John von Neumann is a towering figure in 20th century mathematics and science. From his decisive early contributions to mathematical logic, to his visionary work during the birth of computers, to his forays into military policy, von Neumann trained his other-worldly intelligence on some of the deepest questions facing humankind. At the time of his death in 1957, at the age of 53, he was on the faculty of the Institute for Advanced Study in Princeton. His IAS colleague Freeman Dyson, who himself stands among the world's most brilliant thinkers, has written an article about von Neumann's mathematics, "A Walk through Johnny von Neumann's Garden", which will appear in the February 2013 issue of the Notices of the American Mathematical Society.
"Johnny's unique gift as a mathematician was to transform problems in all areas of mathematics into problems of logic," Dyson writes. "He was able to see intuitively the logical essence of problems and then to use the simple rules of logic to solve the problems." This ability, which forms a leitmotif of the article, allowed von Neumann to make contributions in a wide range of fields.
Dyson describes von Neumann's early work in mathematical logic, including a set of axioms from 1925, which provided one ingredient for Kurt Goedel's revolutionary incompleteness theorems. Those theorems shook the foundations of mathematics. "After Goedel, mathematics could never be the unique compendium of absolute truth that mathematicians from Euclid to Hilbert had imagined," Dyson writes. Many mathematicians looked upon Goedel's discoveries as a disaster for the field. Not von Neumann: "Johnny understood immediately that the new freedom created by Goedel was a gain and not a loss," Dyson writes.
Dyson goes on to discuss von Neumann's work in game theory, quantum mechanics, and dynamical systems, as well as his ground-breaking contributions to the birth of computer science. von Neumann did work for the United States military, initially applying mathematics to improve artillery and antisubmarine weapons. Later he was one of themain scientists working on the Manhattan Project, where his understanding of shock waves was crucial. It was during the Manhattan Project that von Neumann saw, in Dyson's words, "monstrous numerical calculations carried out laboriously by gangs of human computers".This experience led von Neumann to begin thinking about how to develop electronic computers.
von Neumann's role as an adviser to the U.S. military in the 1950s has been controversial, and the article discusses this aspect with a sensitivity that comes from Dyson's personal familiarity with von Neumann. Overall, the article leaves one with a deep impression of the pungency and vitality, as well as the restlessness, of von Neumann's intellect.
"A Walk through Johnny von Neumann's Garden", by Freeman Dyson, will appear on the Notices web site, http://www.ams.org/notices, on January 7, 2013. The Notices is freely available online without subscription.
Members of the press can request an advance copy of the article by writing to Allyn Jackson, AMS, [email protected].
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Founded in 1888 to further mathematical research and scholarship, today the more than 30,000 member American Mathematical Society fulfills its mission through programs and services that promote mathematical research and its uses, strengthen mathematical education, and foster awareness and appreciation of mathematics and its connections to other disciplines and to everyday life.
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Notices of the American Mathematical Society (February 2013)
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