**Johann Peter Gustav Lejeune Dirichlet** (February 13, 1805 - May 5, 1859) was a German mathematician credited with the modern "formal" definition of a function.

His family hailed from the town of Richelet in Belgium, from which his surname "Lejeune Dirichlet" ("le jeune de Richelet" = "the young chap from Richelet") was derived, and that was where his grandfather lived.

Dirichlet was born in Düren, where his father was the postmaster. He was educated in Germany, and then France, where he learnt from many of the most renowned mathematicians of the day. His first paper was on Fermat's Last Theorem. This was a famous conjecture (now proven) that stated that for *n* > 2, the equation *x*^{n} + *y*^{n} = *z*^{n} has no solutions, apart from the trivial ones in which *x*, *y*, or *z* is zero. He produced a partial proof for the case *n* = 5, which was completed by Adrien-Marie Legendre, who was one of the referees. Dirichlet also completed his own proof almost at the same time; he later also produced a full proof for the case *n* = 14.

He married Rebecca Mendelssohn, who came from a distinguished Jewish family, being a granddaughter of the philosopher Moses Mendelssohn, and a sister of the composer Felix Mendelssohn.

- Dirichlet's theorem (number theory, 1835)
- Dirichlet characters (number theory, 1831)
- Dirichlet convolution (number theory)
- Dirichlet kernel (functional analysis, Fourier series)
- Dirichlet series