumann has 3 students and 96 descendants.

marriage https://familysearch.org/ark:/61903/3:1:S3HY-XHL7-NV?i=507

מויקיפדיה:

ג'ון לואיס פון נוימן (28 בדצמבר 1903 - 8 בפברואר 1957) היה מתמטיקאי ואיש אשכולות הונגרי-אמריקאי ממוצא יהודי, שהמיר דתו לנצרות קתולית. היה שותף לשניים מההישגים הטכנולוגיים הבולטים של המאה ה-20: פיתוח פצצת האטום ופיתוח המחשב האלקטרוני. הוא היה גם יוצרה של תורת המשחקים (יחד עם אוסקר מורגנשטרן), תרם תרומה משמעותית לחקר מכניקת הקוונטים, תורת הקבוצות וענפי מתמטיקה נוספים, ושילב בהצלחה רבה פעילות במחקר טהור וכן מחקר שימושי בענפי מדע רבים.

תולדות חייו

פון נוימן נולד בבודפשט למשפחה יהודית נאולוגית, בשם יאנוש ליוש נוימן (Neumann János Lajos). אביו, מקס נוימן, היה בנקאי אמיד ובעל דוקטורט במשפטים. עד גיל 10 למד בבית בהדרכת מורים פרטיים, כמנהג עשירי אירופה. סימני גאונות ניכרו בו כבר בילדותו; יוג'ין ויגנר, חתן פרס נובל לפיזיקה לשנת 1963, שלמד יחד עם פון נוימן בבית הספר התיכון הלותרני, אמר עליו מאוחר יותר: "יש שני סוגי אנשים בעולם: ג'וני פון נוימן - ואנחנו, השאר". המורה למתמטיקה בגימנסיה זיהה מיד את כשרונו המתמטי יוצא הדופן והמליץ להוריו לשכור לו מורה פרטי למתמטיקה. ההורים שכרו את מיכאל פקטה שהיה מרצה באוניברסיטת בודפשט, והוא לימד אותו מתמטיקה גבוהה.

למרות מגבלת הנומרוס קלאוזוס התקבל פון נוימן ללימודי מתמטיקה באוניברסיטת בודפשט, ובגיל 19 פרסם את מאמרו המתמטי הראשון, אותו כתב יחד עם מדריכו מהאוניברסיטה מיכאל פקטה, שהצטרף לאחר זמן לסגל האוניברסיטה העברית בירושלים. פון נוימן קיבל תואר דוקטור למתמטיקה מאוניברסיטת בודפשט בגיל 23 (הדוקטורט שלו עסק בתורת הקבוצות). במקביל ללימודי מתמטיקה, למד גם כימיה באוניברסיטת ברלין והנדסה כימית במכון הטכנולוגי של ציריך, משום שאביו ראה במתמטיקה עיסוק שאין בו פרנסה. בעת לימודיו בציריך למד גם מתמטיקה, אצל ג'ורג' פוליה והרמן וייל.

לאחר סיום לימודיו לימד במשך שנים אחדות באוניברסיטאות של ברלין והמבורג, ובמקביל למד באוניברסיטת גטינגן אצל דויד הילברט, שם גם פגש לראשונה את הפיזיקאי רוברט אופנהיימר.

לאחר שפניותיו לקבלת אשרת הגירה לארצות הברית נדחו כמה פעמים, הוא הוזמן לבסוף ב-1929 לאוניברסיטת פרינסטון בסיוע חבריו. לאחר הטבלתו לנצרות קתולית לצורך נישואיו הראשונים, בסוף 1930 היגר לארצות הברית. בפרינסטון עסק בהוראה עד לשנת 1933, שבה נבחר לאחד מששת חברי הסגל הראשונים במכון למחקר מתקדם, מינוי שבו החזיק עד סוף ימיו, במקביל להיותו מרצה אורח באוניברסיטת פרינסטון.

הזוג התגרש ארבע שנים מאוחר יותר. מנישואיו הראשונים נולדה בתו היחידה, מרינה, פרופסור ידועת שם לסחר ומדיניות בינלאומית באוניברסיטת מישיגן.

עם עליית אדולף היטלר והמפלגה הנאצית לשלטון, ניבא נוימן את השתלטות היטלר על אירופה, ואת התוצאות הרות האסון הצפויות ליהודים שם. בשנת 1937 ו-1938 חזר פעמים אחדות לבודפשט על מנת לארגן את יציאתה של משפחתו מהונגריה לארצות הברית, ושם פגש את אשתו השנייה קלארה (קלארי). הוא הצליח להוציא את משפחתה ואת משפחתו לארצות הברית בשנת 1939, רגע לפני שמלחמת העולם השנייה פרצה במלוא עוזה.

במהלך מלחמת העולם השנייה חבר למדען היהודי יליד ניו יורק ריצ'רד פיינמן, והצטרף למזהירים מפני פיתוח נשק גרעיני על ידי גרמניה והצבא הנאצי. הוא השתתף בפרויקט מנהטן, ופיתח בה את ה'עדשה המפוצצת', אחד הרכיבים העיקריים הנדרשים לפיצוץ גרעיני. פון נוימן היה מהתומכים בהמשך פיתוח הטכנולוגיה הצבאית הגרעינית, לעומת הפורשים והמסתייגים ממנה כמו רוברט אופנהיימר ואלברט איינשטיין. לאחר המלחמה סייע גם לפיתוחה של פצצת המימן, היה חבר הוועדה לתחנות כח גרעיניות, ובשנותיו האחרונות ועד מותו היה ראש הוועדה הסודית של ממשלת ארצות הברית לפיתוח טילים בין-יבשתיים. הוא פעל גם כיועץ לתאגיד ראנד.

בשנת 1928 פרסם מאמר ובו הוכחה ל"משפט המינימקס" שהוא ממשפטי היסוד בתורת המשחקים. בשנת 1944 פרסם, יחד עם אוסקר מורגנשטרן, את הספר Theory of Games and Economic Behavior, שהוא תחילתה של תורת המשחקים כתחום עצמאי.

על ייחודו של פון נוימן כאיש מדע כותבת סילביה נאצר, בספרה "נפלאות התבונה":

ג'ון פון נוימן היה הכוכב הנוצץ ביותר ברקיע המתמטיקה של פרינסטון, ושליח העידן החדש במתמטיקה. בגיל ארבעים וחמש ראו בו כולם את המתמטיקאי הקוסמופוליטי, רב-הפנים והאינטליגנטי ביותר שהניבה המאה העשרים. איש לא היה חשוב ממנו בהעלאה-מחדש של קרנה של המתמטיקה בחיים האינטלקטואלים באמריקה.

פון נוימן היה מחלוצי מדעי המחשב, ותרם לבסיס התאורטי שלהם. בצד המעשי של המחשוב היה בקשר הדוק עם מפתחי המחשבים הראשונים ועיצב את הארכיטקטורה המוכרת לנו של המחשב, לפיה מכיל הזיכרון את התוכנית לביצוע ואת הנתונים שעליהם היא פועלת, והוראות התוכנית מתבצעות באופן סדרתי בזו אחר זו. מחשב מסוג זה קרוי ארכיטקטורת פון נוימן. המחשב שפיתח במכון למחקר מתקדם שימש מודל למחשבים נוספים, ובהם ויצק של מכון ויצמן למדע - המחשב הראשון בישראל. פון נוימן התייחס בזלזול לפיתוחן של שפות התכנות הראשונות, בעיניו די היה בשפת מכונה. במאמר שפרסם נוימן בשנת 1949 כבר הופיעו ניצני הרעיון המקורי של תוכנות "המתרבות" מעצמן, קרי וירוס מחשב.

פון נוימן שילב בין תחומי הפעילות המגוונים שלו. הוא היה מהאסטרטגים של "המלחמה הקרה": הוא רתם את המחשב לפיתוח נשק גרעיני, ואת תורת המשחקים ככלי לחשיבה אסטרטגית אודות השימוש בנשק זה. בין היתר תמך בהתקפה גרעינית על ברית המועצות, מעין מכה מקדימה שתמנע ממנה לפתח פצצה גרעינית. פון נוימן היה אדם אוהב חיים, והרבה לערוך מסיבות בביתו שבפרינסטון. השם MANIAC שניתן לאחד מראשוני המחשבים (ראשי תיבות של Mathematical Analyzer, Numerical Integrator And Computer), מיוחס לחוש ההומור שלו.

פון ניומן סייע לפרסומו של קורט גדל ושל משפטי האי שלמות שלו בקרב הקהילה המתמטית.

פון נוימן נפטר ב־8 בפברואר 1957 בוושינגטון, כשנה וחצי לאחר שהתגלה בגופו סרטן. לקראת מותו על ערש דווי הזמין כומר לצורך וידוי, לפי עיקרון ההימור של פסקל.

לאחר מותו זכה לאותות הוקרה רבים. בסוף שנת 1997 הוקם במכון ויצמן למדע מרכז מחקר על שמו לאימות של מערכות ריאקטיביות. שמו של פון נוימן

נדודיו של פון נוימן, אשר נבעו מרצון לקדם את הקריירה שלו, משתקפים גם בשמות שסיגל לעצמו. הוא נולד בבודפשט בירת הונגריה, נימול כיוחנן (יאנוש) נוימן (Neumann János, בהונגרית שם המשפחה מקדים את השם הפרטי), וזכה לשם החיבה יאנצ'י (Jancsi). בשנת 1913 רכש אביו את תואר האצולה ההונגרי "מרגיטאי" המקביל לתואר האוסטרי "פון מרגיטה". כאשר עבר ללמוד בגרמניה שינה את שמו ליוהאן פון נוימן (Johann von Neumann), וכאשר התאזרח בארצות הברית שינה את שמו הפרטי לג'ון (John), ואת שם משפחתו ביטא "פון ניוּמֶן" (אם כי לא שינה את הכתיב שלו). בארצות הברית כונה ג'וני בפי חבריו. באנציקלופדיה העברית הוא נמצא תחת הערך "נוימן, ג'ון (ינוש) פון".

גם מבחינת דתו, בדומה ליהודים מתבוללים רבים במאות ה-19–20, הפגין פון נוימן גמישות והסתגלות לסביבה. הוא נולד כיהודי למשפחה ניאולוגית. בגיל 26, הוא הוטבל לנצרות הקתולית לצורך נישואיו עם אשתו הראשונה, מרייט. מנישואין אלו יש לו בת, מרינה, פרופסור ידועת שם ביחסים בינלאומיים מאוניברסיטת מישיגן. במכתביו הביע הסתייגות מדת, והציג עצמו כאתאיסט, אך על ערש דווי ביקש להתוודות בפני כומר, לפי עקרון ההימור של פסקל. ייתכן גם שטקס הווידוי נערך ביוזמת הכנסייה בשעה שפון נוימן כבר לא היה בהכרה מלאה "על מנת למנוע טעות".

• John von Neumann Wikipedia, English