who was professor at the University of Berlin before succeeding Gauss at the University of Göttingen. He proved that in any arithmetic series a, a + d, a + 2d,…, where a and d are coprime, there are infinitely many primes; his proof arguably introduced the field of analytic number theory. He gave an early version of the modern definition of a function. He also made contributions to mathematical physics, particularly in potential theory; see Dirichlet problem.