German mathematician, 1805-1859.

**Biography**

Johann Peter Gustav Lejeune Dirichlet was born on February 13, 1805 in Düren, a town about midway between Aachen and Cologne. His name stems from "Le jeune de Richelet" (the young from Richelet), since his grandfather lived in the Belgian town of Richelet. Dirichlet soon developed an interest in mathematics and by the age of 12 he was already spending his allowance on math books. When he was 12 he entered into the Gymnasium in Bonn and after two years there his parents moved him to the Jesuit College in Cologne, where he was lucky enough to be taught by Ohm.

By the age of 16 Dirichlet was ready to go to university, and convinced his parents to let him study mathematics instead of law (like they had wanted). Because of the low standards at German universities at the time Dirichlet decided to study in Paris, where he arrived in May 1822. In Paris he met Fourier and many other prominent mathematicians of the time and undoubtedly benefitted greatly from their company. In the summer of 1823 Dirichlet worked for General Maximilien Sebastién Foy, the leader of the liberal opposition in the Chamber of Deputies. Dirichlet taught German to the General's wife and children, a well paid job which also gave him ample time for his mathematical research in addition to giving him a place to stay at the family's home.

After General Foy died Dirichlet returned to Germany in 1826 to become a professor at the University of Breslau. He could not do this without problems, however, because one of the requirements for teaching in a German university was an habilitation. Dirichlet certainly had the knowledge needed to submit his habilitation thesis, but he did not have the required doctorate. The University of Cologne solved this problem by giving him an honorary doctorate, and he submitted his thesis to Breslau. This detour to the professor position caused great controversy in the German mathematical society and was cause for a large correspondence between professors.

At Breslau Dirichlet was troubled by the low standards (the same reason that convinced him to study in Paris) and with Alexander von Humboldt's help he was appointed to the Military College in Berlin in 1828. Soon after he was also appointed professor at the University of Berlin, which had been his goal when he moved in the first place. He still held his position at the Military College, however, and therefore his workload was rather heavy. In 1831 he was appointed to the Berlin Academy of Sciences and in the same year he married Rebecca Mendelssohn (sister of composer Felix Mendelssohn).

In 1855 Dirichlet's friend and idol, Gauss, died and Dirichlet was offered his chair at the University of Göttingen. Although he liked the University of Berlin very much he couldn't get out of his position at the Military College as long as he was there. His double workload was one of the factors in his decision to accept the offer, along with the desire to follow in Gauss' footsteps. Dirichlet was very happy in Göttingen, where he had plenty of time for research and also had excellent research students. His tenure there was short-lived, however, as he died on May 5, 1859 from a heart failure. A few months earlier his wife, Rebecca, had died from a stroke. His chair at Göttingen was passed on to his old student Riemann.

**Mathematical achivements**

In 1825 Dirichlet published his first paper, concerning Fermat's Last Theorem (x^n+y^n=z^n has no whole-number solutions for n>2). The theorem had already been proved for n=3 and n=4, and in his paper Dirichlet proved it for one of the two instances of n=5 (Legendre, one of the referees for the paper, completed the proof for the other instance). Later on Dirichlet also proved the n=14 case.

In 1828 he published his work on the convergence of Fourier series, proving previous work by Cauchy to be erroneous. Because of this Dirichlet is considered to have founded the theory of Fourier series.

Later, Dirichlet worked on analytic number theory. In 1937 he proved Gauss' conjecture "that in any arithmetic progression with first term coprime to the difference there are infinitely many primes". In the following years he published two more papers on analytic number theory which among other things introduced Dirichlet series.

He also did important work on algebraic number theory and mechanics, in particular the equilibrium of systems and potential theory.

Sources:

http://www-history.mcs.st-andrews.ac.uk/history/Mathematicians/Dirichlet.html

http://www.math.uni-goettingen.de/Personen/Bedeutende_Mathematiker/dirichlet.html (with the help of Babelfish)