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Encyclopedia > John Von Neumann
Born John von Neumann in the 1940s December 28, 1903 Budapest, Austria-Hungary February 8, 1957 (aged 53) Washington DC, USA United States American Mathematics Los Alamos University of Berlin Princeton University University of Pázmány Péter ETH Zurich Leopold Fejer Donald B. Gillies Game theory von Neumann algebra von Neumann architecture Cellular automata Enrico Fermi Award 1956 Converted Roman Catholic; previously Agnostic; born to a non-practicing Jewish family
 Quantum physics $Delta x , Delta p ge frac{hbar}{2}$ Quantum mechanics Introduction to... Mathematical formulation of... John von Neumann, from period while at Los Alamos National Laboratory, taken from a Los Alamos publication (Los Alamos: Beginning of an era, 1943-1945, Los Alamos Scientific Laboratory, 1986). ... is the 362nd day of the year (363rd in leap years) in the Gregorian calendar. ... 1900 (MCMIII) was a common year starting on Thursday (link will display calendar) of the Gregorian calendar or a common year starting on Friday of the 13-day slower Julian calendar. ... Image File history File links Austria-Hungary_flag_1869-1918. ... For other uses, see Budapest (disambiguation). ... Austria-Hungary, also known as the Dual monarchy (or: the k. ... is the 39th day of the year in the Gregorian calendar. ... Year 1957 (MCMLVII) was a common year starting on Tuesday (link displays the 1957 Gregorian calendar). ... Image File history File links This is a lossless scalable vector image. ... Flag Seal Nickname: DC, The District Motto: Justitia Omnibus (Justice for All) Location Location of Washington, D.C., with regard to the surrounding states of Maryland and Virginia. ... Image File history File links This is a lossless scalable vector image. ... Image File history File links This is a lossless scalable vector image. ... Euclid, Greek mathematician, 3rd century BC, as imagined by by Raphael in this detail from The School of Athens. ... Los Alamos usually refers to the United States national laboratory in Los Alamos, New Mexico which was founded during the World War II effort to develop the atomic bomb (the Manhattan Project), was one of the two laboratories developing the USAs nuclear weapons during the Cold War, and is... There is no institution called the University of Berlin, but there are four universities in Berlin, Germany: Humboldt University of Berlin (Humboldt-Universität zu Berlin) Technical University of Berlin (Technische Universität Berlin) Free University of Berlin (Freie Universität Berlin) Berlin University of the Arts (Universität der... Princeton University is a private coeducational research university located in Princeton, New Jersey. ... This article is about EÃ¶tvÃ¶s LorÃ¡nd University, which is often referred to as University of Budapest. ... The ETH Zurich, often called Swiss Federal Institute of Technology, is a science and technology university in the city of Zurich, Switzerland. ... LipÃ³t FejÃ©r (or Leopold FejÃ©r), FejÃ©r LipÃ³t (February 9, 1880, PÃ©cs â€“ October 15, 1959, Budapest) was a Hungarian mathematician. ... Donald Bruce Gillies (October 15, 1928 - July 17, 1975) was a Canadian mathematician and computer scientist, known for his work in game theory, computer design, and minicomputer programming environments. ... Game theory is often described as a branch of applied mathematics and economics that studies situations where multiple players make decisions in an attempt to maximize their returns. ... A von Neumann algebra is a *-algebra of bounded operators on a Hilbert space which is closed in the weak operator topology, or equivalently, in the strong operator topology (under pointwise convergence) and contains the identity operator. ... Design of the Von Neumann architecture For the robotic architecture also named after Von Neumann, see Von Neumann machine The von Neumann architecture is a computer design model that uses a single storage structure to hold both instructions and data. ... A cellular automaton (plural: cellular automata) is a discrete model studied in computability theory and mathematics. ... The Enrico Fermi Award is a U.S. government Presidential award honoring scientists of international stature for their lifetime achievement in the development, use, or production of energy. ... The Roman Catholic Church, most often spoken of simply as the Catholic Church, is the largest Christian church, with over one billion members. ... The term agnosticism and the related agnostic were coined by Thomas Henry Huxley in 1869. ... The word Jew ( Hebrew: יהודי) is used in a wide number of ways, but generally refers to a follower of the Jewish faith, a child of a Jewish mother, or someone of Jewish descent with a connection to Jewish culture or ethnicity and often a combination... Fig. ... Quantum mechanics (QM, or quantum theory) is a physical science dealing with the behaviour of matter and energy on the scale of atoms and subatomic particles / waves. ... The mathematical formulation of quantum mechanics is the body of mathematical formalisms which permits a rigorous description of quantum mechanics. ... Fundamental concepts Decoherence · Interference Uncertainty · Exclusion Transformation theory Ehrenfest theorem · Measurement In quantum mechanics, quantum decoherence is the mechanism by which quantum systems interact with their environments to exhibit probabilistically additive behavior - a feature of classical physics - and give the appearance of wavefunction collapse. ... Interference of two circular waves - Wavelength (decreasing bottom to top) and Wave centers distance (increasing to the right). ... In quantum physics, the Heisenberg uncertainty principle is a mathematical property of a pair of canonical conjugate quantities - usually stated in a form of reciprocity of spans of their spectra. ... The Pauli exclusion principle is a quantum mechanical principle formulated by Wolfgang Pauli in 1925. ... The term transformation theory refers to a procedure used by P. A. M. Dirac in his early formulation of quantum theory, from around 1927. ... The Ehrenfest theorem, named after Paul Ehrenfest, relates the time derivative of the expectation value for a quantum mechanical operator to the commutator of that operator with the Hamiltonian of the system. ... The framework of quantum mechanics requires a careful definition of measurement, and a thorough discussion of its practical and philosophical implications. ... Experiments Double-slit experiment Davisson-Germer experiment Stern–Gerlach experiment EPR paradox · Popper's experiment Schrödinger's cat Double-slit diffraction and interference pattern The double-slit experiment consists of letting light diffract through two slits, which produces fringes or wave-like interference patterns on a screen. ... In 1927 at Bell Labs, Clinton Davisson and Lester Germer fired slow moving electrons at a crystalline Nickel target. ... In quantum mechanics, the Sternâ€“Gerlach experiment, named after Otto Stern and Walther Gerlach, is a celebrated experiment in 1920 on deflection of particles, often used to illustrate basic principles of quantum mechanics. ... In quantum mechanics, the EPR paradox is a thought experiment which challenged long-held ideas about the relation between the observed values of physical quantities and the values that can be accounted for by a physical theory. ... Poppers experiment is an experiment proposed by the 20th century philosopher of science Karl Popper, to test the standard interpretation (the Copenhagen interpretation) of Quantum mechanics. ... SchrÃ¶dingers Cat: If the nucleus in the bottom left decays, the Geiger counter on its right will sense it and trigger the release of the gas. ... Equations Schrödinger equation Pauli equation Klein-Gordon equation Dirac equation For a non-technical introduction to the topic, please see Introduction to quantum mechanics. ... The Pauli equation is a SchrÃ¶dinger equation which handles spin. ... The Klein-Gordon equation (Klein-Fock-Gordon equation or sometimes Klein-Gordon-Fock equation) is the relativistic version of the SchrÃ¶dinger equation. ... In physics, the Dirac equation is a relativistic quantum mechanical wave equation formulated by British physicist Paul Dirac in 1928 and provides a description of elementary spin-Â½ particles, such as electrons, consistent with both the principles of quantum mechanics and the theory of special relativity. ... Advanced theories Quantum field theory Wightman axioms Quantum electrodynamics Quantum chromodynamics Quantum gravity Feynman diagram Quantum field theory (QFT) is the quantum theory of fields. ... In physics the Wightman axioms are an attempt of mathematically stringent, axiomatic formulation of quantum field theory. ... Quantum electrodynamics (QED) is a relativistic quantum field theory of electrodynamics. ... Quantum chromodynamics (abbreviated as QCD) is the theory of the strong interaction (color force), a fundamental force describing the interactions of the quarks and gluons found in hadrons (such as the proton, neutron or pion). ... This article does not cite any references or sources. ... In this Feynman diagram, an electron and positron annihilate and become a quark-antiquark pair. ... Interpretations Copenhagen · Ensemble Hidden variables · Transactional Many-worlds · Consistent histories Quantum logic Consciousness causes collapse It has been suggested that Quantum mechanics, philosophy and controversy be merged into this article or section. ... The Copenhagen interpretation is an interpretation of quantum mechanics formulated by Niels Bohr and Werner Heisenberg while collaborating in Copenhagen around 1927. ... The Ensemble Interpretation, or Statistical Interpretation of Quantum Mechanics, is an interpretation that can be viewed as a minimalist interpretation. ... In physics, a hidden variable theory is urged by a minority of physicists who argue that the statistical nature of quantum mechanics implies that quantum mechanics is incomplete; it is really applicable only to ensembles of particles; new physical phenomena beyond quantum mechanics are needed to explain an individual event. ... The transactional interpretation of quantum mechanics (TIQM) by Professor John Cramer is an unusual interpretation of quantum mechanics that describes quantum interactions in terms of a standing wave formed by retarded (forward in time) and advanced (backward in time) waves. ... The many-worlds interpretation of quantum mechanics or MWI (also known as the relative state formulation, theory of the universal wavefunction, many-universes interpretation, Oxford interpretation or many worlds), is an interpretation of quantum mechanics that claims to resolve all the paradoxes of quantum theory by allowing every possible outcome... In quantum mechanics, the consistent histories approach is intended to give a modern interpretation of quantum mechanics, generalising the conventional Copenhagen interpretation and providing a natural interpretation of quantum cosmology. ... In mathematical physics and quantum mechanics, quantum logic can be regarded as a kind of propositional logic suitable for understanding the apparent anomalies regarding quantum measurement, most notably those concerning composition of measurement operations of complementary variables. ... Consciousness causes collapse is the theory that observation by a conscious observer is responsible for the wavefunction collapse in quantum mechanics. ... Scientists Planck · Schrödinger Heisenberg · Bohr · Pauli Dirac · Bohm · Born de Broglie · von Neumann Einstein · Feynman Everett · Others Max Karl Ernst Ludwig Planck (April 23, 1858 in Kiel, Germany â€“ October 4, 1947 in GÃ¶ttingen, Germany) was a German physicist. ... Bust of SchrÃ¶dinger, in the courtyard arcade of the main building, University of Vienna, Austria. ... Werner Karl Heisenberg (December 5, 1901 â€“ February 1, 1976) was a celebrated German physicist and Nobel laureate, one of the founders of quantum mechanics and acknowledged to be one of the most important physicists of the twentieth century. ... Niels (Henrik David) Bohr (October 7, 1885 â€“ November 18, 1962) was a Danish physicist who made fundamental contributions to understanding atomic structure and quantum mechanics, for which he received the Nobel Prize in 1922. ... This article is about Austrian-Swiss physicist Wolfgang Pauli. ... Paul Adrien Maurice Dirac, OM, FRS (IPA: [dÉªrÃ¦k]) (August 8, 1902 â€“ October 20, 1984) was a British theoretical physicist and a founder of the field of quantum physics. ... David Bohm. ... Max Born (December 11, 1882 in Breslau â€“ January 5, 1970 in GÃ¶ttingen) was a mathematician and physicist. ... Louis-Victor-Pierre-Raymond, 7th duc de Broglie, generally known as Louis de Broglie (August 15, 1892â€“March 19, 1987), was a French physicist and Nobel Prize laureate. ... â€œEinsteinâ€ redirects here. ... Richard Phillips Feynman (May 11, 1918 â€“ February 15, 1988; IPA: ) was an American physicist known for expanding the theory of quantum electrodynamics, the physics of the superfluidity of supercooled liquid helium, and particle theory. ... Hugh Everett III (November 11, 1930 â€“ July 19, 1982) was an American physicist who first proposed the many-worlds interpretation(MWI) of quantum physics, which he called his relative state formulation. ... Below is a list of famous physicists. ... This box: view • talk • edit

The eldest of three brothers, von Neumann was born Neumann János Lajos (Hungarian names have the family name first) in Budapest, Hungary, to a Jewish family. His father was Neumann Miksa (Max Neumann), a lawyer who worked in a bank. His mother was Kann Margit (Margaret Kann). János, nicknamed "Jancsi" (Johnny), was an extraordinary prodigy. At the age of six, he could divide two 8-digit numbers in his head. For other uses, see Budapest (disambiguation). ... The word Jew ( Hebrew: &#1497;&#1492;&#1493;&#1491;&#1497;) is used in a wide number of ways, but generally refers to a follower of the Jewish faith, a child of a Jewish mother, or someone of Jewish descent with a connection to Jewish culture or ethnicity and often a combination... For other uses, see Bank (disambiguation). ... A child prodigy is someone who is a master of one or more skills or arts at an early age. ...

He entered the German speaking Lutheran Gymnasium in Budapest in 1911. In 1913 his father was rewarded with ennoblement for his service to the Austro-Hungarian empire, the Neumann family acquiring the Hungarian mark of Margittai, or the Austrian equivalent von. Neumann János therefore became János von Neumann, a name that he later changed to the German Johann von Neumann. After teaching as history's youngest Privatdozent of the University of Berlin from 1926 to 1930, he, his mother, and his brothers emigrated to the United States; this in the early 1930s, after Hitler's rise to power in Germany. He anglicized Johann to John, he kept the Austrian-aristocratic surname of von Neumann, whereas his brothers adopted surnames Vonneumann and Neumann (using the de Neumann form briefly when first in the US). Fasori GimnÃ¡zium (lit. ... Von (generally in small case only as von) is a German preposition which approximately means of or from. ... Privatdozent (PD or Priv. ... Humboldt-UniversitÃ¤t zu Berlin The Humboldt University of Berlin (German Humboldt-UniversitÃ¤t zu Berlin) is Berlins oldest university, founded in 1810 as the University of Berlin (UniversitÃ¤t zu Berlin) by the liberal Prussian educational reformer and linguist Wilhelm von Humboldt whose university model has strongly influenced... Adolf Hitler Adolf Hitler (April 20, 1889 &#8211; April 30, 1945, standard German pronunciation in the IPA) was the Führer (leader) of the National Socialist German Workers Party (Nazi Party) and of Nazi Germany from 1933 to 1945. ... To anglicise (or in North American English anglicize) is to adapt a foreign word into the English language, often modifying its form to correspond to standard English French demoiselle, meaning little lady. Another common type of anglicisation is the inclusion of a foreign article as part of a noun (eg. ...

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

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

Von Neumann was invited to Princeton, New Jersey in 1930, and was one of four people selected for the first faculty of the Institute for Advanced Study (two of the others were Albert Einstein and Kurt Gödel), where he was a mathematics professor from its formation in 1933 until his death. Nassau Street, Princetons main street. ... Fuld Hall The Institute for Advanced Study is a private institution in Princeton Township, New Jersey, U.S.A., designed to foster pure cutting-edge research by scientists and scholars in a variety of fields without the complications of teaching or funding, or the agendas of sponsorship. ... â€œEinsteinâ€ redirects here. ... Kurt GÃ¶del (IPA: ) (April 28, 1906 BrÃ¼nn, Austria-Hungary (now Brno, Czech Republic) â€“ January 14, 1978 Princeton, New Jersey) was an Austrian American mathematician and philosopher. ...

From 1936 to 1938 Alan Turing was a visitor at the Institute, where he completed a Ph.D. dissertation under the supervision of Alonzo Church at Princeton. This visit occurred shortly after Turing's publication of his 1936 paper "On Computable Numbers with an Application to the Entscheidungsproblem" which involved the concepts of logical design and the universal machine. Von Neumann must have known of Turing's ideas but it is not clear whether he applied them to the design of the IAS machine ten years later. Alan Mathison Turing, FRS,OBE (23 June 1912 â€“ 7 June 1954) was an English mathematician, logician, and cryptographer. ... â€¹ The template below (Expand) is being considered for deletion. ... The Entscheidungsproblem (German for decision problem) is the challenge in symbolic logic to find a general algorithm which decides for given first-order statements whether they are universally valid or not. ... The IAS Computer, 1952 (courtesy of the Smithsonian) The IAS machine was the first electronic digital computer built by the Institute for Advanced Study (IAS), Princeton, NJ, USA. The paper describing the design of the IAS machine was edited by John von Neumann, (see Von Neumann architecture). ...

In 1937 he became a naturalized citizen of the US. In 1938 von Neumann was awarded the Bôcher Memorial Prize for his work in analysis. Naturalization is the process whereby a person becomes a national of a nation, or a citizen of a country, other than the one of his birth. ... The BÃ´cher Memorial Prize was founded by the American Mathematical Society in 1923 in memory of Maxime BÃ´cher with an initial endowment of \$1,450 (contributed by members of that society). ...

Von Neumann married twice. He married Mariette Kövesi in 1930. When he proposed to her, he was incapable of expressing anything beyond "You and I might be able to have some fun together, seeing as how we both like to drink."[citation needed] Von Neumann agreed to convert to Catholicism in order to marry and remained a Catholic until his death. The couple divorced in 1937. He then married Klara Dan in 1938. Von Neumann had one child, by his first marriage, a daughter named Marina. She is a distinguished professor of international trade and public policy at the University of Michigan. Topics in Christianity Movements Â· Denominations Ecumenism Â· Preaching Â· Prayer Music Â· Liturgy Â· Calendar Symbols Â· Art Â· Criticism Important figures Apostle Paul Â· Church Fathers Constantine Â· Athanasius Â· Augustine Anselm Â· Aquinas Â· Palamas Â· Luther Calvin Â· Wesley Arius Â· Marcion of Sinope Pope Â· Archbishop of Canterbury Patriarch of Constantinople Christianity Portal This box:      The Roman Catholic Church or Catholic... Marina von Neumann Whitman, born March 6, 1935, is Professor of Business Administration and Public Policy at the Michigan University Ross School of Business. ... The University of Michigan, Ann Arbor (U of M, U-M or simply Michigan) is a coeducational public research university in the state of Michigan, and one of the foremost universities in the United States. ...

Von Neumann was diagnosed with bone cancer or pancreatic cancer in 1957, possibly caused by exposure to radioactivity while observing A-bomb tests in the Pacific or in later work on nuclear weapons at Los Alamos, New Mexico. (Fellow nuclear pioneer Enrico Fermi had died of stomach cancer in 1954.) Von Neumann died within a few months of the initial diagnosis, in excruciating pain. The cancer had spread to his brain, inhibiting mental ability. When at Walter Reed Hospital in Washington, D.C., he invited Roman Catholic priest (Father Anselm Strittmatter), who administered him the last Sacraments.[3] He died under military security lest he reveal military secrets while heavily medicated. John Von Neumann was buried at Princeton Cemetery in Princeton, Mercer County, New Jersey. A sarcoma is a cancer of the bone, cartilage, fat, muscle, blood vessels, or other connective or supportive tissue. ... Pancreatic cancer is a malignant tumour within the pancreatic gland. ... Radioactivity may mean: Look up radioactivity in Wiktionary, the free dictionary. ... The mushroom cloud of the atomic bombing of Nagasaki, Japan, in 1945 lifted nuclear fallout some 18km (60,000 feet) above the epicenter. ... Los Alamos usually refers to the United States national laboratory in Los Alamos, New Mexico which was founded during the World War II effort to develop the atomic bomb (the Manhattan Project), was one of the two laboratories developing the USAs nuclear weapons during the Cold War, and is... Capital Santa Fe Largest city Albuquerque Area  Ranked 5th  - Total 121,665 sq mi (315,194 kmÂ²)  - Width 342 miles (550 km)  - Length 370 miles (595 km)  - % water 0. ... Enrico Fermi (September 29, 1901 â€“ November 28, 1954) was an Italian physicist most noted for his work on the development of the first nuclear reactor, and for his contributions to the development of quantum theory, particle physics and statistical mechanics. ... Stomach cancer (also called gastric cancer) can develop in any part of the stomach and may spread throughout the stomach and to other organs; particularly the esophagus and the small intestine. ... Walter Reed Army Medical Center is a hospital run by the United States Army. ... For other uses, see Washington, D.C. (disambiguation). ... The Roman Catholic Church, most often spoken of simply as the Catholic Church, is the largest Christian church, with over one billion members. ... Princeton Cemetery is located in Borough of Princeton, New Jersey. ... Nassau Street, Princetons main street. ... Mercer County is the name of several counties in the United States: Mercer County, Illinois Mercer County, Kentucky Mercer County, Missouri Mercer County, New Jersey Mercer County, North Dakota Mercer County, Ohio Mercer County, Pennsylvania Mercer County, West Virginia This is a disambiguation page &#8212; a navigational aid which lists... Official language(s) English de facto Capital Trenton Largest city Newark Area  Ranked 47th  - Total 8,729 sq mi (22,608 kmÂ²)  - Width 70 miles (110 km)  - Length 150 miles (240 km)  - % water 14. ...

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

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

Image File history File links Information. ...

## Logic

The axiomatization of mathematics, on the model of Euclid's Elements, had reached new levels of rigor and breadth at the end of the 19th century, particularly in arithmetic (thanks to Richard Dedekind and Giuseppe Peano) and geometry (thanks to David Hilbert). At the beginning of the twentieth century, set theory, the new branch of mathematics invented by Georg Cantor, and thrown into crisis by Bertrand Russell with the discovery of his famous paradox (on the set of all sets which do not belong to themselves), had not yet been formalized. Euclid (Greek: ), also known as Euclid of Alexandria, was a Greek mathematician of the Hellenistic period who flourished in Alexandria, Egypt, almost certainly during the reign of Ptolemy I (323 BC-283 BC). ... The frontispiece of Sir Henry Billingsleys first English version of Euclids Elements, 1570 Euclids Elements (Greek: ) is a mathematical and geometric treatise, consisting of 13 books, written by the Hellenistic mathematician Euclid in Alexandria circa 300 BC. It comprises a collection of definitions, postulates (axioms), propositions (theorems... Richard Dedekind Julius Wilhelm Richard Dedekind (October 6, 1831 â€“ February 12, 1916) was a German mathematician who did important work in abstract algebra and the foundations of the real numbers. ... Giuseppe Peano Giuseppe Peano (August 27, 1858 â€“ April 20, 1932) was an Italian mathematician and philosopher best known for his contributions to set theory. ... David Hilbert (January 23, 1862, KÃ¶nigsberg, East Prussia â€“ February 14, 1943, GÃ¶ttingen, Germany) was a German mathematician, recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. ... Set theory is the mathematical theory of sets, which represent collections of abstract objects. ... Georg Ferdinand Ludwig Philipp Cantor (March 3, 1845, St. ... Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS, (18 May 1872 â€“ 2 February 1970), was a British philosopher, logician, mathematician, advocate for social reform, and pacifist. ... Part of the foundation of mathematics, Russells paradox (also known as Russells antinomy), discovered by Bertrand Russell in 1901, showed that the naive set theory of Frege leads to a contradiction. ...

The problem of an adequate axiomatization of set theory was resolved implicitly about twenty years later (by Ernst Zermelo and Abraham Frankel) by way of a series of principles which allowed for the construction of all sets used in the actual practice of mathematics, but which did not explicitly exclude the possibility of the existence of sets which belong to themselves. In his doctoral thesis of 1925, von Neumann demonstrated how it was possible to exclude this possibility in two complementary ways: the axiom of foundation and the notion of class. Ernst Friedrich Ferdinand Zermelo (July 27, 1871, Berlin, German Empire â€“ May 21, 1953, Freiburg im Breisgau, West Germany) was a German mathematician, whose work has major implications for the foundations of mathematics and hence on philosophy. ... Abraham Frankel was a distant relation of Hermann Bondi. ... The axiom of regularity (also known as the axiom of foundation) is one of the axioms of Zermelo-Fraenkel set theory. ... In set theory and its applications throughout mathematics, a class is a collection of sets (or sometimes other mathematical objects) that can be unambiguously defined by a property that all its members share. ...

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

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

With this contribution of von Neumann, the axiomatic system of the theory of sets became fully satisfactory, and the next question was whether or not it was also definitive, and not subject to improvement. A strongly negative answer arrived in September of 1930 at the historical mathematical Congress of Königsberg, in which Kurt Gödel announced his first theorem of incompleteness: the usual axiomatic systems are incomplete, in the sense that they cannot prove every truth which is expressible in their language. This result was sufficiently innovative as to confound the majority of mathematicians of the time. But von Neumann, who had participated at the Congress, confirmed his fame as an instantaneous thinker, and in less than a month was able to communicate to Gödel himself an interesting consequence of his theorem: the usual axiomatic systems are unable to demonstrate their own consistency. It is precisely this consequence which has attracted the most attention, even if Gödel originally considered it only a curiosity, and had derived it independently anyway (it is for this reason that the result is called Gödel's second theorem, without mention of von Neumann.) Kaliningrad (Russian: ; Lithuanian: KaraliauÄius; German  , Polish: KrÃ³lewiec; briefly Russified as Kyonigsberg), is a seaport and the administrative center of Kaliningrad Oblast, the Russian exclave between Poland and Lithuania on the Baltic Sea. ... Kurt GÃ¶del (IPA: ) (April 28, 1906 BrÃ¼nn, Austria-Hungary (now Brno, Czech Republic) â€“ January 14, 1978 Princeton, New Jersey) was an Austrian American mathematician and philosopher. ... In mathematical logic, GÃ¶dels incompleteness theorems, proved by Kurt GÃ¶del in 1931, are two theorems stating inherent limitations of all but the most trivial formal systems for arithmetic of mathematical interest. ...

## Quantum mechanics

At the International Congress of Mathematicians of 1900, David Hilbert presented his famous list of twenty-three problems considered central for the development of the mathematics of the new century. The sixth of these was the axiomatization of physical theories. Among the new physical theories of the century the only one which had yet to receive such a treatment by the end of the 1930s was quantum mechanics. QM found itself in a condition of foundational crisis similar to that of set theory at the beginning of the century, facing problems of both philosophical and technical natures. On the one hand, its apparent non-determinism had not been reduced to an explanation of a deterministic form. On the other, there still existed two independent but equivalent heuristic formulations, the so-called matrix mechanical formulation due to Werner Heisenberg and the wave mechanical formulation due to Erwin Schrödinger, but there was not yet a single, unified satisfactory theoretical formulation. The International Congress of Mathematicians (ICM) is the biggest congress in mathematics. ... David Hilbert (January 23, 1862, KÃ¶nigsberg, East Prussia â€“ February 14, 1943, GÃ¶ttingen, Germany) was a German mathematician, recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. ... Hilberts sixth problem is to axiomatize those branches of science in which mathematics is prevalent. ... Werner Karl Heisenberg (December 5, 1901 â€“ February 1, 1976) was a celebrated German physicist and Nobel laureate, one of the founders of quantum mechanics and acknowledged to be one of the most important physicists of the twentieth century. ... Bust of SchrÃ¶dinger, in the courtyard arcade of the main building, University of Vienna, Austria. ...

After having completed the axiomatization of set theory, von Neumann began to confront the axiomatization of QM. He immediately realized, in 1926, that a quantum system could be considered as a point in a so-called Hilbert space, analogous to the 6N dimension (N is the number of particles, 3 general coordinate and 3 canonical momentum for each) phase space of classical mechanics but with infinitely many dimensions (corresponding to the infinitely many possible states of the system) instead: the traditional physical quantities (e.g. position and momentum) could therefore be represented as particular linear operators operating in these spaces. The physics of quantum mechanics was thereby reduced to the mathematics of the linear Hermitian operators on Hilbert spaces. For example, the famous uncertainty principle of Heisenberg, according to which the determination of the position of a particle prevents the determination of its momentum and vice versa, is translated into the non-commutativity of the two corresponding operators. This new mathematical formulation included as special cases the formulations of both Heisenberg and Schrödinger, and culminated in the 1932 classic The Mathematical Foundations of Quantum Mechanics. However, physicists generally ended up preferring another approach to that of von Neumann (which was considered elegant and satisfactory by mathematicians). This approach was formulated in 1930 by Paul Dirac. The mathematical concept of a Hilbert space (named after the German mathematician David Hilbert) generalizes the notion of Euclidean space in a way that extends methods of vector algebra from the plane and three-dimensional space to spaces of functions. ... In mathematics, a linear transformation (also called linear operator or linear map) is a function between two vector spaces that respects the arithmetical operations addition and scalar multiplication defined on vector spaces, or, in other words, it preserves linear combinations. Definition and first consequences Formally, if V and W are... In quantum physics, the Heisenberg uncertainty principle is a mathematical property of a pair of canonical conjugate quantities - usually stated in a form of reciprocity of spans of their spectra. ... Paul Adrien Maurice Dirac, OM, FRS (IPA: [dÉªrÃ¦k]) (August 8, 1902 â€“ October 20, 1984) was a British theoretical physicist and a founder of the field of quantum physics. ...

In any case, von Neumann's abstract treatment permitted him also to confront the foundational issue of determinism vs. non-determinism and in the book he demonstrated a theorem according to which quantum mechanics could not possibly be derived by statistical approximation from a deterministic theory of the type used in classical mechanics. This demonstration contained a conceptual error, but it helped to inaugurate a line of research which, through the work of John Stuart Bell in 1964 on Bell's Theorem and the experiments of Alain Aspect in 1982, demonstrated that quantum physics requires a notion of reality substantially different from that of classical physics. John Stuart Bell is a physicist who is best known for creating an experiment which involves splitting a molecule in half and changing the rotational rate of the electrons of one of the halved molecules. ... Bells theorem is the most famous legacy of the late Irish phyisicist John Bell. ... Alain Aspect is a French physicist. ...

In a complementary work of 1936, von Neumann proved (along with Garrett Birkhoff) that quantum mechanics also requires a logic substantially different from the classical one. For example, light (photons) cannot pass through two successive filters which are polarized perpendicularly (e.g. one horizontally and the other vertically), and therefore, a fortiori, it cannot pass if a third filter polarized diagonally is added to the other two, either before or after them in the succession. But if the third filter is added in between the other two, the photons will indeed pass through. And this experimental fact is translatable into logic as the non-commutativity of conjunction $(Aland B)ne (Bland A)$. It was also demonstrated that the laws of distribution of classical logic, $Plor(Qland R)=(Plor Q)land(Plor R)$ and $Pland (Qlor R)=(Pland Q)lor(Pland R)$, are not valid for quantum theory. The reason for this is that a quantum disjunction, unlike the case for classical disjunction, can be true even when both of the disjuncts are false and this is, in turn, attributable to the fact that it is frequently the case, in quantum mechanics, that a pair of alternatives are semantically determinate, while each of its members are necessarily indeterminate. This latter property can be illustrated by a simple example. Suppose we are dealing with particles (such as electrons) of semi-integral spin (angular momentum) for which there are only two possible values: positive or negative. Then, a principle of indetermination establishes that the spin, relative to two different directions (e.g. x and y) results in a pair of incompatible quantities. Suppose that the state ɸ of a certain electron verifies the proposition "the spin of the electron in the x direction is positive." By the principle of indeterminacy, the value of the spin in the direction y will be completely indeterminate for ɸ. Hence, ɸ can verify neither the proposition "the spin in the direction of y is positive" nor the proposition "the spin in the direction of y is negative." Nevertheless, the disjunction of the propositions "the spin in the direction of y is positive or the spin in the direction of y is negative" must be true for ɸ. In the case of distribution, it is therefore possible to have a situation in which $A land (Blor C)= Aland 1 = A$, while $(Aland B)lor (Aland C)=0lor 0=0$. Garrett Birkhoff (January 19, 1911, Princeton, New Jersey, USA - November 22, 1996, Water Mill, New York, USA) was an American mathematician. ... This page includes English translations of several Latin phrases and abbreviations such as . ...

## Economics

Up until the 1930s economics involved a great deal of mathematics and numbers, but almost all of this was either superficial or irrelevant. It was used, for the most part, to provide uselessly precise formulations and solutions to problems which were intrinsically vague. Economics found itself in a state similar to that of physics of the 17th century: still waiting for the development of an appropriate language in which to express and resolve its problems. While physics had found its language in the infinitesimal calculus, von Neumann proposed the language of game theory and a general equilibrium theory for economics. Infinitesimal calculus is an area of mathematics pioneered by Gottfried Leibniz based on the concept of infinitesimals, as opposed to the calculus of Isaac Newton, which is based upon the concept of the limit. ... Game theory is often described as a branch of applied mathematics and economics that studies situations where multiple players make decisions in an attempt to maximize their returns. ... General Equilbrium (linear) supply and demand curves. ...

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

Von Neumann eventually improved and extended the minimax theorem to include games involving imperfect information and games with more than two players. This work culminated in the 1944 classic Theory of Games and Economic Behavior (written with Oskar Morgenstern). This resulted in such public attention that The New York Times did a front page story, the likes of which only Einstein had previously earned. In 1944 Princeton University Press published Theory of Games and Economic Behavior, a book by the mathematician John von Neumann and economist Oskar Morgenstern. ... Oskar Morgenstern (January 24, 1902 - July 26, 1977) was an German- American economist who, working with John von Neumann, helped found the mathematical field of game theory. ... The New York Times is a daily newspaper published in New York City by Arthur Ochs Sulzberger Jr. ... Einstein redirects here. ...

Von Neumann's second important contribution in this area was the solution, in 1937, of a problem first described by Leon Walras in 1874, the existence of situations of equilibrium in mathematical models of market development based on supply and demand. He first recognized that such a model should be expressed through disequations and not equations, and then he found a solution to Walras problem by applying a fixed-point theorem derived from the work of Luitzen Brouwer. The lasting importance of the work on general equilibria and the methodology of fixed point theorems is underscored by the awarding of Nobel prizes in 1972 to Kenneth Arrow and, in 1983, to Gerard Debreu. Marie-Ésprit-Léon Walras (December 16, 1834 in Évreux, France - January 5, 1910 in Clarens, near Montreux, Switzerland) was a French economist, considered by Joseph Schumpeter as the greatest of all economists. He was a mathematical economist associated with the creation of the general equilibrium theory. ... In mathematics, a fixed-point theorem is a result saying that a function F will have at least one fixed point (a point x for which F(x) = x), under some conditions on F that can be stated in general terms. ... Luitzen Egbertus Jan Brouwer (February 27, 1881 - December 2, 1966), usually cited as L. E. J. Brouwer, was a Dutch mathematician, a graduate of the University of Amsterdam, who worked in topology, set theory, measure theory and complex analysis. ... Kenneth Joseph Arrow (born August 23, 1921) is an American economist, joint winner of the Nobel Prize in Economics with John Hicks in 1972, and the youngest person ever to receive this award, at 51. ... Gerard Debreu was a naturalized US citizen from France Gerard Debreu (July 4, 1921 â€“ December 31, 2004) was a French economist and mathematician (In July 1975, he became a naturalized citizen of the United States). ...

Von Neumann was also the inventor of the method of proof, used in game theory, known as backward induction (which he first published in 1944 in the book co-authored with Morgenstern, Theory of Games and Economic Behaviour).[5] In game theory, backward induction is one of dynamic programming algorithms used to compute subgame perfect equilibria in sequential games. ...

## Armaments

After obtaining US citizenship, von Neumann took an interest in 1937 in applied mathematics, and then developed an expertise in explosives. This led him to a large number of military consultancies, primarily for the Navy, which in turn led to his involvement in the Manhattan Project. The Manhattan Project resulted in the creation of the first nuclear weapons, and the first-ever nuclear detonation, known as the Trinity test of July 16, 1945. ...

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

Von Neumann took part in the design of the explosive lenses needed to compress the plutonium core of the Trinity test device and the "Fat Man" weapon that was later dropped on Nagasaki. Upon his appointment to the committee to select potential targets for the USA's arsenal of atomic weapons, he had proposed the city of Kyoto as his first choice, but this was dismissed by Secretary of War Henry Stimson. Image File history File links John_von_Neumann_ID_badge. ... Los Alamos National Laboratory, aerial view from 1995. ... The first nuclear weapons, though large, cumbersome and inefficient, provided the basic design building blocks of all future weapons. ... General Name, Symbol, Number plutonium, Pu, 94 Chemical series actinides Group, Period, Block n/a, 7, f Appearance silvery white Standard atomic weight (244) gÂ·molâˆ’1 Electron configuration [Rn] 5f6 7s2 Electrons per shell 2, 8, 18, 32, 24, 8, 2 Physical properties Phase solid Density (near r. ... The Trinity test was the first test of a nuclear weapon, conducted by the United States on July 16, 1945 at , thirty miles (48 km) southeast of Socorro on what is now White Sands Missile Range, headquartered near Alamogordo, New Mexico. ... Fat Man is the codename of the atomic bomb that was detonated over Nagasaki, Japan, by the United States on August 9, 1945. ... Kyoto )   is a city in the central part of the island of HonshÅ«, Japan. ... The Secretary of War was a member of the United States Presidents Cabinet, beginning with George Washingtons administration. ... Henry L. Stimson Henry Lewis Stimson (September 21, 1867 - October 20, 1950) was an American politician. ...

One of his discoveries was that large bombs are more devastating when detonated above the ground because of the force of shock waves. The most notable application of this occurred in August 1945, when the first atomic weapons were detonated over Hiroshima and Nagasaki at the very altitude calculated by him to produce the most damage. After the war, Robert Oppenheimer remarked that the physicists involved in the Manhattan project had "known sin". Von Neumann's rather arch response was that "sometimes someone confesses a sin in order to take credit for it". The Japanese city of Hiroshima ) is the capital of Hiroshima Prefecture, and the largest city in the ChÅ«goku region of western HonshÅ«, the largest of Japans islands. ... Nagasaki ) ( ) is the capital and the largest city of Nagasaki Prefecture in Japan. ... J. Robert Oppenheimer[1] (April 22, 1904 â€“ February 18, 1967) was an American theoretical physicist, best known for his role as the director of the Manhattan Project, the World War II effort to develop the first nuclear weapons, at the secret Los Alamos laboratory in New Mexico. ...

Von Neumann continued unperturbed in his work and became, along with Edward Teller, one of the sustainers of the hydrogen bomb project. He then collaborated with spy Klaus Fuchs on further development of the bomb, and in 1946 the two filed a secret patent on "Improvement in Methods and Means for Utilizing Nuclear Energy", which outlined a scheme for using a fission bomb to compress fusion fuel to initiate a thermonuclear reaction. (Herken, pp. 171, 374). Though this was not the key to the hydrogen bomb — the Teller-Ulam design — it was judged to be a move in the right direction. Edward Teller (original Hungarian name Teller Ede) (January 15, 1908 â€“ September 9, 2003) was a Austria-Hungary-born American theoretical physicist, known colloquially as the father of the hydrogen bomb. ... Klaus Fuchs ID badge at Los Alamos. ... In physics, nuclear fusion (a thermonuclear reaction) is a process in which two nuclei join, forming a larger nucleus and releasing energy. ... The mushroom cloud of the atomic bombing of Nagasaki, Japan, in 1945 lifted nuclear fallout some 18 km (60,000 feet) above the epicenter. ... The basics of the Tellerâ€“Ulam configuration: a fission bomb uses radiation to compress and heat a separate section of fusion fuel. ...

## Computer science

Von Neumann's hydrogen bomb work was also played out in the realm of computing, where he and Stanislaw Ulam developed simulations on von Neumann's digital computers for the hydrodynamic computations. During this time he contributed to the development of the Monte Carlo method, which allowed complicated problems to be approximated using random numbers. Because using lists of "truly" random numbers was extremely slow for the ENIAC, von Neumann developed a form of making pseudorandom numbers, using the middle-square method. Though this method has been criticized as crude, von Neumann was aware of this: he justified it as being faster than any other method at his disposal, and also noted that when it went awry it did so obviously, unlike methods which could be subtly incorrect. StanisÅ‚aw Ulam in the 1950s. ... Monte Carlo methods are a widely used class of computational algorithms for simulating the behavior of various physical and mathematical systems, and for other computations. ... It has been suggested that this article or section be merged into randomness. ... ENIAC ENIAC, short for Electronic Numerical Integrator And Computer,[1] was the first large-scale, electronic, digital computer capable of being reprogrammed to solve a full range of computing problems,[2] although earlier computers had been built with some of these properties. ... A pseudo-random number is a number belonging to a sequence which appears to be random, but can in fact be generated by a finite computation. ... One iteration of the middle-square method, showing a six digit seed, which is then squared, and the resulting value has its middle six digits as the output value (and also as the next seed for the sequence). ...

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. A cellular automaton (plural: cellular automata) is a discrete model studied in computability theory, mathematics, and theoretical biology. ... Self-replication is the process by which some things make copies of themselves. ... The Nobili-Pesavento 29-state approximation of von Neumanns universal constructor, with a tape of instructions extending to the right. ... A natural satellite is an object that orbits a planet or other body larger than itself and which is not man-made. ... For details on the physical properties of bodies in the asteroid belt see Asteroid and Main-belt comet. ... In mathematics, exponential growth (or geometric growth) occurs when the growth rate of a function is always proportional to the functions current size. ...

He is credited with at least one contribution to the study of algorithms. Donald Knuth cites von Neumann as the inventor, in 1945, of the merge sort algorithm, in which the first and second halves of an array are each sorted recursively and then merged together. His algorithm for simulating a fair coin with a biased coin [1] is used in the "software whitening" stage of some hardware random number generators. Donald Ervin Knuth ( or Ka-NOOTH[1], Chinese: [2]) (b. ... A merge sort algorithm used to sort an array of 7 integer values. ... Coin flipping or coin tossing is the practice of throwing a coin in the air to resolve a dispute between two parties. ... In computing, a hardware random number generator is an apparatus that generates random numbers from a physical process. ...

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. Hydrodynamics is fluid dynamics applied to liquids, such as water, alcohol, oil, and blood. ... Introduction The shock wave is one of several different ways in which a gas in a supersonic flow can be compressed. ... Introduction The shock wave is one of several different ways in which a gas in a supersonic flow can be compressed. ...

## 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. Fuld Hall The Institute for Advanced Study is a private institution in Princeton Township, New Jersey, U.S.A., designed to foster pure cutting-edge research by scientists and scholars in a variety of fields without the complications of teaching or funding, or the agendas of sponsorship. ... Nassau Street, Princetons main street. ... â€œEinsteinâ€ redirects here. ... â€œCIAâ€ redirects here. ... The United States Army is the largest and oldest branch of the armed forces of the United States. ... Alternate meanings: See RAND (disambiguation) The RAND Corporation is an American think tank first formed to offer research and analysis to the U.S. military. ... Standard Oil (Esso) was a predominant integrated oil producing, transporting, refining, and marketing company. ... IBM redirects here. ...

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

## Honors

U.S. postage stamp commemorating von Neumann

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. Image File history File links John von Neumann 2005 stamp released by the US Postal Service This image of a postage stamp may be copyrighted and/or have other restrictions on its reproduction imposed by the issuing authority. ... Image File history File links John von Neumann 2005 stamp released by the US Postal Service This image of a postage stamp may be copyrighted and/or have other restrictions on its reproduction imposed by the issuing authority. ... The John von Neumann Theory Prize of the Institute for Operations Research and Management Science (INFORMS, previously The Institute of Management Science, TIMS, and the Operations Research Society of America, ORSA) is awarded annually to an individual (or sometimes group) who have made fundamental and sustained contributions to theory in... INFORMS is The Institute for Operations Research and the Management Sciences. ... Operations Research or Operational Research (OR) is an interdisciplinary branch of mathematics which uses methods like mathematical modeling, statistics, and algorithms to arrive at optimal or good decisions in complex problems which are concerned with optimizing the maxima (profit, faster assembly line, greater crop yield, higher bandwidth, etc) or minima...

The IEEE John von Neumann Medal is awarded annually by the IEEE "for outstanding achievements in computer-related science and technology." The IEEE John von Neumann Medal was established by the IEEE Board of Directors in 1990 and may be presented annually for outstanding achievements in computer-related science and technology. ... The Institute of Electrical and Electronics Engineers or IEEE (pronounced as eye-triple-ee) is an international non-profit, professional organization incorporated in the State of New York, United States. ...

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. For the country formerly called Siam see Thailand SIAM is an acronym for Society for Industrial and Applied Mathematics. ...

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

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

On May 4, 2005 the United States Postal Service issued the American Scientists commemorative postage stamp series, a set of four 37-cent self-adhesive stamps in several configurations. The scientists depicted were John von Neumann, Barbara McClintock, Josiah Willard Gibbs, and Richard Feynman. is the 124th day of the year (125th in leap years) in the Gregorian calendar. ... Year 2005 (MMV) was a common year starting on Saturday (link displays full calendar) of the Gregorian calendar. ... USPS and Usps redirect here. ... A selection of Hong Kong postage stamps A postage stamp is evidence of pre-paying a fee for postal services. ... Barbara McClintock (June 16, 1902 â€“ September 2, 1992) was a pioneering American scientist and one of the worlds most distinguished cytogeneticists. ... Josiah Willard Gibbs (February 11, 1839 New Haven â€“ April 28, 1903 New Haven) was one of the very first American theoretical physicists and chemists. ... Richard Phillips Feynman (May 11, 1918 â€“ February 15, 1988; IPA: ) was an American physicist known for expanding the theory of quantum electrodynamics, the physics of the superfluidity of supercooled liquid helium, and particle theory. ...

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

A von Neumann algebra is a *-algebra of bounded operators on a Hilbert space which is closed in the weak operator topology, or equivalently, in the strong operator topology (under pointwise convergence) and contains the identity operator. ... In mathematics, the von Neumann conjecture, disproved in recent years, stated that a topological group G is not amenable if and only if G contains a subgroup that is a free group on two generators. ... Quantum statistical mechanics is the study of statistical ensembles of quantum mechanical systems. ... In mathematics and in theoretical physics, the Stoneâ€“von Neumann theorem is any one of a number of different formulations of the uniqueness of the canonical commutation relations between position and momentum operators. ... In foundations of mathematics, von Neumannâ€“Bernaysâ€“GÃ¶del set theory (NBG) is an axiom system for set theory designed to yield the same results as Zermelo-Fraenkel set theory, together with the axiom of choice (ZFC), but with only a finite number of axioms, that is without axiom schemas. ... In axiomatic set theory and related branches of mathematics, the Von Neumann universe, or Von Neumann hierarchy of sets is the class of all sets, divided into a transfinite hierarchy of individual sets. ... The von Neumann bicommutant theorem relates the closure of a set of bounded operators on a Hilbert space in certain topologies to the bicommutant of that set. ... In mathematics, a ring R is von Neumann regular if for every a in R there exists an x in R with a = axa. ... Design of the Von Neumann architecture For the robotic architecture also named after Von Neumann, see Von Neumann machine The von Neumann architecture is a computer design model that uses a single storage structure to hold both instructions and data. ... The Nobili-Pesavento 29-state approximation of von Neumanns universal constructor, with a tape of instructions extending to the right. ... A von Neumann probe is a specific example of a hypothetical concept based on the work of Hungarian-born American mathematician and physicist John von Neumann. ... A von Neumann probe is a specific example of a hypothetical concept based on the work of Hungarian-born American mathematician and physicist John von Neumann. ...

### Students

Donald Bruce Gillies (October 15, 1928 - July 17, 1975) was a Canadian mathematician and computer scientist, known for his work in game theory, computer design, and minicomputer programming environments. ... Dr. Israel Halperin (1911-2007) was a Canadian mathematician and social activist. ...

## Notes

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

## References

• Steve J. Heims, 1980. John von Neumann and Norbert Wiener, from Mathematics to the technologies of life and death. MIT Press.
• Gregg Herken, 2002. Brotherhood of the Bomb: The Tangled Lives and Loyalties of Robert Oppenheimer, Ernest Lawrence, and Edward Teller.
• Israel, Giorgio, and Gasca, Ana Millan, 1995. The World as a Mathematical Game: John von Neumann, Twentieth Century Scientist.
• Norman Macrae, 1992. John von Neumann.
• Robert Slater. Portraits in Silicon, pp 23-33. ISBN 0-262-69131-0.

Norman Macrae is a British author, born in 1923. ...

Wikiquote has a collection of quotations related to:
• Jean van Heijenoort, 1967. A Source Book in Mathematical Logic, 1879-1931. Harvard Univ. Press.
• 1923. "On the introduction of transfinite numbers," 346-54.
• 1925. "An axiomatization of set theory," 393-413.
• 1932. Mathematical Foundations of Quantum Mechanics, Beyer, R. T., trans., Princeton U. Press 1996 edition: ISBN ISBN 0-691-02893-1
• 1944. (with Oskar Morgenstern) Theory of Games and Economic Behavior. Princeton Univ. Press.
• 1966. (with Arthur W. Burks) Theory of Self-Reproducing Automata. Univ. of Illinois Press.

Secondary: Image File history File links This is a lossless scalable vector image. ... Wikiquote is a sister project of Wikipedia, using the same MediaWiki software. ... Jean van Heijenoort (prounounced highenort) (July 23, 1912, Creil France - March 29, 1986, Mexico City) was a pioneer historian of mathematical logic. ... Oskar Morgenstern (January 24, 1902 - July 26, 1977) was an German- American economist who, working with John von Neumann, helped found the mathematical field of game theory. ... In 1944 Princeton University Press published Theory of Games and Economic Behavior, a book by the mathematician John von Neumann and economist Oskar Morgenstern. ... Arthur Walter Burks (born October 13, 1915 in Duluth, Minnesota) is an American mathematician who in the 1940s as a senior engineer on the project contributed to the design of the ENIAC, the first general-purpose electronic digital computer. ...

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

Norman Macrae is a British author, born in 1923. ... William Poundstone is an American author, columnist, and skeptic. ...

Results from FactBites:

 John von Neumann - Wikipedia, the free encyclopedia (3752 words) Von Neumann was invited to Princeton University in 1930, and was one of four people selected for the first faculty of the Institute for Advanced Study (with no teaching duties), where he was a mathematics professor from its formation in 1933 until his death. Von Neumann proved that the most effective way large-scale mining operations such as mining an entire moon or asteroid belt could be accomplished is through the use of self-replicating machines, to take advantage of the exponential growth of such mechanisms. Von Neumann had experienced a lightning-like academic career similar to the velocity of his own intellect, obtaining at the age of twenty-nine one of the first five professorships at the newly born Institute for Advanced Study at Princeton (another had gone to Albert Einstein).
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