Divyanshu67/squad_v2 huggingface dataset:
John_von_Neumann

Von Neumann was born Neumann János Lajos (in Hungarian the family name comes first), Hebrew name Yonah, in Budapest, Kingdom of Hungary, which was then part of the Austro-Hungarian Empire, to wealthy Jewish parents of the Haskalah. He was the eldest of three children. He had two younger brothers: Michael, born in 1907, and Nicholas, who was born in 1911. His father, Neumann Miksa (Max Neumann) was a banker, who held a doctorate in law. He had moved to Budapest from Pécs at the end of the 1880s. Miksa's father and grandfather were both born in Ond (now part of the town of Szerencs), Zemplén County, northern Hungary. John's mother was Kann Margit (Margaret Kann); her parents were Jakab Kann and Katalin Meisels. Three generations of the Kann family lived in spacious apartments above the Kann-Heller offices in Budapest; von Neumann's family occupied an 18-room apartment on the top floor.

Question: Where was Von Neumann born?
Answer: Budapest

Question: Did Von Neumann have any siblings?
Answer: two younger brothers

Question: What occupation did Von Neumann father hold?
Answer: banker

Question: When did Von Neuman's father move from Pecs to Budapest?
Answer: end of the 1880s

Question: What was Von Neumann's mother's name?
Answer: Kann Margit
John_von_Neumann

In 1913, his father was elevated to the nobility for his service to the Austro-Hungarian Empire by Emperor Franz Joseph. The Neumann family thus acquired the hereditary appellation Margittai, meaning of Marghita. The family had no connection with the town; the appellation was chosen in reference to Margaret, as was those chosen coat of arms depicting three marguerites. Neumann János became Margittai Neumann János (John Neumann of Marghita), which he later changed to the German Johann von Neumann.

Question: In what year was Von Neumann's father elevated to nobility?
Answer: 1913

Question: What Emperor elevated Von Neumann's father to nobility?
Answer: Emperor Franz Joseph

Question: What town did Von Neumann's family become associated when elevated to nobility?
Answer: Marghita

Question: What was Von Neumann's given name as member of Austro-Hungarian nobility?
Answer: Margittai Neumann János
John_von_Neumann

Formal schooling did not start in Hungary until the age of ten. Instead, governesses taught von Neumann, his brothers and his cousins. Max believed that knowledge of languages other than Hungarian was essential, so the children were tutored in English, French, German and Italian. By the age of 8, von Neumann was familiar with differential and integral calculus, but he was particularly interested in history, reading his way through Wilhelm Oncken's Allgemeine Geschichte in Einzeldarstellungen. A copy was contained in a private library Max purchased. One of the rooms in the apartment was converted into a library and reading room, with bookshelves from ceiling to floor.

Question: At what age did schooling begin in Hungary?
Answer: ten

Question: Who taught children before they began school in Hungary?
Answer: governesses

Question: What languages were Von Neumann and his siblings taught?
Answer: English, French, German and Italian

Question: At what age was Von Neumann familiar with calculus?
Answer: 8
John_von_Neumann

Von Neumann entered the Lutheran Fasori Evangelikus Gimnázium in 1911. This was one of the best schools in Budapest, part of a brilliant education system designed for the elite. Under the Hungarian system, children received all their education at the one gymnasium. Despite being run by the Lutheran Church, the majority of its pupils were Jewish. The school system produced a generation noted for intellectual achievement, that included Theodore von Kármán (b. 1881), George de Hevesy (b. 1885), Leó Szilárd (b. 1898), Eugene Wigner (b. 1902), Edward Teller (b. 1908), and Paul Erdős (b. 1913). Collectively, they were sometimes known as Martians. Wigner was a year ahead of von Neumann at the Lutheran School. When asked why the Hungary of his generation had produced so many geniuses, Wigner, who won the Nobel Prize in Physics in 1963, replied that von Neumann was the only genius.

Question: What did Von Neumann enter in 1911?
Answer: Lutheran Fasori Evangelikus Gimnázium

Question: In what room did children get education in Hungary?
Answer: gymnasium

Question: What collective name was given to the generation of scholars produced by the Hungarian school system?
Answer: Martians

Question: In what year did Wigner win Nobel Prize?
Answer: 1963
John_von_Neumann

Although Max insisted von Neumann attend school at the grade level appropriate to his age, he agreed to hire private tutors to give him advanced instruction in those areas in which he had displayed an aptitude. At the age of 15, he began to study advanced calculus under the renowned analyst Gábor Szegő. On their first meeting, Szegő was so astounded with the boy's mathematical talent that he was brought to tears. Some of von Neumann's instant solutions to the problems in calculus posed by Szegő, sketched out on his father's stationery, are still on display at the von Neumann archive in Budapest. By the age of 19, von Neumann had published two major mathematical papers, the second of which gave the modern definition of ordinal numbers, which superseded Georg Cantor's definition. At the conclusion of his education at the gymnasium, von Neumann sat for and won the Eötvös Prize, a national prize for mathematics.

Question: At what age did Von Neumann begin to study advance calculus?
Answer: 15

Question: Who did Von Neumann begin his studies of advanced calculus under?
Answer: Gábor Szegő

Question: By 19 how many papers had Von Neumann published?
Answer: two major mathematical papers

Question: Von Neumann's modern definition of ordinal numbers superseded whose definition?
Answer: Georg Cantor

Question: What prize did Von Neuman win at the conclusion of his gymansium formal education?
Answer: Eötvös Prize, a national prize for mathematics
John_von_Neumann

Since there were few posts in Hungary for mathematicians, and those were not well-paid, his father wanted von Neumann to follow him into industry and therefore invest his time in a more financially useful endeavor than mathematics. So it was decided that the best career path was to become a chemical engineer. This was not something that von Neumann had much knowledge of, so it was arranged for him to take a two-year non-degree course in chemistry at the University of Berlin, after which he sat the entrance exam to the prestigious ETH Zurich, which he passed in September 1923. At the same time, von Neumann also entered Pázmány Péter University in Budapest, as a Ph.D. candidate in mathematics. For his thesis, he chose to produce an axiomatization of Cantor's set theory. He passed his final examinations for his Ph.D. soon after graduating from ETH Zurich in 1926. He then went to the University of Göttingen on a grant from the Rockefeller Foundation to study mathematics under David Hilbert.

Question: What career path was decided upon for Von Neuman?
Answer: chemical engineer

Question: At what university was it arranged for Von Neumann to enter a chemistry program?
Answer: University of Berlin

Question: Where did Von Neumann study as a PHD candidate?
Answer: Pázmány Péter University in Budapest

Question: What was the topic of Von Neuman's thesis?
Answer: axiomatization of Cantor's set theory
John_von_Neumann

Von Neumann's habilitation was completed on December 13, 1927, and he started his lectures as a privatdozent at the University of Berlin in 1928. By the end of 1927, von Neumann had published twelve major papers in mathematics, and by the end of 1929, thirty-two papers, at a rate of nearly one major paper per month. His reputed powers of speedy, massive memorization and recall allowed him to recite volumes of information, and even entire directories, with ease. In 1929, he briefly became a privatdozent at the University of Hamburg, where the prospects of becoming a tenured professor were better, but in October of that year a better offer presented itself when he was invited to Princeton University in Princeton, New Jersey.

Question: Where did Von Neumann begin to lecture in 1928?
Answer: University of Berlin

Question: By the end of 1927 how many papers had Von Neuman written?
Answer: twelve major papers in mathematics

Question: How many papers had Von Neumann written by 1929?
Answer: thirty-two papers

Question: What better offer came for Von Neumann in 1930?
Answer: Princeton University
John_von_Neumann

On New Year's Day in 1930, von Neumann married Mariette Kövesi, who had studied economics at the Budapest University. Before his marriage he was baptized a Catholic. Max had died in 1929. None of the family had converted to Christianity while he was alive, but afterwards they all did. They had one child, a daughter, Marina, who is now a distinguished professor of business administration and public policy at the University of Michigan. The couple divorced in 1937. In October 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.

Question: When did Von Neumann get married?
Answer: New Year's Day in 1930

Question: What was Von Neumann's wife's name?
Answer: Mariette Kövesi

Question: Before marriage what faith did Von Neumann join?
Answer: he was baptized a Catholic.

Question: What was Von Neumann's child's name?
Answer: Marina

Question: When did Von Neumann get married for a second time?
Answer: October 1938
John_von_Neumann

In 1933, von Neumann was offered a lifetime professorship on the faculty of the Institute for Advanced Study when the institute's plan to appoint Hermann Weyl fell through. He remained a mathematics professor there until his death, although he announced that shortly before his intention to resign and become a professor at large at the University of California. His mother, brothers and in-laws followed John to the United States in 1939. Von Neumann anglicized his first name to John, keeping the German-aristocratic surname of von Neumann. His brothers changed theirs to "Neumann" and "Vonneumann". Von Neumann became a naturalized citizen of the United States in 1937, and immediately tried to become a lieutenant in the United States Army's Officers Reserve Corps. He passed the exams easily, but was ultimately rejected because of his age. His prewar analysis is often quoted. Asked about how France would stand up to Germany he said "Oh, France won't matter."

Question: In what year was Von Neumann offered a lifetime professorship? 
Answer: 1933

Question: In what year did Von Neumann's mother and siblings join him in U.S?
Answer: 1939

Question: In what year did Von Neumann become a naturalized citizen of US?
Answer: 1937

Question: Why was Neuman rejected from joining US Army?
Answer: age
John_von_Neumann

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). He was a non-smoker. At Princeton he received complaints for regularly playing extremely loud German march music on his gramophone, which distracted those in neighbouring offices, including Albert Einstein, from their work. Von Neumann did some of his best work blazingly fast in noisy, chaotic environments, and once admonished his wife for preparing a quiet study for him to work in. He never used it, preferring the couple's living room with its television playing loudly.

Question: What type of "off color" humor did Von Neumann especially enjoy?
Answer: limericks

Question: What complaints did Von Neumann's neighbor's have?
Answer: regularly playing extremely loud German march music

Question: What famous neighbor did Von Neumann have that may have been distracted by the music Von Neumann played?
Answer: Albert Einstein,
John_von_Neumann

Von Neumann's closest friend in the United States was mathematician Stanislaw Ulam. A later friend of Ulam's, Gian-Carlo Rota writes: "They would spend hours on end gossiping and giggling, swapping Jewish jokes, and drifting in and out of mathematical talk." When von Neumann was dying in hospital, every time Ulam would visit he would come prepared with a new collection of jokes to cheer up his friend. He believed that much of his mathematical thought occurred intuitively, and he would often go to sleep with a problem unsolved, and know the answer immediately upon waking up.

Question: What mathematician was Von Nemann's closest friend?
Answer: Stanislaw Ulam

Question: What topics of conversation would Ulam and Von Neumann typically share?
Answer: gossiping and giggling, swapping Jewish jokes, and drifting in and out of mathematical talk

Question: What would Ulam use to cheer up Von Neumann in the hospital?
Answer: a new collection of jokes
John_von_Neumann

The axiomatization of mathematics, on the model of Euclid's Elements, had reached new levels of rigour 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 20th 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–Fraenkel set theory 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 belongs 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.

Question: What caused a setback in naive set theory at the beginning of 20th century?
Answer: Russell's paradox

Question: Who resolved the problem of adequate axiomatization of set theory?
Answer: Ernst Zermelo and Abraham Fraenkel

Question: What 2 techniques did Von Neumann use to exclude sets in his doctoral thesis in 1925?
Answer: the axiom of foundation and the notion of class.
John_von_Neumann

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.

Question: What is the method to demonstrate that no contradictions were created by the addition of axiom of foundation?
Answer: method of inner models

Question: Zermelo and Fraenkel's axiom of foundation established that every set be constructed how?
Answer: from the bottom up in an ordered succession of steps

Question: What excluded a set from belonging to itself in set theory?
Answer: if one set belongs to another then the first must necessarily come before the second in the succession
John_von_Neumann

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.

Question: What is a proper class?
Answer: a class which does not belong to other classes

Question: Under what approach does an axiom impede a set of all sets which do not belong to themselves?
Answer: Zermelo–Fraenkel

Question: Under Von Neumann's approach can a class of all sets that do not belong to themselves be constructed?
Answer: class of all sets which do not belong to themselves can be constructed, but it is a proper class and not a set.
John_von_Neumann

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.

Question: In 1930 who gave a strongly negative answer to Von Neuman's approach to the axiomatic system of theory of sets?
Answer: Kurt Gödel

Question: What was the central theme of Godel's announcement that the axiomatic system was not complete?
Answer: they cannot prove every truth which is expressible in their language

Question: Where was Godel's statement about axiomatic system made in 1930?
Answer: Congress of Königsberg
John_von_Neumann

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. However, Gödel had already discovered this consequence, now known as his second incompleteness theorem and sent von Neumann a preprint of his article containing both incompleteness theorems. Von Neumann acknowledged Gödel's priority in his next letter. He never thought much of "the American system of claiming personal priority for everything."

Question: How long did it take von Neumann to figure a response to theory of incompleteness?
Answer: less than a month

Question: What was the consequence of the theory of incompleteness?
Answer: usual axiomatic systems are unable to demonstrate their own consistency

Question: Upon revising the theory of incompleteness, what was the name of the new Godel theory?
Answer: second incompleteness theorem
John_von_Neumann

In a series of famous papers, von Neumann made spectacular contributions to measure theory. The work of Banach had implied that the problem of measure has a positive solution if n = 1 or n = 2 and a negative solution in all other cases. Von Neumann's work argued that the "problem is essentially group-theoretic in character, and that, in particular, for the solvability of the problem of measure the ordinary algebraic concept of solvability of a group is relevant. Thus, according to von Neumann, it is the change of group that makes a difference, not the change of space."

Question: In what way did von Neumann make spectacular contributions to measure theory?
Answer: In a series of famous papers

Question: What concept was relevant to the solvability of the problem of measure?
Answer: algebraic concept of solvability of a group is relevant

Question: According to von Neumann what is the most important part of the problem of measure?
Answer: change of group that makes a difference, not the change of space
John_von_Neumann

In a number of von Neumann's papers, the methods of argument he employed are considered even more significant than the results. In anticipation of his later study of dimension theory in algebras of operators, von Neumann used results on equivalence by finite decomposition, and reformulated the problem of measure in terms of functions. In his 1936 paper on analytic measure theory, he used the Haar theorem in the solution of Hilbert's fifth problem in the case of compact groups. In 1938, he was awarded the Bôcher Memorial Prize for his work in analysis.

Question: What is often considered more important than the results of von Neumann's papers?
Answer: methods of argument he employed

Question: In 1938 what was von Neumann awarded?
Answer: Bôcher Memorial Prize

Question: What did von Neumann use the Haar theorem to solve in a 1936 paper?
Answer: Hilbert's fifth problem in the case of compact groups
John_von_Neumann

Von Neumann introduced the study of rings of operators, through the von Neumann algebras. A von Neumann algebra is a *-algebra of bounded operators on a Hilbert space that is closed in the weak operator topology and contains the identity operator. The von Neumann bicommutant theorem shows that the analytic definition is equivalent to a purely algebraic definition as an algebra of symmetries. The direct integral was introduced in 1949 by John von Neumann. One of von Neumann's analyses was to reduce the classification of von Neumann algebras on separable Hilbert spaces to the classification of factors.

Question: What is von Neumann algebra?
Answer: algebra of bounded operators on a Hilbert space that is closed in the weak operator topology and contains the identity operator

Question: What does the von Neumann bicommutant theorem show?
Answer: the analytic definition is equivalent to a purely algebraic definition as an algebra of symmetries.

Question: When was direct integral introduced by von Neumann?
Answer: 1949

Question: What was introduced in von Neumann algebras?
Answer: study of rings of operators
John_von_Neumann

Von Neumann worked on lattice theory between 1937 and 1939. Von Neumann provided an abstract exploration of dimension in completed complemented modular topological lattices: "Dimension is determined, up to a positive linear transformation, by the following two properties. It is conserved by perspective mappings ("perspectivities") and ordered by inclusion. The deepest part of the proof concerns the equivalence of perspectivity with "projectivity by decomposition"—of which a corollary is the transitivity of perspectivity." Garrett Birkhoff writes: "John von Neumann's brilliant mind blazed over lattice theory like a meteor".

Question: What did von Neumann work on in 1937 - 39?
Answer: lattice theory

Question: What properties determine dimension in lattice theory?
Answer: conserved by perspective mappings ("perspectivities") and ordered by inclusion

Question: Who wrote that "John von Neumann's brilliant mind blazed over lattice theory like a meteor?"
Answer: Garrett Birkhoff
John_von_Neumann

Additionally, "[I]n the general case, von Neumann proved the following basic representation theorem. Any complemented modular lattice L having a "basis" of n≥4 pairwise perspective elements, is isomorphic with the lattice ℛ(R) of all principal right-ideals of a suitable regular ring R. This conclusion is the culmination of 140 pages of brilliant and incisive algebra involving entirely novel axioms. Anyone wishing to get an unforgettable impression of the razor edge of von Neumann's mind, need merely try to pursue this chain of exact reasoning for himself—realizing that often five pages of it were written down before breakfast, seated at a living room writing-table in a bathrobe."

Question: What type of axioms were used by von Neumann in his lattice work?
Answer: novel axioms

Question: How long was von Neumann's lattice theory paper?
Answer: 140 pages

Question: In what room did von Neumann often write at home?
Answer: living room writing-table
John_von_Neumann

Von Neumann was the first to establish a rigorous mathematical framework for quantum mechanics, known as the Dirac–von Neumann axioms, with his 1932 work Mathematical Foundations of Quantum Mechanics. After having completed the axiomatization of set theory, he began to confront the axiomatization of quantum mechanics. He realized, in 1926, that a state of a quantum system could be represented by a point in a (complex) Hilbert space that, in general, could be infinite-dimensional even for a single particle. In this formalism of quantum mechanics, observable quantities such as position or momentum are represented as linear operators acting on the Hilbert space associated with the quantum system.

Question: Who established the framework for quantum mechanics?
Answer: Von Neumann

Question: What paper did von Neumann produce in 1932?
Answer: Mathematical Foundations of Quantum Mechanics

Question: What von Neumann work preceded the axiomatiztion of quatum mechanics?
Answer: axiomatization of set theory
John_von_Neumann

The physics of quantum mechanics was thereby reduced to the mathematics of Hilbert spaces and linear operators acting on them. For example, the uncertainty principle, 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. When Heisenberg was informed von Neumann had clarified the difference between an unbounded operator that was a Self-adjoint operator and one that was merely symmetric, Heisenberg replied "Eh? What is the difference?"

Question: What are the physics of quantum mechanics?
Answer: mathematics of Hilbert spaces and linear operators acting on them

Question: What is the uncertainty principle?
Answer: determination of the position of a particle prevents the determination of its momentum and vice versa

Question: The physics of quantum mechanics included special cases for what work?
Answer: formulations of both Heisenberg and Schrödinger
John_von_Neumann

Von Neumann's abstract treatment permitted him also to confront the foundational issue of determinism versus non-determinism, and in the book he presented a proof that the statistical results of quantum mechanics could not possibly be averages of an underlying set of determined "hidden variables," as in classical statistical mechanics. In 1966, John S. Bell published a paper arguing that the proof contained a conceptual error and was therefore invalid. However, in 2010, Jeffrey Bub argued that Bell had misconstrued von Neumann's proof, and pointed out that the proof, though not valid for all hidden variable theories, does rule out a well-defined and important subset. Bub also suggests that von Neumann was aware of this limitation, and that von Neumann did not claim that his proof completely ruled out hidden variable theories.

Question: Von Neumann's abstract treatment allowed him to work on what foundational issue?
Answer: determinism versus non-determinism

Question: What was John Bell's argument?
Answer: proof contained a conceptual error and was therefore invalid

Question: What did Jeffrey Bub argue in 2010?
Answer: Bell had misconstrued von Neumann's proof

Question: Did von Neumann rule hidden variable theories?
Answer: von Neumann did not claim that his proof completely ruled out hidden variable theories
John_von_Neumann

In a chapter of The Mathematical Foundations of Quantum Mechanics, von Neumann deeply analyzed the so-called measurement problem. He concluded that the entire physical universe could be made subject to the universal wave function. Since something "outside the calculation" was needed to collapse the wave function, von Neumann concluded that the collapse was caused by the consciousness of the experimenter (although this view was accepted by Eugene Wigner, the Von Neumann–Wigner interpretation never gained acceptance amongst the majority of physicists).

Question: What results came from von Neumann's deep analysis of the measurement problem?
Answer: physical universe could be made subject to the universal wave function

Question: What "outside of calculation" variable could initiate collapse in von Neumann's conclusion?
Answer: consciousness of the experimenter

Question: Were von Neumann's conclusions of collapse of entire universe cause accepted widely?
Answer: Von Neumann–Wigner interpretation never gained acceptance amongst the majority of physicists
John_von_Neumann

In a famous paper of 1936 with Garrett Birkhoff, the first work ever to introduce quantum logics, von Neumann and Birkhoff first proved that quantum mechanics requires a propositional calculus substantially different from all classical logics and rigorously isolated a new algebraic structure for quantum logics. The concept of creating a propositional calculus for quantum logic was first outlined in a short section in von Neumann's 1932 work, but in 1936, the need for the new propositional calculus was demonstrated through several proofs. For example, photons cannot pass through two successive filters that 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. This experimental fact is translatable into logic as the non-commutativity of conjunction . It was also demonstrated that the laws of distribution of classical logic,  and , are not valid for quantum theory.

Question: With whom did von Neuman work on a paper in 1936 that introduce quantum logic?
Answer: Garrett Birkhoff

Question: What concept was created for quatum logic?
Answer: propositional calculus

Question: What is the difference of logic in quantum theory?
Answer: laws of distribution of classical logic,  and , are not valid for quantum theory
John_von_Neumann

Von Neumann founded the field of game theory as a mathematical discipline. Von Neumann 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 that will result in the minimization of his maximum loss.

Question: What year was game theory established?
Answer: 1928

Question: What discipline is game theory derived from?
Answer: mathematical discipline.

Question: what are the possible strategies in minimax theory?
Answer: a pair of strategies for both players that allows each to minimize his maximum losses

Question: What must a player consider when determining every possible strategy?
Answer: all the possible responses of his adversary.
John_von_Neumann

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 , while .

Question: What is the difference of quantum disjunction from classic?
Answer: can be true even when both of the disjuncts are false

Question: What is frequently the case in quantum mechanics when a pair of alternatives are semantically determinate?
Answer: each of its members are necessarily indeterminate

Question: How can quantum disjuction be illustrated?
Answer: illustrated by a simple example
John_von_Neumann

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). 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). Morgenstern wrote a paper on game theory and thought he would show it to von Neumann because of his interest in the subject. He read it and said to Morgenstern that he should put more in it. This was repeated a couple of times, and then von Neumann became a coauthor and the paper became 100 pages long. Then it became a book. 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.

Question: What is optimal strategy?
Answer: minimize the maximum loss for each player

Question: What von Neumann work was published in 1944?
Answer: Theory of Games and Economic Behavior

Question: Who was co-author with von Neman on the Theory of Games and Economic Behavior?
Answer: Oskar Morgenstern
John_von_Neumann

Von Neumann raised the intellectual and mathematical level of economics in several stunning publications. For his model of an expanding economy, von Neumann proved the existence and uniqueness of an equilibrium using his generalization of the Brouwer 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

Question: How did von Neumann raise the level of economics?
Answer: several stunning publications

Question: What did von Neumann prove with his model of expanding economy?
Answer: uniqueness of an equilibrium using his generalization of the Brouwer fixed-point theorem

Question: What did von Neumann consider for his model of expanding economy?
Answer: matrix pencil  A − λB with nonnegative matrices A and B
John_von_Neumann

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.

Question: In von Neumann's model what does p represent?
Answer: p represents the prices of the goods

Question: In von Neumann's model what does q represent?
Answer: q represents the "intensity" at which the production process would run

Question: What is the rate of qrowth equal to?
Answer: rate of growth equals the interest rate

Question: Was the economic model successful?
Answer: proving that the growth rate equals the interest rate were remarkable achievements, even for von Neumann
John_von_Neumann

Von Neumann's famous 9-page paper started life as a talk at Princeton and then became a paper in Germany, which was eventually translated into English. His interest in economics that led to that paper began as follows: When lecturing at Berlin in 1928 and 1929 he spent his summers back home in Budapest, and so did the economist Nicholas Kaldor, and they hit it off. Kaldor recommended that von Neumann read a book by the mathematical economist Léon Walras. Von Neumann found some faults in that book and corrected them, for example, replacing equations by inequalities. He noticed that Walras's General Equilibrium Theory and Walras' Law, which led to systems of simultaneous linear equations, could produce the absurd result that the profit could be maximized by producing and selling a negative quantity of a product. He replaced the equations by inequalities, introduced dynamic equilibria, among other things, and eventually produced the paper.

Question: When did von Neumann's interest in economics begin?
Answer: When lecturing at Berlin in 1928 and 1929

Question: What economist did von Neumann get to know that spurred the interest in economics?
Answer: Nicholas Kaldor

Question: In who's book did von Neuman find errors in the author's equations?
Answer: Léon Walras
John_von_Neumann

Von Neumann made fundamental contributions in exploration of problems in numerical hydrodynamics. For example, with Robert D. Richtmyer he developed an algorithm defining artificial viscosity that improved the understanding of shock waves. A 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 mathematics of artificial viscosity smoothed the shock transition without sacrificing basic physics. Other well known contributions to fluid dynamics included the classic flow solution to blast waves, and the co-discovery of the ZND detonation model of explosives.

Question: The algorithm defining artificial viscosity is a fundamental contribution to what area?
Answer: numerical hydrodynamics

Question: What did the math of artificial viscosity do?
Answer: smoothed the shock transition without sacrificing basic physics

Question: What was the problem of computers solving fluid dynamics?
Answer: they tried to put too many computational grid points at regions of sharp discontinuity (shock waves)
John_von_Neumann

Von Neumann's principal contribution to the atomic bomb was in the concept and design of the explosive lenses needed to compress the plutonium core of 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. He also eventually came up with the idea of using more powerful shaped charges and less fissionable material to greatly increase the speed of "assembly".

Question: What principal contribution did von Neumann make to atomic bomb?
Answer: concept and design of the explosive lenses needed to compress the plutonium core

Question: Did von Nemann think that the atomic bomb design was not workable?
Answer: he was one of its most persistent proponents, encouraging its continued development

Question: What additional ideas did von Neumann contribute to Atomic bomb?
Answer: more powerful shaped charges and less fissionable material to greatly increase the speed of "assembly"
John_von_Neumann

When it turned out that there would not be enough uranium-235 to make more than one bomb, the implosive lens project was greatly expanded and von Neumann's idea was implemented. Implosion was the only method that could be used with the plutonium-239 that was available from the Hanford Site. He established the design of the explosive lenses required, but there remained concerns about "edge effects" and imperfections in the explosives. His calculations showed that implosion would work if it did not depart by more than 5% from spherical symmetry. After a series of failed attempts with models, this was achieved by George Kistiakowsky, and the construction of the Trinity bomb was completed in July 1945.

Question: what change was made when shortage of uranium 235 was apparent?
Answer: implosive lens project was greatly expanded

Question: What was the tolerance limit for implosion "edge effect"?
Answer: not depart by more than 5% from spherical symmetry

Question: Who constructed Trinity bomb?
Answer: George Kistiakowsky

Question: In what year was Trinity bomb completed?
Answer: 1945
John_von_Neumann

Along with four other scientists and various military personnel, von Neumann was included in the target selection committee responsible for choosing the Japanese cities of Hiroshima and Nagasaki as the first targets of the atomic bomb. Von Neumann oversaw computations related to the expected size of the bomb blasts, estimated death tolls, and the distance above the ground at which the bombs should be detonated for optimum shock wave propagation and thus maximum effect. The cultural capital Kyoto, which had been spared the bombing inflicted upon militarily significant cities, 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 L. Stimson.

Question: What other people worked with von Neumann on target selection?
Answer: four other scientists and various military personnel

Question: What role did von Neuman play in the selection of targets?
Answer: oversaw computations

Question: What was von Neumann's first choice for target city?
Answer: Kyoto

Question: Who dismissed von Neuamann's primary target city?
Answer: Secretary of War Henry L. Stimson.
John_von_Neumann

On July 16, 1945, with numerous other Manhattan Project personnel, von Neumann was an eyewitness to the first atomic bomb blast, code named Trinity, conducted as a test of the implosion method device, at the bombing range near Alamogordo Army Airfield, 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 (21 TJ) 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. It was in von Neumann's 1944 papers that the expression "kilotons" appeared for the first time. 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."

Question: On what day was the first atomic blast?
Answer: July 16, 1945

Question: Where did the first atomic blast test take place?
Answer: Alamogordo Army Airfield,

Question: What was the power of the first atomic blast?
Answer: between 20 and 22 kilotons
John_von_Neumann

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 nuclear fusion. 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 Soviet Union as part of his nuclear espionage, but it was not used in the Soviets' 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."

Question: With whom did von Neumann collaborate for further development of the hydrogen bomb?
Answer: Klaus Fuchs

Question: What improvement did von Neumann see in the nuclear weaponry?
Answer: using a fission bomb to compress fusion fuel to initiate nuclear fusion

Question: What country was afforded access to design of improved nuclear weapon through espionage?
Answer: Soviet Union
John_von_Neumann

In 1950, von Neumann became a consultant to the Weapons Systems Evaluation Group (WSEG), whose function was to advise the Joint Chiefs of Staff and the United States Secretary of Defense on the development and use of new technologies. He also became an adviser to the Armed Forces Special Weapons Project (AFSWP), which was responsible for the military aspects on nuclear weapons.Over the following two years, he also became a consultant to the Central Intelligence Agency (CIA), a member of the influential General Advisory Committee of the Atomic Energy Commission, a consultant to the newly established Lawrence Livermore National Laboratory, and a member of the Scientific Advisory Group of the United States Air Force.

Question: In 1950 von Neumann became a consultant for what organization?
Answer: Weapons Systems Evaluation Group

Question: What military organization did von NEumann also consult with for military aspect of nuclear weapons?
Answer: Armed Forces Special Weapons Project

Question: What committee did von Neumann serve on within the Atomic Energy Commission?
Answer: General Advisory Committee
John_von_Neumann

In 1955, von Neumann became a commissioner of the AEC. He accepted this position and used it to further the production of compact hydrogen bombs suitable for Intercontinental ballistic missile delivery. He involved himself in correcting the severe shortage of tritium and lithium 6 needed for these compact weapons, and he argued against settling for the intermediate range missiles that the Army wanted. He was adamant that H-bombs delivered into the heart of enemy territory by an ICBM would be the most effective weapon possible, and that the relative inaccuracy of the missile wouldn't be a problem with an H-bomb. He said the Russians would probably be building a similar weapon system, which turned out to be the case. Despite his disagreement with Oppenheimer over the need for a crash program to develop the hydrogen bomb, he testified on the latter's behalf at the 1954 Oppenheimer security hearing, at which he asserted that Oppenheimer was loyal, and praised him for his helpfulness once the program went ahead.

Question: In what year did von Neumann become commissioner of the AEC?
Answer: 1955

Question: What were compact hydrogen bombs useful for?
Answer: Intercontinental ballistic missile delivery

Question: What was the concern with longer range ICBM with Hbomb?
Answer: relative inaccuracy of the missile

Question: Von Neumann testified at whose hearing about loyalty and help?
Answer: Oppenheimer
John_von_Neumann

Von Neumann is credited with the equilibrium strategy of mutual assured destruction, providing the deliberately humorous acronym, MAD. (Other humorous acronyms coined by von Neumann include his computer, the Mathematical Analyzer, Numerical Integrator, and Computer—or MANIAC). He also "moved heaven and earth" to bring MAD about. His goal was to quickly develop ICBMs and the compact hydrogen bombs that they could deliver to the USSR, and he knew the Soviets were doing similar work because the CIA interviewed German rocket scientists who were allowed to return to Germany, and von Neumann had planted a dozen technical people in the CIA. The Russians believed that bombers would soon be vulnerable, and they shared von Neumann's view that an H-bomb in an ICBM was the ne plus ultra of weapons, and they believed that whoever had superiority in these weapons would take over the world, without necessarily using them. He was afraid of a "missile gap" and took several more steps to achieve his goal of keeping up with the Soviets:

Question: What was MAD?
Answer: mutual assured destruction

Question: What was the goal of MAD?
Answer: quickly develop ICBMs and the compact hydrogen bombs that they could deliver to the USSR

Question: What were Russians opinions of future weaponry?
Answer: Russians believed that bombers would soon be vulnerable, and they shared von Neumann's view that an H-bomb in an ICBM was the ne plus ultra of weapons

Question: What was the concern of a missile gap?
Answer: keeping up with the Soviets