The son of a Latin teacher, Hadamard was born at Versailles in France and educated at the Ecole Normale Supérieure in Paris. He taught first at the University of Bordeaux from 1893 until 1897, before returning to Paris to the Sorbonne. In 1909 he took up the chair of mathematics at the Collège de France where he remained until his retirement in 1937.

In his long life Hadamard worked in many areas of mathematics, but remains best known for his proof in 1896 of the prime number theorem.

Mathematicians have long been interested in prime numbers. There is no simple formula for determining primes, but it is possible to say something about the distribution of prime numbers. If P_n is the nth prime number, π(n) is used to denote the number of primes between 1 and n. Both Gauss and Legendre used the formula π(n) = n/log_e n.

This does not work at small values of n but Gauss and Legendre suspected that the ratio of log_e n to π(n)/n would approach 1 as n approaches infinity. They were, however, unable to prove it. Hadamard and, independently, Charles de la Vallée-Poussin produced proofs in 1896 using the Riemann zeta function.