Johann Peter Gustav Lejeune Dirichlet

Lejeune Dirichlet
Johann Peter Gustav Lejeune Dirichlet
Born	February 13, 1805(1805-02-13) Düren, French Empire
Died	May 5, 1859 (aged 54) Göttingen, Hanover
Residence	Germany
Nationality	German
Fields	Mathematician
Institutions	University of Berlin University of Breslau University of Göttingen
Alma mater	University of Bonn
Doctoral advisor	Simeon Poisson Joseph Fourier
Doctoral students	Ferdinand Eisenstein Leopold Kronecker Rudolf Lipschitz Carl Wilhelm Borchardt
Known for	Dirichlet function Dirichlet eta function

Johann Peter Gustav Lejeune Dirichlet (pronounced [ləʒœn diʀiçle]; 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 Richelette in Belgium, from which his surname "Lejeune Dirichlet" ("le jeune de Richelette", French for "the young chap from Richelette") was derived.^[1] That was also where his grandfather lived.

Dirichlet was born in Düren, where his father was the postmaster. He learned from Georg Ohm at the Jesuit gymnasium in Cologne. His first paper was on Fermat's last theorem comprising a partial proof for the case , which was completed by Adrien-Marie Legendre, who was one of the referees. Dirichlet completed his own proof almost at the same time; later he produced a full proof for the case .

He graduated from the University of Bonn in 1827 and taught as a Privatdozent at the University of Breslau, later teaching at the University of Berlin. In 1855 Dirichlet began teaching at the University of Göttingen.

In 1831, he married Rebecca Henriette Mendelssohn Bartholdy, who came from a distinguished family of converts from Judaism to Christianity; she was a granddaughter of the philosopher Moses Mendelssohn, daughter of Abraham Mendelssohn Bartholdy and a sister of the composers Felix Mendelssohn Bartholdy and Fanny Mendelssohn.

Ferdinand Eisenstein, Leopold Kronecker, and Rudolf Lipschitz were his students. After his death, Dirichlet's lectures and other results in number theory were collected, edited and published by his friend and fellow mathematician Richard Dedekind under the title Vorlesungen über Zahlentheorie (Lectures on Number Theory).

See also

• Theorems named Dirichlet's theorem:
  • Dirichlet's approximation theorem (diophantine approximation)
  • Dirichlet's theorem on arithmetic progressions (number theory, specifically prime numbers)
  • Dirichlet's theorem on diophantine approximation (number theory and approximation)
  • Dirichlet's unit theorem (algebraic number theory and rings)
• Dirichlet beta function
• Dirichlet characters (number theory, specifically Zeta and L-functions. 1831)
• Dirichlet conditions (Fourier transform)
• Dirichlet convolution (number theory and Arithmetic functions)
• Dirichlet density (number theory)
• Dirichlet distribution (probability theory)
• Dirichlet form
• Dirichlet kernel (functional analysis, Fourier series)
• Dirichlet problem (partial differential equations)
• Dirichlet series (analytic number theory)
• Dirichlet's test (analysis)
• Dirichlet tessellation, also called a Voronoi diagram (geometry)
• Dirichlet boundary condition (differential equations)
• Dirichlet function (topology)
• Pigeonhole principle/Dirichlet's box (or drawer) principle (combinatorics)
• Dirichlet divisor problem (currently unsolved) (Number theory)
• Dirichlet eta function (number theory)
• Latent Dirichlet allocation
• Class number formula
• Dirichlet integral
• Dirichlet principle
• Generalized Dirichlet distribution (probability theory)

References

External links

• The Life and Work of Gustav Lejeune Dirichlet (1805–1859) by Jürgen Elstrodt.
• Johann Peter Gustav Lejeune Dirichlet at the Mathematics Genealogy Project.
• O'Connor, John J.; Robertson, Edmund F., "Johann Peter Gustav Lejeune Dirichlet", MacTutor History of Mathematics archive 
• Dirichlet, Johann Peter Gustav Lejeune, Vorlesungen über Zahlentheorie. Braunschweig, 1863. "Number Theory for the Millennium".
• Biography of Dirichlet found at Fermat's Last Theorem Blog.