Dirichlet was born in Düren, Germany, the son of the local postmaster. The young Dirichlet was intensely interested in mathematics. At the age of 14, he attended the University of Cologne where he studied under scientific luminaries such as Georg Ohm. He then traveled to Paris to enter the College de France. While there, he tutored the children of an influential politician who introduced Dirichlet to Paris' intelligentsia, including the famous mathematician Jean-Baptiste-Joseph Fourier.

Dirichlet's primary interest was in number theory, being notably influenced by the work of Carl Friedrich Gauss. In 1837, Dirichlet presented a proof of the theorem that bears his name on the occurrence of an infinite number of prime numbers in certain types of arithmetic sequences of integers. His thorough explorations into the nature of general number theory advanced this field of mathematics considerably. Dirichlet's interests, however, did not lie in theoretical matters alone. He performed important studies in applied mathematics such as the analysis of vibrating strings and use of the Fourier series. He also consolidated and refined mathematical terminology by proposing the modern definition of a function.

Dirichlet eventually returned to Germany and took on different teaching positions over the course of several years. He is reputed to have been an excellent teacher, yet was of a modest and shy character. By the age of 23, he was already a professor at the University of Berlin, and remained there for 27 years, maintaining a strong influence in German mathematical circles. In 1855 Dirichelt was offered a prestigious professorship at the University of Göttingen. Dirichelt accepted the post but did not teach there long. In the summer of 1858 he suffered a massive heart attack and died the following spring. Dirichelt is remembered and respected for his many mathematical discoveries and for his modern approach to the problems of mathematical analysis.