Dirichlet, (Peter Gustav) Lejeune (1805-1859)

German mathematician whose work in applying analytical techniques to mathematical theory resulted in the fundamental development of the theory of numbers. He was also a physicist interested in dynamics.

Dirichlet was born in Düren, near Aachen, and studied at Cologne and the Collège de France, in Paris. He became professor at the University of Berlin at the age of 23, and at Göttingen in 1855.

Dirichlet's papers included studies on quadratic forms, the number theory of irrational fields (including the integral complex numbers), and the theory of units. His most important work was on the convergence of the Fourier series, which led him to the modern notion of a generalized function. In 1837 he presented his first paper on analytic number theory, proving Dirichlet's theorem: in every arithmetical sequence a, a + d, a + 2d, and so on, where a and d are relatively prime (that is, have no common divisors other than 1), there is an infinite number of prime numbers.

Dirichlet applied his mathematical knowledge to various aspects of physics, such as an analysis of vibrating strings, and to astronomy in a critique of the ideas about the stability of the Solar System proposed by French mathematician Pierre Laplace.

Dirichlet's Vorlesungen über Zahlentheorie/Lectures in Number Theory was published posthumously 1863.