Applied Mathematics

Other Areas of Applied Mathematics

How does the Monte Carlo method work?

The Monte Carlo method has been used for centuries, but it was not truly thought of as a “viable” mathematical technique until around the first half of the 20th century. Some people say it was named after the city in the Monaco principality because of the simple random number generator of roulette played in the Monaco casinos; others say the method’s creator was honoring a relative having a propensity toward gambling.

It’s known that Italian physicist Enrico Fermi (1901–1954) not only used the method to calculate neutron diffusion, but invented the Fermiac, a Monte Carlo mechanical device to determine the criticality in nuclear reactors. Further foundations of the method were laid down in the 1940s by Hungarian mathematician John von Neumann (1903–1957), along with Polish mathematician Stanislaw Ulam (1909–1984); and Nicholas Metropolis would go on to invent the computer chess program MANIAC I—the first to beat a human player—based on von Neumann’s work. Simply put, the Monte Carlo method gives approximate numerical solutions to a number of problems that are too difficult to solve analytically by performing specific statistical sampling experiments. Although forms of the method have been known for a while, it was initially developed for numerical integrations in statistical physics problems during the early days of electronic computing.

But there is more to the Monte Carlo method than meets the computation. First, it’s actually thought of now as a true numerical method that addresses some of the most complex mathematical applications. The list of applications seems endless, including cancer therapy, Dow-Jones forecasts, and stellar evolution. Second, there is more than one Monte Carlo method. For example, one method, called the Markov chain Monte Carlo method, has played a critical role in such diverse fields as physics, statistics, computer science, and structural biology. And the list of applications is long, especially in its usefulness and power for all types of prediction.


Italian physicist Enrico Fermi used the Monte Carlo method to calculate neutron diffusion and to invent a device that determined criticality in nuclear reactors.


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