Johann Peter Gustav Lejeune Dirichlet was a German mathematician, born on 13 February 1805 and died on 5 May 1859. In number theory he proved special cases of Fermat's Last Theorem and created analytic number theory. In analysis he advanced the theory of Fourier series and was one of the first to give the modern formal definition of a function. In mathematical physics he studied potential theory, boundary-value problems, heat diffusion and hydrodynamics. His surname is Lejeune Dirichlet, but he is commonly called Dirichlet, particularly for results named after him.
Facts
Connections
Attributed Works
Source Dirichlet Eta Function (Wikipedia)
Source Dirichlet Function (Wikipedia)
Source Pigeonhole principle (Wikipedia)
In Branch
Source Peter Gustav Lejeune Dirichlet (Wikipedia)
Source Peter Gustav Lejeune Dirichlet (Wikipedia)
Source Peter Gustav Lejeune Dirichlet (Wikipedia)
Source Peter Gustav Lejeune Dirichlet (Wikipedia)
Mentored
Source Alfred Enneper (Wikipedia)
Source Carl Anton Bjerknes (Wikipedia)
Source Elwin Bruno Christoffel (MacTutor)
Source Gustav Conrad Bauer (Wikipedia)
Source Leopold Kronecker (Wikipedia)
Source MacTutor History of Mathematics: Philipp Ludwig von Seidel (MacTutor biography)
Mentored By
Source Peter Gustav Lejeune Dirichlet (Wikipedia)
Source Peter Gustav Lejeune Dirichlet (Wikipedia)
Principal Result
Source Peter Gustav Lejeune Dirichlet (Wikipedia)
Source Peter Gustav Lejeune Dirichlet (Wikipedia)
Proofs Credited
Source Class number formula (Wikipedia)
Source Dirichlet Kernel (Wikipedia)
Source Dirichlet's approximation theorem, Wikipedia
Source Dirichlet's Theorem on Arithmetic Progressions (Wikipedia)
Source Dirichlet's Unit Theorem (Wikipedia)
Source Heine-Borel Theorem (Wikipedia)
In the Other Atlases
Same As
Also in Science Atlas: the same subject.
Nationality
Also in Geography Atlas: the nationality of this subject.
Source Peter Gustav Lejeune Dirichlet (Wikipedia)Lead paragraph [nationality-culture]Quote, Lead paragraph [nationality-culture]
was a German mathematician
Sources
1. Peter Gustav Lejeune Dirichlet (Wikipedia)
Lead paragraph
he proved special cases of Fermat's Last Theorem and created an
Lead paragraph [nationality-culture]
was a German mathematician
Principal Result: Dirichlet's Approximation Theorem, Article text
He first used the pigeonhole principle, a basic counting argument, in the proof of a theorem in diophantine approximation, later named after him Dirichlet's approximation theorem.
Principal Result: Dirichlet Function, Article text
It also introduced the Dirichlet function as an example of a function that is not integrable (the definite integral was still a developing topic at the time) and, in the proof of the theorem for the Fourier series, introduced the Dirichlet kernel and the Dirichlet integral.
In Branch: Number Theory, Lead paragraph [in-branch]
In number theory
In Branch: Analytic Number Theory, Lead paragraph [in-branch 2]
created analytic number theory
In Branch: Analysis, Lead paragraph [in-branch 3]
In analysis
In Branch: Potential Theory, Lead paragraph [in-branch 4]
potential theory
- Mentored By: Carl Friedrich Gauss, Infobox, doctoral advisor or academic advisors
- Mentored By: Siméon Denis Poisson, Infobox, doctoral advisor or academic advisors
View the SourceElwin Bruno Christoffel (MacTutor)
Mentored: Elwin Bruno Christoffel, Biography, Berlin studiesQuote, Mentored: Elwin Bruno Christoffel, Biography, Berlin studies
Christoffel is rightly thought of as a student of Dirichlet
Alfred Enneper (Wikipedia)
Mentored: Alfred Enneper, Lead, doctorateQuote, Mentored: Alfred Enneper, Lead, doctorate
under the supervision of Peter Gustav Lejeune Dirichlet
Carl Anton Bjerknes (Wikipedia)
Mentored: Carl Anton Bjerknes, Biography, teachersQuote, Mentored: Carl Anton Bjerknes, Biography, teachers
A pupil of Peter Gustav Lejeune Dirichlet, Gabriel Lamé and Augustin-Louis Cauchy
Gustav Conrad Bauer (Wikipedia)
Mentored: Gustav Conrad Bauer, Education and familyQuote, Mentored: Gustav Conrad Bauer, Education and family
Bauer received in 1842 his Promotierung under Peter Gustav Lejeune Dirichlet
MacTutor History of Mathematics: Philipp Ludwig von Seidel (MacTutor biography)
MacTutor History of MathematicsMentored: Philipp Ludwig von Seidel, Biography, university studiesQuote, Mentored: Philipp Ludwig von Seidel, Biography, university studies
Seidel entered the University of Berlin in 1840 and studied under Dirichlet and Encke.
Dirichlet's Unit Theorem (Wikipedia)
Wikimedia FoundationProofs Credited: Dirichlet's Unit Theorem, Lead paragraphQuote, Proofs Credited: Dirichlet's Unit Theorem, Lead paragraph
In mathematics, Dirichlet's unit theorem is a basic result in algebraic number theory due to Peter Gustav Lejeune Dirichlet. It determines the rank
Dirichlet's approximation theorem, Wikipedia
Proofs Credited: Dirichlet's Approximation Theorem, Lead paragraphQuote, Proofs Credited: Dirichlet's Approximation Theorem, Lead paragraph
In number theory, Dirichlet's theorem on Diophantine approximation, also called Dirichlet's approximation theorem, states that for any real numbers
Dirichlet Kernel (Wikipedia)
Proofs Credited: Dirichlet Kernel, Lead paragraphQuote, Proofs Credited: Dirichlet Kernel, Lead paragraph
In mathematical analysis, the Dirichlet kernel, is the collection of periodic functions defined as
Dirichlet Function (Wikipedia)
Attributed Works: Dirichlet Function, Lead paragraphQuote, Attributed Works: Dirichlet Function, Lead paragraph
In mathematics, the Dirichlet function is the indicator function
Dirichlet Eta Function (Wikipedia)
Attributed Works: Dirichlet Eta Function, Lead paragraphQuote, Attributed Works: Dirichlet Eta Function, Lead paragraph
In mathematics, in the area of analytic number theory, the Dirichlet eta function is defined by the following Dirichlet series, which converges for any complex number having real part greater
Leopold Kronecker (Wikipedia)
Mentored: Leopold Kronecker, Infobox, doctoral advisor or academic advisorsQuote, Mentored: Leopold Kronecker, Infobox, doctoral advisor or academic advisors
Back in Berlin, Kronecker studied mathematics with Peter Gustav Lejeune Dirichlet and in 1845 defended his dissertation in algebraic number theory written under Dirichlet's supervision.
Dirichlet's Theorem on Arithmetic Progressions (Wikipedia)
Wikimedia FoundationProofs Credited: Dirichlet's Theorem on Arithmetic Progressions, LeadQuote, Proofs Credited: Dirichlet's Theorem on Arithmetic Progressions, Lead
The theorem is named after the German mathematician Peter Gustav Lejeune Dirichlet, who proved it in 1837.
Heine-Borel Theorem (Wikipedia)
Wikimedia FoundationProofs Credited: Heine-Borel Theorem, LeadQuote, Proofs Credited: Heine-Borel Theorem, Lead
Peter Gustav Lejeune Dirichlet was the first to prove this and implicitly he used the existence of a finite subcover of a given open cover of a closed interval in his proof.
Class number formula (Wikipedia)
Proofs Credited: Class Number Formula, LeadQuote, Proofs Credited: Class Number Formula, Lead
Peter Gustav Lejeune Dirichlet published a proof of the class number formula for quadratic fields in 1839, but it was stated in the language of quadratic forms rather than classes of ideals.
Pigeonhole principle (Wikipedia)
Wikimedia FoundationAttributed Works: Pigeonhole Principle, Lead sectionQuote, Attributed Works: Pigeonhole Principle, Lead section
it is commonly called Dirichlet's box principle or Dirichlet's drawer principle after an 1834 treatment of the principle by Peter Gustav Lejeune Dirichlet
Reader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.