John von Neumann

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John von Neumann

John von Neumann in the 1940s
Born December 28, 1903(1903-12-28)
Budapest, Austria-Hungary
Died February 8, 1957(1957-02-08) (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
Doctoral advisor Lipót Fejér
Doctoral students Donald B. Gillies
Israel Halperin
John P. Mayberry
Other notable students Paul Halmos
Clifford Hugh Dowker
Known for von Neumann Equation
Abelian von Neumann algebra
Artificial viscosity
Axiom of regularity
Backward induction
Duality Theorem
Durbin–Watson statistic
Game theory
Ergodic theory
Lattice theory
Lifting theory
Inner model
Merge sort
Middle-square method
Radiation implosion
Operator theory
von Neumann algebra
von Neumann architecture
Von Neumann bicommutant theorem
Von Neumann cellular automaton
Von Neumann Ordinals
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
Monte Carlo method
Quantum statistical mechanics
Von Neumann extractor
Von Neumann ergodic theorem
Direct integral
Ultrastrong topology
Von Neumann–Morgenstern utility theorem
Notable awards Enrico Fermi Award (1956)

John von Neumann (English pronunciation: /vɒn ˈnɔɪmən/) (December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician and polymath who made major contributions to many fields,[1] including set theory, functional analysis, quantum mechanics, ergodic theory, continuous geometry, economics and game theory, computer science, numerical analysis, hydrodynamics, and statistics, as well as many other mathematical fields. He is generally regarded as one of the greatest mathematicians in modern history.[2] The mathematician Jean Dieudonné called von Neumann "the last of the great mathematicians",[3] while Peter Lax described him as possessing the most "fearsome technical prowess" and "scintillating intellect" of the century.[4] 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.[5]

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[1][6] and the concepts of cellular automata,[1] the universal constructor, and the digital computer. In a short list of facts about his life he submitted to the National Academy of Sciences, he stated "The part of my work I consider most essential is that on quantum mechanics, which developed in Göttingen in 1926, and subsequently in Berlin in 1927–1929. Also, my work on various forms of operator theory, Berlin 1930 and Princeton 1935–1939; on the ergodic theorem, Princeton, 1931–1932." Along with Teller and Stanisław Ulam, von Neumann worked out key steps in the nuclear physics involved in thermonuclear reactions and the hydrogen bomb.


[edit] Biography

The eldest of three brothers, von Neumann was born – Neumann János Lajos (Hungarian pronunciation: [ˈnojmɒn ˈjaːnoʃ ˈlɒjoʃ]; in Hungarian the family name comes first) on December 28, 1903 in Budapest, Austro-Hungarian Empire, to wealthy Jewish parents.[7][8][9] His father was Neumann Miksa (Max Neumann) who came to Budapest from Pécs at the end of 1880s, passed doctor of law examinations and worked for a bank. His mother was Kann Margit (Margaret Kann).[10]

János, nicknamed "Jancsi" (Johnny), was a child prodigy, with an aptitude for languages, memorization, and mathematics. By the age of six, he could exchange jokes in Classical Greek, memorize telephone directories, and display prodigious mental calculation abilities.[11] He entered the German-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, he began to study advanced calculus under Gábor Szegő at the age of 15. On their first meeting, Szegő was so astounded with the boy's mathematical talent that he was brought to tears.[12] 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.[1] 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 the end of year 1927 Neumann had published twelve major papers in mathematics, and by the end of year 1929 thirty-two, at a rate of nearly one major paper per month.[10]

Excerpt from the university calendars for 1928 and 1928/29 of the Friedrich-Wilhelms-Universität Berlin announcing Neumann's lectures on axiomatic set theory and logics, problems in quantum mechanics and special mathematical functions

His father, 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[citation needed] 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 U.S. In 1938, he was awarded the Bôcher Memorial Prize for his work in analysis.

Gravestone of John von Neumann

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 are part of von Neumann's legend originate.

In 1955, von Neumann was diagnosed with what was either bone or pancreatic cancer.[13] Von Neumann died a year and a half later. 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. This move shocked some of von Neumann's friends in view of his reputation as an agnostic.[14] Von Neumann, however, is reported to have said in explanation that Pascal had a point, referring to Pascal's wager.[15] Father Strittmatter administered the last sacraments to him.[16] 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.[17]

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.

[edit] 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 the axiom schema of Richard Dedekind and Charles Sanders Peirce) and geometry (thanks to David Hilbert). At the beginning of the twentieth century, efforts to base mathematics on naive set theory suffered a setback due to Russell's paradox (on the set of all sets that do not belong to themselves).

The problem of an adequate axiomatization of set theory was resolved implicitly about twenty years later (by Ernst Zermelo and Abraham Fraenkel). Zermelo and Fraenkel provided a series of principles that allowed for the construction of the sets used in the everyday practice of mathematics: But they did not explicitly exclude the possibility of the existence of a set that belong to itself. In his doctoral thesis of 1925, von Neumann demonstrated two techniques to exclude such sets: 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.[18] It is precisely this consequence which has attracted the most attention, even if Gödel originally considered it only a curiosity, and had derived it independently anyway (it is for this reason that the result is called Gödel's second theorem, without mention of von Neumann.)

[edit] Quantum mechanics

Quantum mechanics
\Delta x\, \Delta p \ge \frac{\hbar}{2}
Uncertainty principle
Mathematical formulations
v · d · e

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.

[edit] Economics and game theory

Von Neumann raised the intellectual and mathematical level of economics in several stunning publications. Von Neumann's proved his minimax theorem in 1928. This theorem establishes that in 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 pair of strategies for both players that allows each to minimize his maximum losses (hence the name minimax). When examining every possible strategy, a player must consider all the possible responses of his adversary. The player then plays out the strategy which will result in the minimization of his maximum loss. Such strategies, which minimize the maximum loss for each player, are called optimal. Von Neumann showed that their minimaxes are equal (in absolute value) and contrary (in sign). Another result he proved during his German period was the nonexistence of a static equilibrium. An equilibrium can only exist in an expanding economy. Paul Samuelson edited an anniversary volume dedicated to this short German paper in 1972 and stated in the introduction that von Neumann was the only mathematician ever to make a significant contribution to economic theory.

Von Neumann improved and extended the minimax theorem to include games involving imperfect information and games with more than two players, publishing this result in his 1944 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. In this book, von Neumann declared that economic theory needed to use functional analytic methods, especially convex sets and topological fixed point theorem, rather than the traditional differential calculus, because the maximum–operator did not preserve differentiable functions. Independently, Leonid Kantorovich's functional analytic work on mathematical economics also focused attention on optimization theory, non-differentiability, and vector lattices. Von Neumann's functional-analytic techniques—the use of duality pairings of real vector spaces to represent prices and quantities, the use of supporting and separating hyperplanes and convex set, and fixed-point theory—have been the primary tools of mathematical economics ever since.[19]

For his model of an expanding economy, von Neumann proved the existence and uniqueness of an equilibrium using his generalization of Brouwer's fixed point theorem. Von Neumann's model of an expanding economy considered the matrix pencil  A − λB with nonnegative matrices A and B; von Neumann sought probability vectors p and q and a positive number λ that would solve the complementarity equation

pT (Aλ Bq = 0,

along with two inequality systems expressing economic efficiency. In this model, the (transposed) probability vector p represents the prices of the goods while the probability vector q represents the "intensity" at which the production process would run. The unique solution λ represents the growth factor which is 1 plus the rate of growth of the economy; the rate of growth equals the interest rate. Proving the existence of a positive growth rate and proving that the growth rate equals the interest rate were remarkable achievements, even for von Neumann.[20][21][22] Von Neumann's results have been viewed as a special case of linear programming, where von Neumann's model uses only nonnegative matrices.[23] The study of von Neumann's model of an expanding economy continues to interest mathematical economists with interests in computational economics.[24][25][26] This paper has been called the greatest paper in mathematical economics by several authors, who recognized its introduction of fixed-point theorems, linear inequalities, complementary slackness, and saddlepoint duality.

Building on his results on matrix games and on his model of an expanding economy, Von Neumann also invented the theory of duality in linear programming, after George B. Dantzig described his work in a few minutes, after an impatient von Neumann asked him to get to the point. Then, Dantzig listened dumbfounded while von Neumann provided an hour lecture on convex sets, fixed-point theory, and duality, conjecturing the equivalence between matrix games and linear programming. Later, von Neumann suggested a new method of linear programming, using the homogeneous linear system of Gordan (1873) which was later popularized by Karmarkar's algorithm. Von Neumann's method used a pivoting algorithm between simplices, with the pivoting decision determined by a nonnegative least squares subproblem with a convexity constraint (projecting the zero-vector onto the convex hull of the active simplex). Von Neumann's algorithm was the first interior-point method of linear programming. However, it was not competitive with the simplex algorithm of Dantzig.[27]

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 used fixed point theorems to establish equilibria for noncooperative games and for bargaining problems in his Ph.D thesis. Arrow and Debreu also used linear programming, as did Nobel laureates Tjalling Koopmans, Leonid Kantorovich, Wassily Leontief, Paul Samuelson, Robert Dorfman, Robert Solow, and Leonid Hurwicz.

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).[28]

[edit] Mathematical statistics and econometrics

Von Neumann made some fundamental contributions to mathematical statistics. In 1941, he derived the exact distribution of the ratio of mean square successive difference to the variance for normally distributed variables.[29] This ratio was applied to the residuals from regression models and is commonly known as the Durbin–Watson statistic[30] for testing the null hypothesis that the errors are serially independent against the alternative that they follow a stationary first order autoregression. Subsequently, John Denis Sargan and Alok Bhargava[31] extended the results for testing if the errors on a regression model follow a Gaussian random walk (i.e. possess a unit root) against the alternative that they are a stationary first order autoregression. Von Neumann's contributions to statistics have had a major impact on econometric methodology.

[edit] Nuclear weapons

John von Neumann's wartime Los Alamos ID badge photo.

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.[32]

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.[33] 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.[34]

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.[32]

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.[35] 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."[36]

[edit] The ICBM Committee

Shortly before his death, when he was already quite ill, von Neumann headed the top secret von Neumann ICBM committee. Its purpose was to decide on the feasibility of building an ICBM large enough to carry a thermonuclear weapon. Von Neumann had long argued that while the technical obstacles were indeed formidable, they could be overcome in time. The SM-65 Atlas passed its first fully functional test in 1959, two years after his death.

[edit] 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 is to this day the basis of modern computer design, unlike the earliest computers that were 'programmed' by altering the electronic circuitry. Although the single-memory, stored program architecture is 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.[37]

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.[38] 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.[39] His algorithm for simulating a fair coin with a biased coin[40] 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 solved hydrodynamic or aerodynamic problems, they tried 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.[41] Von Neumann entered government service (Manhattan Project) primarily because he felt that, if freedom and civilization were to survive, it would have to be because the U.S. would triumph over totalitarianism from the right (Nazism and Fascism) and totalitarianism from the left (Soviet Communism).[42]

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.[43]

[edit] Personality

Von Neumann invariably wore a conservative grey flannel business suit, once riding down the Grand Canyon astride a mule in a three-piece pin-stripe,[42] and he enjoyed throwing large parties at his home in Princeton, occasionally twice a week.[44] His white clapboard house at 26 Westcott Road was one of the largest in Princeton.[45] 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.[46]

Von Neumann liked to eat and drink; his wife, Klara, said that he could count everything except calories. He enjoyed Yiddish and "off-color" humor (especially limericks).[16]

[edit] Honors

[edit] Selected works

[edit] See also

PhD Students

[edit] Biographical material

Popular periodicals

[edit] Notes

  1. ^ a b c d e f Ed Regis (1992-11-08). "Johnny Jiggles the Planet". The New York Times. Retrieved 2008-02-04. 
  2. ^ Impagliazzo, p. vii
  3. ^ Dictionary of Scientific Bibliography, ed. C. C. Gillispie, Scibners, 1981
  4. ^ Impagliazzo, p. 7
  5. ^ Doran, p. 2
  6. ^ Nelson, David (2003). The Penguin Dictionary of Mathematics. London: Penguin. pp. 178–179. ISBN 0-141-01077-0. 
  7. ^ Doran, p. 1
  8. ^ Nathan Myhrvold, "John von Neumann". Time, March 21, 1999. Accessed September 5, 2010
  9. ^ Clay Blair, Jr. "Passing of a Great Mind". Life, February 25, 1957; p. 104
  10. ^ a b Norman Macrae (June 2000). John Von Neumann: The Scientific Genius Who Pioneered the Modern Computer, Game Theory, Nuclear Deterrence, and Much More. AMS Bookstore. pp. 37–38. ISBN 9780821826768. Retrieved 24 March 2011. 
  11. ^ William Poundstone, Prisoner's dilemma (Oxford, 1993), introduction
  12. ^ Impagliazzo, p. 5
  13. ^ 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.
  14. ^ The question of whether or not von Neumann had formally converted to Catholicism upon his marriage to Mariette Kövesi (who was Catholic) is addressed in Halmos, P.R. "The Legend of von Neumann", The American Mathematical Monthly, Vol. 80, No. 4. (April 1973), pp. 382–394. He was baptised Roman Catholic, but certainly was not a practicing member of that religion after his divorce.
  15. ^ Marion Ledwig. "The Rationality of Faith", citing Macrae, p. 379.
  16. ^ a b Halmos, P.R. "The Legend of von Neumann", The American Mathematical Monthly, Vol. 80, No. 4. (April 1973), pp. 382–394
  17. ^ John von Neumann at Find a Grave[1]
  18. ^ John von Neumann (2005). Miklós Rédei. ed. John von Neumann: Selected letters. History of Mathematics. 27. American Mathematical Society. p. 123. ISBN 0-8218-3776-1. 
  19. ^ Blume, Lawrence E. (2008c). "Convexity". In Durlauf, Steven N.; Blume, Lawrence E. The New Palgrave Dictionary of Economics (Second ed.). Palgrave Macmillan. doi:10.1057/9780230226203.0315. 
  20. ^ For this problem to have a unique solution, it suffices that the nonnegative matrices A and B satisfy an irreducibility condition, generalizing that of the Perron–Frobenius theorem of nonnegative matrices, which considers the (simplified) eigenvalue problem
    A − λ I q = 0,
    where the nonnegative matrix A must be square and where the diagonal matrix I is the identity matrix. Von Neumann's irreducibility condition was called the "whales and wranglers" hypothesis by David Champernowne, who provided a verbal and economic commentary on the English translation of von Neumann's article. Von Neumann's hypothesis implied that every economic process used a positive amount of every economic good. Weaker "irreducibility" conditions were given by David Gale and by John Kemeny, Oskar Morgenstern, and Gerald L. Thompson in the 1950s and then by Stephen M. Robinson in the 1970s.
  21. ^ David Gale. The theory of linear economic models. McGraw–Hill, New York, 1960.
  22. ^ Morgenstern, Oskar; Thompson, Gerald L. (1976). Mathematical theory of expanding and contracting economies. Lexington Books. Lexington, Massachusetts: D. C. Heath and Company. pp. xviii+277. ISBN 0669000892. 
  23. ^ Alexander Schrijver, Theory of Linear and Integer Programming. John Wiley & sons, 1998, ISBN 0-471-98232-6.
  24. ^
    • Rockafellar, R. Tyrrell. Monotone processes of convex and concave type. Memoirs of the American Mathematical Society. Providence, R.I.: American Mathematical Society. pp. i+74. ISBN 0821812777. 
    • Rockafellar, R. T. (1974). "Convex algebra and duality in dynamic models of production". In Josef Loz and Maria Loz. Mathematical models in economics (Proc. Sympos. and Conf. von Neumann Models, Warsaw, 1972). Amsterdam: North-Holland and Polish Adademy of Sciences (PAN). pp. 351–378. 
    • Rockafellar, R. T. (1970 (Reprint 1997 as a Princeton classic in mathematics)). Convex analysis. Princeton, NJ: Princeton University Press. ISBN 0691080690. 
  25. ^ Kenneth Arrow, Paul Samuelson, John Harsanyi, Sidney Afriat, Gerald L. Thompson, and Nicholas Kaldor. (1989). Mohammed Dore, Sukhamoy Chakravarty, Richard Goodwin. ed. John Von Neumann and modern economics. Oxford:Clarendon. pp. 261. 
  26. ^ Chapter 9.1 "The von Neumann growth model" (pages 277–299): Yinyu Ye. Interior point algorithms: Theory and analysis. Wiley. 1997.
  27. ^ George B. Dantzig and Mukund N. Thapa. 2003. Linear Programming 2: Theory and Extensions. Springer-Verlag.
  28. ^ John MacQuarrie. "Mathematics and Chess". School of Mathematics and Statistics, University of St Andrews, Scotland. Retrieved 2007-10-18. "Others claim he used a method of proof, known as 'backwards induction' that was not employed until 1953, by von Neumann and Morgenstern. Ken Binmore (1992) writes, Zermelo used this method way back in 1912 to analyze Chess. It requires starting from the end of the game and then working backwards to its beginning. (p.32)" 
  29. ^ von Neumann, John. (1941). "Distribution of the ratio of the mean square successive difference to the variance". Annals of Mathematical Statistics, 12, 367–395. (JSTOR)
  30. ^ Durbin, J., and Watson, G. S. (1950) "Testing for Serial Correlation in Least Squares Regression, I." Biometrika 37, 409–428.
  31. ^ Sargan, J.D. and Alok Bhargava (1983). "Testing residuals from least squares regression for being generated by the Gaussian random walk". Econometrica, 51, p. 153–174.
  32. ^ a b Lillian Hoddeson ... . With contributions from Gordon Baym ...; "Lillian Hoddeson, Paul W. Henriksen, Roger A. Meade, Catherine Westfall (1993). Critical Assembly: A Technical History of Los Alamos during the Oppenheimer Years, 1943–1945. Cambridge, UK: Cambridge University Press. ISBN 0-521-44132-3. 
  33. ^ Rhodes, Richard (1986). The Making of the Atomic Bomb. New York: Touchstone Simon & Schuster. ISBN 0-684-81378-5. 
  34. ^ Groves, Leslie (1962). Now It Can Be Told: The Story of the Manhattan Project. New York: Da Capo. ISBN 0-306-80189-2. 
  35. ^ Herken, pp. 171, 374
  36. ^ Bernstein, Jeremy (2010). "John von Neumann and Klaus Fuchs: an Unlikely Collaboration". Physics in Perspective 12: 36. Bibcode 2010PhP....12...36B. doi:10.1007/s00016-009-0001-1. 
  37. ^ The 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.
  38. ^ John von Neumann (1966). Arthur W. Burks. ed. Theory of Self-Reproducing Automata. Urbana and London: Univ. of Illinois Press. ISBN 0598377980.  PDF reprint
  39. ^ Knuth, Donald (1998). The Art of Computer Programming: Volume 3 Sorting and Searching. Boston: Addison–Wesley. pp. 159. ISBN 0-201-89685-0. 
  40. ^ von Neumann, John (1951). "Various techniques used in connection with random digits". National Bureau of Standards Applied Math Series 12: 36. 
  41. ^ Mathematical Association of American documentary, especially comments by Morgenstern regarding this aspect of von Neumann's personality
  42. ^ a b "Conversation with Marina Whitman". Gray Watson ( Retrieved 2011-01-30. 
  43. ^ Macrae, p. 332; Heims, pp. 236–247.
  44. ^ Macrae, pp. 170–171
  45. ^ Ed Regis. Who Got Einstein's Office?: Eccentricity and Genius at the Institute for Advanced Study. Perseus Books 1988 p 103
  46. ^ Nancy Stern (January 20, 1981). "An Interview with Cuthbert C. Hurd". Charles Babbage Institute, University of Minnesota. Retrieved June 3, 2010. 
  47. ^ "Introducing the John von Neumann Computer Society". John von Neumann Computer Society. Retrieved 2008-05-20. 
  48. ^ a b John von Neumann at the Mathematics Genealogy Project.. Accessed 2011-03-05.
  49. ^ 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).

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

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