◀ ▲ ▶History / 19th-century / Person: Dirichlet, Johann Peter Gustav Lejeune

Person: Dirichlet, Johann Peter Gustav Lejeune

Lejeune Dirichlet is best known for his proof that in any arithmetic progression with first term coprime to the difference there are infinitely many primes.

Mathematical Profile (Excerpt):

• By the age of 16 Dirichlet had completed his school qualifications and was ready to enter university.
• However, the standards in German universities were not high at this time so Dirichlet decided to study in Paris.
• It is interesting to note that some years later the standards in German universities would become the best in the world and Dirichlet himself would play a hand in the transformation.
• Dirichlet set off for France carrying with him Gauss's Disquisitiones arithmeticae Ⓣ(Investigations in arithmetic) a work he treasured and kept constantly with him as others might do with the Bible.
• In Paris by May 1822, Dirichlet soon contracted smallpox.
• From the summer of 1823 Dirichlet was employed by General Maximilien Sébastien Foy, living in his house in Paris.
• Dirichlet's first paper was to bring him instant fame since it concerned the famous Fermat's Last Theorem.
• Dirichlet proved case 1 and presented his paper to the Paris Academy in July 1825.
• On 28 November 1825 General Foy died and Dirichlet decided to return to Germany.
• There was a problem for Dirichlet since in order to teach in a German university he needed an habilitation.
• Although Dirichlet could easily submit an habilitation thesis, this was not allowed since he did not hold a doctorate, nor could he speak Latin, a requirement in the early nineteenth century.
• The problem was nicely solved by the University of Cologne giving Dirichlet an honorary doctorate, thus allowing him to submit his habilitation thesis on polynomials with a special class of prime divisors to the University of Breslau.
• From 1827 Dirichlet taught at Breslau but Dirichlet encountered the same problem which made him choose Paris for his own education, namely that the standards at the university were low.
• The Military College was not the attraction, of course, rather it was that Dirichlet had an agreement that he would be able to teach at the University of Berlin.
• Dirichlet had a lifelong friend in Jacobi, who taught at Königsberg, and the two exerted considerable influence on each other in their researches in number theory.
• However, Jacobi was not a wealthy man and Dirichlet, after visiting Jacobi and discovering his plight, wrote to Alexander von Humboldt asking him to help obtain some financial assistance for Jacobi from Friedrich Wilhelm IV.
• Dirichlet then made a request for assistance from Friedrich Wilhelm IV, supported strongly by Alexander von Humboldt, which was successful.
• Dirichlet obtained leave of absence from Berlin for eighteen months and in the autumn of 1843 set off for Italy with Jacobi and Borchardt.
• Schläfli and Steiner were also with them, Schläfli's main task being to act as their interpreter but he studied mathematics with Dirichlet as his tutor.
• Dirichlet did not remain in Rome for the whole period, but visited Sicily and then spent the winter of 1844/45 in Florence before returning to Berlin in the spring of 1845.
• Dirichlet had a high teaching load at the University of Berlin, being also required to teach in the Military College and in 1853 he complained in a letter to his pupil Kronecker that he had thirteen lectures a week to give in addition to many other duties.
• Dirichlet did not accept the offer from Göttingen immediately but used it to try to obtain better conditions in Berlin.
• The quieter life in Göttingen seemed to suit Dirichlet.
• We should now look at Dirichlet's remarkable contributions to mathematics.
• Shortly after publishing this paper Dirichlet published two further papers on analytic number theory, one in 1838 with the next in the following year.
• These papers introduce Dirichlet series and determine, among other things, the formula for the class number for quadratic forms.
• This work led him to the Dirichlet problem concerning harmonic functions with given boundary conditions.
• Dirichlet is also well known for his papers on conditions for the convergence of trigonometric series and the use of the series to represent arbitrary functions.
• Dirichlet's work is published in Crelle's Journal in 1828.
• Because of this work Dirichlet is considered the founder of the theory of Fourier series.
• important parts of mathematics were influenced by Dirichlet.
• With Dirichlet began the golden age of mathematics in Berlin.

Born 13 February 1805, Düren, French Empire (now Germany). Died 5 May 1859, Göttingen, Hanover (now Germany).

View full biography at MacTutor

Tags relevant for this person:

Algebra, Analysis, Origin Germany, Number Theory, Special Numbers And Numerals

Thank you to the contributors under CC BY-SA 4.0!

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non-Github:

@J-J-O'Connor

@E-F-Robertson

References

Adapted from other CC BY-SA 4.0 Sources:

1. O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive