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# Johann Peter Gustav Lejeune Dirichlet

Johann Peter Gustav Lejeune Dirichlet (German pronunciation: [ləˈʒœn diʁiˈkleː]; 13 February 1805 – 5 May 1859) was a German mathematician credited with the modern formal definition of a function .

Biography

His family was from Richelette, a small community 5 km north east of Liège in Belgium, from which his surname "Lejeune Dirichlet" ("le jeune de Richelette", French for "the youth from Richelette") was derived.[1]

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 n = 5, which was completed by Adrien-Marie Legendre, one of the referees. Dirichlet completed his own proof almost at the same time; later he produced a full proof for the case n = 14.

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 and was appointed to fill the vacant chair of Carl Friedrich Gauss upon the latter's death.[2] In 1854, he was elected a foreign member of the Royal Swedish Academy of Sciences.

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). Dirichlet's brain is preserved in the anatomical collection of the University of Göttingen, along with the brain of Gauss.

See also

* Theorems named Dirichlet's theorem:

o Dirichlet's approximation theorem (diophantine approximation)

o Dirichlet's theorem on arithmetic progressions (number theory, specifically prime numbers)

o Dirichlet's theorem on diophantine approximation (number theory and approximation)

o Dirichlet's unit theorem (algebraic number theory and rings)

* Dirichlet beta function

* Dirichlet cell, polygon

* Dirichlet characters (number theory, specifically Zeta and L-functions. 1831)

* Dirichlet conditions (Fourier series)

* 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 stability criterion (Dynamical systems)

* 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)

* Dirichlet process

References

1. ^ Elstrodt, Jürgen (2007). "The Life and Work of Gustav Lejeune Dirichlet (1805–1859)" (PDF). Clay Mathematics Proceedings. http://www.uni-math.gwdg.de/tschinkel/gauss-dirichlet/elstrodt-new.pdf. Retrieved 2007-12-25.

2. ^ Marcus du Sautoy, The Music of the Primes, (HarperCollins 2003)

* 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, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Dirichlet.html .

* 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.

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