- Person
- John von Neumann
- Lived
- 1903–1957
- Field
- Mathematics & computing
- From
- Hungarian-American
The story
Some problems in physics are far too complicated to solve with equations alone, such as tracking huge numbers of neutrons bouncing through a material. In 1946 physicists at Los Alamos were studying how neutrons travel through the core of a nuclear weapon. They had most of the necessary data but could not solve the problem by conventional methods.
The mathematician Stanislaw Ulam found inspiration while recovering from an illness and playing solitaire. Rather than calculate the odds of winning a hand by pure reasoning, he realised it would be more practical to play many times and count the successes, and that the new fast computers could do this for physics problems. Later in 1946 he described the idea to his close friend John von Neumann, and the two began to plan actual calculations.
Instead of solving the equations exactly, they used random numbers to simulate many possible histories of a system, then averaged the results to approximate the answer. Because the work was secret it needed a code name, and their colleague Nicholas Metropolis suggested Monte Carlo, after the casino in Monaco. In the spring of 1948 von Neumann, Metropolis and others programmed the ENIAC to perform the first fully automated Monte Carlo calculations. Von Neumann also devised clever tricks for producing usable random numbers, including the middle-square method and a way to simulate a fair coin using a biased one, still used in some hardware random number generators.
In the 1950s the method spread into physics, physical chemistry and operations research, helped by funding and publications from the RAND Corporation and the US Air Force.
Monte Carlo simulation has since spread far beyond its origins. It is used to calculate radiation doses, design heat shields and aerodynamic shapes, analyse the reliability of engineering systems, plan wireless networks, guide robots, assess climate data for the Intergovernmental Panel on Climate Change, model financial risk and power game-playing artificial intelligence.
Why it matters
Monte Carlo methods are among the most widely used computational tools in science, medicine, engineering and finance.
About John von Neumann
Budapest-born mathematician whose 1945 EDVAC report set out the stored-program design behind almost every computer, and who helped found game theory and modern quantum mechanics.
More about John von Neumann
- Von Neumann warned of CO2 warming in 1955In 1955 John von Neumann noted that carbon dioxide from burning coal and oil might already have changed the atmosphere enough to cause general warming.
- Von Neumann's ergodic theorem earned 'immortality'John von Neumann's 1932 papers on ergodic theory were so important that Paul Halmos said they alone would have guaranteed him mathematical immortality.
- Von Neumann launched computer weather forecastingIn 1950 John von Neumann and Jule Charney used ENIAC to make the first numerical weather forecasts; in 1955 routine computer forecasting began in the US.
- John von Neumann founded game theoryJohn von Neumann proved the minimax theorem in 1928 and, with Oskar Morgenstern, published Theory of Games and Economic Behavior in 1944, founding game theory.
- Von Neumann's IAS computer was copied worldwideThe IAS machine John von Neumann built in Princeton from 1946 became the blueprint for early computers worldwide, and its design shaped IBM's first scientific computers.
- John von Neumann invented merge sort in 1945In 1945 John von Neumann invented merge sort, one of the most widely used methods for putting data in order, in what Donald Knuth called his first computer program.
- Von Neumann gave quantum mechanics its mathematicsIn his 1932 book Mathematical Foundations of Quantum Mechanics, John von Neumann set out the first rigorous mathematical framework for quantum theory.
- Von Neumann designed a machine that copies itselfIn the late 1940s John von Neumann designed a self-reproducing 'universal constructor' and, with Stanislaw Ulam, created the field of cellular automata.
- John von Neumann wrote the blueprint for modern computersJohn von Neumann's 1945 report on the EDVAC gave the first published description of the stored-program computer, the design behind almost every computer since.
Sources
- John von Neumann Wikipedia
- Monte Carlo method Wikipedia
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