romikgosai/squad_modified huggingface dataset:
Von Neumann's mathematical analysis of the structure of self-replication preceded the discovery of the structure of DNA. In a short list of facts about his life he submitted to the National Academy of Sciences, he stated "The part of my work I consider most essential is that on quantum mechanics, which developed in Göttingen in 1926, and subsequently in Berlin in 1927–1929. Also, my work on various forms of operator theory, Berlin 1930 and Princeton 1935–1939; on the ergodic theorem, Princeton, 1931–1932."

Questions and answers:
["
Q: Von Neumann's study of what preceded the discovery of DNA?
A: mathematical analysis of the structure of self-replication", '
Q: What part of his work did Von Neumann consider to be his most important?
A: quantum mechanics', '
Q: Where was quantum mechanics developed?
A: Göttingen', '
Q: What work did Von Nemann do in Berlin in 1930 and Princeton 1935 - 39?
A: operator theory', "
Q: What was the topic of Von Neumann's work at Princeton in 1931 - 32?
A: ergodic theorem"]
During World War II he worked on the Manhattan Project with J. Robert Oppenheimer and Edward Teller, developing the mathematical models behind the explosive lenses used in the implosion-type nuclear weapon. After the war, he served on the General Advisory Committee of the United States Atomic Energy Commission, and later as one of its commissioners. He was a consultant to a number of organizations, including the United States Air Force, the Armed Forces Special Weapons Project, and the Lawrence Livermore National Laboratory. Along with theoretical physicist Edward Teller, mathematician Stanislaw Ulam, and others, he worked out key steps in the nuclear physics involved in thermonuclear reactions and the hydrogen bomb.

Questions and answers:
['
Q: With whom did Von Neumann work on the Manhattan Project?
A: J. Robert Oppenheimer and Edward Teller', '
Q: Post World War II, in what role did Von Neumann work?
A: General Advisory Committee of the United States Atomic Energy Commission', '
Q: For what organizations was Von Neumann a consultant after World War II?
A: United States Air Force, the Armed Forces Special Weapons Project, and the Lawrence Livermore National Laboratory', '
Q: What keys steps did Von Neumann work out that contributed to weapons of war?
A: key steps in the nuclear physics involved in thermonuclear reactions and the hydrogen bomb']
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.

Questions and answers:
['
Q: Where was Von Neumann born?
A: Budapest', '
Q: Did Von Neumann have any siblings?
A: two younger brothers', '
Q: What occupation did Von Neumann father hold?
A: banker', "
Q: When did Von Neuman's father move from Pecs to Budapest?
A: end of the 1880s", "
Q: What was Von Neumann's mother's name?
A: Kann Margit"]
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.

Questions and answers:
["
Q: In what year was Von Neumann's father elevated to nobility?
A: 1913", "
Q: What Emperor elevated Von Neumann's father to nobility?
A: Emperor Franz Joseph", "
Q: What town did Von Neumann's family become associated when elevated to nobility?
A: Marghita", "
Q: What was Von Neumann's given name as member of Austro-Hungarian nobility?
A: Margittai Neumann János"]
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.

Questions and answers:
['
Q: At what age did schooling begin in Hungary?
A: ten', '
Q: Who taught children before they began school in Hungary?
A: governesses', '
Q: What languages were Von Neumann and his siblings taught?
A: English, French, German and Italian', '
Q: At what age was Von Neumann familiar with calculus?
A: 8']
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.

Questions and answers:
['
Q: What did Von Neumann enter in 1911?
A: Lutheran Fasori Evangelikus Gimnázium', '
Q: In what room did children get education in Hungary?
A: gymnasium', '
Q: What collective name was given to the generation of scholars produced by the Hungarian school system?
A: Martians', '
Q: In what year did Wigner win Nobel Prize?
A: 1963']
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.

Questions and answers:
['
Q: At what age did Von Neumann begin to study advance calculus?
A: 15', '
Q: Who did Von Neumann begin his studies of advanced calculus under?
A: Gábor Szegő', '
Q: By 19 how many papers had Von Neumann published?
A: two major mathematical papers', "
Q: Von Neumann's modern definition of ordinal numbers superseded whose definition?
A: Georg Cantor", '
Q: What prize did Von Neuman win at the conclusion of his gymansium formal education?
A: Eötvös Prize, a national prize for mathematics']
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.

Questions and answers:
['
Q: What career path was decided upon for Von Neuman?
A: chemical engineer', '
Q: At what university was it arranged for Von Neumann to enter a chemistry program?
A: University of Berlin', '
Q: Where did Von Neumann study as a PHD candidate?
A: Pázmány Péter University in Budapest', "
Q: What was the topic of Von Neuman's thesis?
A: axiomatization of Cantor's set theory"]
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.

Questions and answers:
['
Q: Where did Von Neumann begin to lecture in 1928?
A: University of Berlin', '
Q: By the end of 1927 how many papers had Von Neuman written?
A: twelve major papers in mathematics', '
Q: How many papers had Von Neumann written by 1929?
A: thirty-two papers', '
Q: What better offer came for Von Neumann in 1930?
A: Princeton University']
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.

Questions and answers:
["
Q: When did Von Neumann get married?
A: New Year's Day in 1930", "
Q: What was Von Neumann's wife's name?
A: Mariette Kövesi", '
Q: Before marriage what faith did Von Neumann join?
A: he was baptized a Catholic.', "
Q: What was Von Neumann's child's name?
A: Marina", '
Q: When did Von Neumann get married for a second time?
A: October 1938']
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."

Questions and answers:
['
Q: In what year was Von Neumann offered a lifetime professorship? 
A: 1933', "
Q: In what year did Von Neumann's mother and siblings join him in U.S?
A: 1939", '
Q: In what year did Von Neumann become a naturalized citizen of US?
A: 1937', '
Q: Why was Neuman rejected from joining US Army?
A: age']
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.

Questions and answers:
['
Q: What type of "off color" humor did Von Neumann especially enjoy?
A: limericks', "
Q: What complaints did Von Neumann's neighbor's have?
A: regularly playing extremely loud German march music", '
Q: What famous neighbor did Von Neumann have that may have been distracted by the music Von Neumann played?
A: Albert Einstein,']
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.

Questions and answers:
["
Q: What mathematician was Von Nemann's closest friend?
A: Stanislaw Ulam", '
Q: What topics of conversation would Ulam and Von Neumann typically share?
A: gossiping and giggling, swapping Jewish jokes, and drifting in and out of mathematical talk', '
Q: What would Ulam use to cheer up Von Neumann in the hospital?
A: a new collection of jokes']
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.

Questions and answers:
["
Q: What caused a setback in naive set theory at the beginning of 20th century?
A: Russell's paradox", '
Q: Who resolved the problem of adequate axiomatization of set theory?
A: Ernst Zermelo and Abraham Fraenkel', '
Q: What 2 techniques did Von Neumann use to exclude sets in his doctoral thesis in 1925?
A: the axiom of foundation and the notion of class.']
The axiom of foundation established that every set can be constructed from the bottom up in an ordered succession of steps by way of the principles of Zermelo and Fraenkel, in such a manner that if one set belongs to another then the first must necessarily come before the second in the succession, hence excluding the possibility of a set belonging to itself. To demonstrate that the addition of this new axiom to the others did not produce contradictions, von Neumann introduced a method of demonstration, called the method of inner models, which later became an essential instrument in set theory.

Questions and answers:
['
Q: What is the method to demonstrate that no contradictions were created by the addition of axiom of foundation?
A: method of inner models', "
Q: Zermelo and Fraenkel's axiom of foundation established that every set be constructed how?
A: from the bottom up in an ordered succession of steps", '
Q: What excluded a set from belonging to itself in set theory?
A: if one set belongs to another then the first must necessarily come before the second in the succession']
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.

Questions and answers:
['
Q: What is a proper class?
A: a class which does not belong to other classes', '
Q: Under what approach does an axiom impede a set of all sets which do not belong to themselves?
A: Zermelo–Fraenkel', "
Q: Under Von Neumann's approach can a class of all sets that do not belong to themselves be constructed?
A: class of all sets which do not belong to themselves can be constructed, but it is a proper class and not a set."]
With this contribution of von Neumann, the axiomatic system of the theory of sets became fully satisfactory, and the next question was whether or not it was also definitive, and not subject to improvement. A strongly negative answer arrived in September 1930 at the historic mathematical Congress of Königsberg, in which Kurt Gödel announced his first theorem of incompleteness: the usual axiomatic systems are incomplete, in the sense that they cannot prove every truth which is expressible in their language. This result was sufficiently innovative as to confound the majority of mathematicians of the time.

Questions and answers:
["
Q: In 1930 who gave a strongly negative answer to Von Neuman's approach to the axiomatic system of theory of sets?
A: Kurt Gödel", "
Q: What was the central theme of Godel's announcement that the axiomatic system was not complete?
A: they cannot prove every truth which is expressible in their language", "
Q: Where was Godel's statement about axiomatic system made in 1930?
A: Congress of Königsberg"]
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."

Questions and answers:
['
Q: How long did it take von Neumann to figure a response to theory of incompleteness?
A: less than a month', '
Q: What was the consequence of the theory of incompleteness?
A: usual axiomatic systems are unable to demonstrate their own consistency', '
Q: Upon revising the theory of incompleteness, what was the name of the new Godel theory?
A: second incompleteness theorem']
Von Neumann founded the field of continuous geometry. It followed his path-breaking work on rings of operators. In mathematics, continuous geometry is an analogue of complex projective geometry, where instead of the dimension of a subspace being in a discrete set 0, 1, ..., n, it can be an element of the unit interval [0,1]. Von Neumann was motivated by his discovery of von Neumann algebras with a dimension function taking a continuous range of dimensions, and the first example of a continuous geometry other than projective space was the projections of the hyperfinite type II factor.

Questions and answers:
['
Q: What field did Von Neuman establish?
A: continuous geometry.', '
Q: What is the distinction of continuous geometry?
A: instead of the dimension of a subspace being in a discrete set 0, 1, ..., n, it can be an element of the unit interval', '
Q: What was the first example of continuous geometry?
A: projections of the hyperfinite type II factor']
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."

Questions and answers:
['
Q: In what way did von Neumann make spectacular contributions to measure theory?
A: In a series of famous papers', '
Q: What concept was relevant to the solvability of the problem of measure?
A: algebraic concept of solvability of a group is relevant', '
Q: According to von Neumann what is the most important part of the problem of measure?
A: change of group that makes a difference, not the change of space']
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.

Questions and answers:
["
Q: What is often considered more important than the results of von Neumann's papers?
A: methods of argument he employed", '
Q: In 1938 what was von Neumann awarded?
A: Bôcher Memorial Prize', "
Q: What did von Neumann use the Haar theorem to solve in a 1936 paper?
A: Hilbert's fifth problem in the case of compact groups"]