John von Neumann
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John von Neumann (/vɒn ˈnɔɪmən/ von NOY-mən; Hungarian: Neumann János Lajos [ˈnɒjmɒn ˈjaːnoʃ ˈlɒjoʃ]; December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician, physicist, computer scientist, engineer and polymath. He was regarded as having perhaps the widest coverage of any mathematician of his time[13] and was said to have been "the last representative of the great mathematicians who were equally at home in both pure and applied mathematics".[14][15] He integrated pure and applied sciences.
Von Neumann made major contributions to many fields, including mathematics (mathematical logic, measure theory, functional analysis, ergodic theory, group theory, lattice theory, representation theory, operator algebras, matrix theory, geometry, and numerical analysis), physics (quantum mechanics, hydrodynamics & ballistics, nuclear physics and quantum statistical mechanics), economics (game theory and general equilibrium theory), computing (Von Neumann architecture, linear programming, numerical meteorology, scientific computing, self-replicating machines, stochastic computing), and statistics. He was a pioneer of the application of operator theory to quantum mechanics in the development of functional analysis, and a key figure in the development of game theory and the concepts of cellular automata, the universal constructor and the digital computer.
Von Neumann published over 150 papers in his life: about 60 in pure mathematics, 60 in applied mathematics, 20 in physics, and the remainder on special mathematical subjects or non-mathematical subjects.[16] His last work, an unfinished manuscript written while he was dying in hospital, was later published in book form as The Computer and the Brain.
His analysis of the structure of self-replication preceded the discovery of the structure of DNA. In a shortlist of facts about his life he submitted to the National Academy of Sciences, he wrote, "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."[17]
During World War II, von Neumann worked on the Manhattan Project with theoretical physicist Edward Teller, mathematician Stanislaw Ulam and others, problem-solving key steps in the nuclear physics involved in thermonuclear reactions and the hydrogen bomb. He developed the mathematical models behind the explosive lenses used in the implosion-type nuclear weapon and coined the term "kiloton" (of TNT) as a measure of the explosive force generated.[18] During this time and after the war, he consulted for a vast number of organizations including the Office of Scientific Research and Development, the Army's Ballistic Research Laboratory, the Armed Forces Special Weapons Project and the Oak Ridge National Laboratory.[19]
At the peak of his influence in the 1950s he was the chair for a number of critical Defense Department committees including the Strategic Missile Evaluation Committee and the ICBM Scientific Advisory Committee. He was also a member of the influential Atomic Energy Commission in charge of all atomic energy development in the country. He played a key role alongside Bernard Schriever and Trevor Gardner in contributing to the design and development of the United States' first ICBM programs.[20] During this time he was considered the nation's foremost expert on nuclear weaponry and the leading defense scientist at the Pentagon. As a Hungarian émigré, concerned that the Soviets would achieve nuclear superiority, he designed and promoted the policy of mutually assured destruction to limit the arms race.[21]
In honor of his achievements and contributions to the modern world, he was named in 1999 the Financial Times Person of the Century, as a representative of the century's characteristic ideal that the power of the mind could shape the physical world, and of the "intellectual brilliance and human savagery" that defined the 20th century.[22][23][24]
Life and education
At the peak of his influence in the 1950s he was the chair for a number of critical Defense Department committees including the Strategic Missile Evaluation Committee and the ICBM Scientific Advisory Committee. He was also a member of the influential Atomic Energy Commission in charge of all atomic energy development in the country. He played a key role alongside Bernard Schriever and Trevor Gardner in contributing to the design and development of the United States' first ICBM programs.[20] During this time he was considered the nation's foremost expert on nuclear weaponry and the leading defense scientist at the Pentagon. As a Hungarian émigré, concerned that the Soviets would achieve nuclear superiority, he designed and promoted the policy of mutually assured destruction to limit the arms race.[21]
In honor of his achievements and contributions to the modern world, he was named in 1999 the Financial Times Person of the Century, as a representative of the century's characteristic ideal that the power of the mind could shape the physical world, and of the "intellectual brilliance and human savagery" that defined the 20th century.[22][23][24]
Life and education
Neumann János became margittai Neumann János (John Neumann de Margitta), which he later changed to the German Johann von Neumann.[34]
Child prodigy[edit]
Von Neumann was a child prodigy. When he was six years old, he could divide two eight-digit numbers in his head[35][36] and could converse in Ancient Greek. When the six-year-old von Neumann caught his mother staring aimlessly, he asked her, "What are you calculating?"[37]
When they were young, von Neumann, his brothers and his cousins were instructed by governesses. Von Neumann's father believed that knowledge of languages other than their native Hungarian was essential, so the children were tutored in English, French, German and Italian.[38] By the age of eight, von Neumann was familiar with differential and integral calculus, and by twelve he had read and understood Borel's Théorie des Fonctions.[39] But he was also particularly interested in history. He read his way through Wilhelm Oncken's 46-volume world history series Allgemeine Geschichte in Einzeldarstellungen (General History in Monographs).[40] 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.[41]
Von Neumann entered the Lutheran Fasori Evangélikus Gimnázium in 1914.[42] Eugene Wigner was a year ahead of von Neumann at the Lutheran School and soon became his
friend.[43] This was one of the best schools in Budapest and was part of a brilliant education system designed for the elite. Under the Hungarian system, children received all their education at the one gymnasium. The Hungarian school system produced a generation noted for intellectual achievement, which included Theodore von Kármán (born 1881), George de Hevesy (born 1885), Michael Polanyi (born 1891), Leó Szilárd (born 1898), Dennis Gabor (born 1900), Eugene Wigner (born 1902), Edward Teller (born 1908), and Paul Erdős (born 1913).[44] Collectively, they were sometimes known as "The Martians".[45]
Although von Neumann's father insisted von Neumann attend school at the grade level appropriate to his age, he agreed to hire private tutors to give von Neumann 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.[43] On their first meeting, Szegő was so astounded with the boy's mathematical talent that he was brought to tears.[46] Some of von Neumann's instant solutions to the problems that Szegő posed in calculus are sketched out on his father's stationery and are still on display at the von Neumann archive in Budapest.[43] As for his other subjects, he received a grade of A for all barring B's in geometrical drawing, writing and music, and a C for physical education.[47] 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.[48] At the conclusion of his education at the gymnasium, von Neumann sat for and won the Eötvös Prize, a national prize for mathematics.[49]
University studies[edit]
According to his friend Theodore von Kármán, von Neumann's father wanted John to follow him into industry and thereby invest his time in a more financially useful endeavor than mathematics. In fact, his father asked von Kármán to persuade his son not to take mathematics as his major.[50] Von Neumann and his father 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 for the entrance exam to the prestigious ETH Zurich,[51] which he passed in September 1923.[52] At the same time, von Neumann also entered Pázmány Péter University in Budapest,[53] as a Ph.D. candidate in mathematics. For his thesis, he chose to produce an axiomatization of Cantor's set theory.[54][55] He graduated as a chemical engineer from ETH Zurich in 1926 (although Wigner says that von Neumann was never very attached to the subject of chemistry), and passed his final examinations with summa cum laude for his Ph.D. in mathematics (with minors in experimental physics and chemistry) simultaneously with his chemical engineering degree, of which Wigner wrote, "Evidently a Ph.D. thesis and examination did not constitute an appreciable effort."[56][57] He then went to the University of Göttingen on a grant from the Rockefeller Foundation to study mathematics under David Hilbert.[58] Hermann Weyl, in his obituary of Emmy Noether, remembers how in the winter of 1926-1927 von Neumann,
mathematical papers, the second of which gave the modern definition of ordinal numbers, which superseded Georg Cantor's definition.[48] At the conclusion of his education at the gymnasium, von Neumann sat for and won the Eötvös Prize, a national prize for mathematics.[49]
University studies[edit]
According to his friend Theodore von Kármán, von Neumann's father wanted John to follow him into industry and thereby invest his time in a more financially useful endeavor than mathematics. In fact, his father asked von Kármán to persuade his son not to take mathematics as his major.[50] Von Neumann and his father 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 for the entrance exam to the prestigious ETH Zurich,[51] which he passed in September 1923.[52] At the same time, von Neumann also entered Pázmány Péter University in Budapest,[53] as a Ph.D. candidate in mathematics. For his thesis, he chose to produce an axiomatization of Cantor's set theory.[54][55] He graduated as a chemical engineer from ETH Zurich in 1926 (although Wigner says that von Neumann was never very attached to the subject of chemistry), and passed his final examinations with summa cum laude for his Ph.D. in mathematics (with minors in experimental physics and chemistry) simultaneously with his chemical engineering degree, of which Wigner wrote, "Evidently a Ph.D. thesis and examination did not constitute an appreciable effort."[56][57] He then went to the University of Göttingen on a grant from the Rockefeller Foundation to study mathematics under David Hilbert.[58] Hermann Weyl, in his obituary of Emmy Noether, remembers how in the winter of 1926-1927 von Neumann,
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