# Peter Gustav Lejeune Dirichlet (nonfiction)

**Johann Peter Gustav Lejeune Dirichlet**(German: [ləˈʒœn diʀiˈkleː]; 13 February 1805 – 5 May 1859) was a German mathematician who made deep contributions to number theory (including creating the field of analytic number theory), and to the theory of Fourier series and other topics in mathematical analysis. He is credited with being one of the first mathematicians to give the modern formal definition of a function.

His first original research, comprising part of a proof of Fermat's Last Theorem for the case n=5, brought him immediate fame, being the first advance in the theorem since Fermat's own proof of the case n=4 and Euler's proof for n=3. Adrien-Marie Legendre, one of the referees, soon completed the proof for this case; Dirichlet completed his own proof a short time after Legendre, and a few years later produced a full proof for the case n=14. In June 1825 he was accepted to lecture on his partial proof for the case n=5 at the French Academy of Sciences, an exceptional feat for a 20-year-old student with no degree. His lecture at the Academy had also put Dirichlet in close contact with Joseph Fourier and Siméon Denis Poisson, who raised his interest in theoretical physics, especially Fourier's analytic theory of heat.

While teaching at the University of Breslau, Dirichlet continued his number theoretic research, publishing important contributions to the biquadratic reciprocity law which at the time was a focal point of Gauss's research.

Dirichlet had a good reputation with students for the clarity of his explanations and enjoyed teaching, especially as his University lectures tended to be on the more advanced topics in which he was doing research: number theory (he was the first German professor to give lectures on number theory), analysis and mathematical physics. He advised the doctoral theses of several important German mathematicians, as Gotthold Eisenstein, Leopold Kronecker, Rudolf Lipschitz and Carl Wilhelm Borchardt, while being influential in the mathematical formation of many other scientists, including Elwin Bruno Christoffel, Wilhelm Weber, Eduard Heine, Ludwig von Seidel and Julius Weingarten. At the Military Academy Dirichlet managed to introduce differential and integral calculus in the curriculum, significantly raising the level of scientific education there.

Holding liberal views, Dirichlet and his family supported the 1848 revolution; he even guarded with a rifle the palace of the Prince of Prussia. After the revolution failed, the Military Academy closed temporarily, causing him a large loss of income. When it reopened, the environment became more hostile to him, as officers to whom he was teaching would ordinarily be expected to be loyal to the constituted government. A portion of the press who were not with the revolution pointed him out, as well as Jacobi and other liberal professors, as "the red contingent of the staff".

Number theory was Dirichlet's main research interest, a field in which he found several deep results and in proving them introduced some fundamental tools, many of which were later named after him. In 1837, he published Dirichlet's theorem on arithmetic progressions, using mathematical analysis concepts to tackle an algebraic problem and thus creating the branch of analytic number theory. In proving the theorem, he introduced the Dirichlet characters and L-functions.

In the summer of 1858, during a trip to Montreux, Dirichlet suffered a heart attack. On 5 May 1859, he died in Göttingen, several months after the death of his wife Rebecka.

## In the News

## Fiction cross-reference

## Nonfiction cross-reference

- Fermat's Last Theorem (nonfiction)
- Joseph Fourier (nonfiction)
- Leonhard Euler (nonfiction)
- Leopold Kronecker (nonfiction)
- Mathematician (nonfiction)
- Siméon Denis Poisson (nonfiction)

External links:

- Peter Gustav Lejeune Dirichlet @ Wikipedia