Blaise Pascal is well known as a brilliant mathematician and physicist before devoting himself to theology and philosophy. Among his mathematical works is the important Traité du triangle arithmétique of 1654. Although the table of integers defined therein had already been studied several centuries earlier by Yang Hui and Omar Khayyam, it is under the name of "Pascal's triangle" that it is known to this day. The numbers appearing in Pascal's triangle (called binomial coefficients) are useful in many situations, from the remarkable identities of algebra to complex combinatorial problems, including calculating the chances of winning the lottery. Arithmetic (or number theory) is the branch of mathematics that deals with the properties of integers, in particular questions of divisibility and prime numbers (those that are divisible only by 1 and themselves). The mathematical concepts that have been invented, since the Greeks, and more particularly in the 19th and 20th centuries by mathematicians to unravel the mysteries of prime numbers are particularly rich. Among these, the Riemann zeta function plays a central role. Binomial coefficients have arithmetic properties, some of which are well known, but others have only recently been discovered, shedding new light on research on prime numbers. Conference of the "A text, a mathematician" cycle of the French Mathematical Society. February 13, 2008 at the National Library of France.