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John Von Neumann, the Last Great Polymath

By Paige Thompson

R egarded as the foremost mathematician of his time John Von Neumann made unparalleled significant contributions across a remarkable range of fields including mathematics, physics, economics, and computing.

He was born to a wealthy non-observant Jewish family in Budapest. At the age of six, he could converse in Ancient Greek and by the time he was eight was familiar with differential and integral calculus. At eleven, he entered one of the best schools in Hungary and was part of a schooling system for the elite that produced a remarkable generation noted for their intellectual achievement. These included: Edward Teller (hydrogen bomb), Dennis Gabor (holography, Nobel Prize winner), Leo Szilard (nuclear chain reaction), George de Hevesy (radioactive traces, Nobel Prize winner) and Eugene Wigner (theoretical physicist, Nobel Prize winner). Wigner was asked on the receipt of his Nobel Prize if he thought there was a reason why Hungary had produced so many geniuses. His response: Von Neumann was the only genius.

John Von Neumann

His next years in education were highlighted by various awards and the publication of two major mathematical papers at age 19. At the urging of his father Von Neumann entered University to study chemistry. He graduated as a chemical engineer while simultaneously achieving his Ph.D. in mathematics. After becoming the youngest elected privatdozent at University of Berlin, Von Neumann was offered a lifetime professorship at the Institute for Advanced Study, at Princeton University.

Due to his expertise in mathematically modelling explosions, particularly shaped charges, Von Neumann became involved with the Manhattan project. His major contribution to the atomic race was in the design of the explosive lenses used in the plutonium core of bomb. He witnessed the first test of the bomb and was part of the team that selected the city. After the war, Von Neumann worked closely with Edward Teller and Lause Fuchs on the development of the hydrogen bomb. Ever the polymath, during the beginning of the Cold War Von Neumann was also credited for development of mutual assured destruction (MAD) as an international political strategy. In 1956 Eisenhower presented him with the Presidential Medal of Freedom for increasing the scientific progression of the United States and resolving “some of the most difficult technical problems of national defence”.

Despite these remarkable contributions Von Neumann is perhaps best known for the foundation of an entirely different field. In 1944 Von Neumann with Oskar Morgenstern published what he become most famous for – The Theory of Games and Economic Behaviour. This book not only had a remarkable impact on economics, politics, mathematics and social behaviour but created an entirely new discipline of study. The influence of Game Theory extended beyond the academic world into economics, politics and popular culture. It most famously was embraced by the American think tank the RAND Corporation, charged with formulating military strategy for the atomic age. It led to the momentous discovery by RAND scientists in 1950 of the so-called "prisoner's dilemma" - a mind-bending game in which two or more people may betray the common good for individual gain.

In 1945 Von Neumann initiated a new project to create an electronic computing instrument, building on the work of the ENIAC and the EDVAC teams. Frank Aydelotte, director of the IAS, introduced the project to the board by saying: “I think it is soberly true to say that the existence of such a computer would open up to mathematicians, physicists, and other scholars area of knowledge in the same remarkable way that the two-hundred-inch telescope promises to bring under observation universes which at the present moment are entirely outside the range of any instrument now existing.” Von Neumann predicted that the device would be at the very least 10,000 times faster than the human and computer machine collaborations currently in use.

While a team was assembled, Von Neumann worked closely with Herman Goldstine on a tentative aid to programming the machine. The result is ‘Planning and coding of problems for an electronic computing instrument.’ It was the first theoretical discussion of programming, the first use of ‘flow diagram’ (which eventually became flow chart and finally, flowchart) as a logically complete and precise notation for expressing a mathematical problem, and eventually formed the basis for all computer programming.

The team at the Institute began to see the finish line of their project within five years. Julian Bigelow, an engineer on the team, summed up the excitement: “It was happening here … and we were lucky to be in on it… A tidal wave of computational power was about to break and inundate everything in science and much elsewhere, and things would never be the same afterwards.” When testing the arithmetic unit of the machine, the team actually set Von Neumann up to compete against the computer. When Von Neumann’s calculations began to fail first, they were satisfied. By the summer of 1951 the unit was functional.

While its main use initially was to produce calculations for the hydrogen bomb, the computer was also used to perform the wold’s first mathematical and numeric weather forecasts. These forecasts and Von Neumann’s wider interest in weather systems led to his study on polar ice caps and absorption of solar radiation. He was one of the first scientists to promote the theory of global warming noting that the burning of coal would result in a “general warming of the earth”.

It’s hard to comprehend the remarkable nature and sheer breadth of influence that Von Neumann’s intelligence had on the progress of mathematics, science and computing in the 20th century. Four years into the computing project at IAS, Von Neumann declared: “It would appear that we have reached the limits of what is possible to achieve with computer technology, although one should be careful with such statements, as they tend to sound pretty silly in five years.”

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