ABSTRACT
Generally, Monte-Carlo methods refer to algorithms using random simulation. The advantage of Monte-Carlo methods relies on its capacity to explore high-dimensional spaces of configurations to get some information. Concurrent with this upheaval, another revolution was coming, the one in computer science. The first computational project on thermonuclear reactions was launched, gathering Metropolis, von Neumann and Enrico Fermi. A mathematician, Stanislaw Ulam, participating in one of the presentations of the project in 1946, is impressed by the speed of computations and the quality of the available numerical results: he understands immediately that the appearance of modern computer will lead to a new era in experimental mathematics. For the numerical integration, it is commonly accepted that if the dimension is low, the discretization and quadrature formulas are the most efficient, and also that it is preferable to use a Quasi Monte-Carlo method for medium dimensions, while for high dimensions, the Monte-Carlo method has the advantage.
