Pierre de Fermat — French mathematician. He gave the modern definition of a function. In more advanced work, he was concerned to see analysis applied to number theory and mathematical physics. Subjects: Science and technology — Mathematics and Computer Science. View all related items in Oxford Reference ». All Rights Reserved.
Under the terms of the licence agreement, an individual user may print out a PDF of a single entry from a reference work in OR for personal use for details see Privacy Policy and Legal Notice. Oxford Reference. 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 set off for Italy with Jacobi and Borchardt.
After stopping in several towns and attending a mathematical meeting in Lucca, they arrived in Rome on 16 November Dirichlet had a high teaching load at the University of Berlin, being also required to teach in the Military College and in he complained in a letter to his pupil Kronecker that he had thirteen lectures a week to give in addition to many other duties. He requested of the Prussian Ministry of Culture that he be allowed to end lecturing at the Military College. He had more time for research and some outstanding research students.
However, sadly he was not to enjoy the new life for long. In the summer of he lectured at a conference in Montreux but while in the Swiss town he suffered a heart attack.
We should now look at Dirichlet's remarkable contributions to mathematics. We have already commented on his contributions to Fermat's Last Theorem made in Around this time he also published a paper inspired by Gauss 's work on the law of biquadratic reciprocity.
Details are given in [ 13 ] where Rowe discusses the importance of the intellectual and personal relationship between Gauss and Dirichlet.
He proved in that in any arithmetic progression with first term coprime to the difference there are infinitely many primes. This had been conjectured by Gauss. Davenport wrote in see [ 16 ] :- Analytic number theory may be said to begin with the work of Dirichlet, and in particular with Dirichlet's memoir of on the existence of primes in a given arithmetic progression.
Shortly after publishing this paper Dirichlet published two further papers on analytic number theory, one in 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.
He also proposed in the modern definition of a function:- If a variable y is so related to a variable x that whenever a numerical value is assigned to x, there is a rule according to which a unique value of y is determined, then y is said to be a function of the independent variable x. In mechanics he investigated the equilibrium of systems and potential theory. These investigations began in with papers which gave methods to evaluate multiple integrals and he applied this to the problem of the gravitational attraction of an ellipsoid on points both inside and outside.
He turned to Laplace 's problem of proving the stability of the solar system and produced an analysis which avoided the problem of using series expansion with quadratic and higher terms disregarded. This work led him to the Dirichlet problem concerning harmonic functions with given boundary conditions. Some work on mechanics later in his career is of quite outstanding importance.
In he studied the problem of a sphere placed in an incompressible fluid, in the course of this investigation becoming the first person to integrate the hydrodynamic equations exactly. 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.
These series had been used previously by Fourier in solving differential equations. Dirichlet's work is published in Crelle's Journal in Earlier work by Poisson on the convergence of Fourier series was shown to be non-rigorous by Cauchy.
Rent this article via DeepDyve. Wilson What was Jakob Steiner like? Mathematical Intelligencer 40 3 , 51— A typed version of the Hirst diaries is held at the Royal Institution in London. It was edited by W.
Brock and R. MacLeod and published in microfiche by Mansell, London, in The quotations included here from pages —, —, —, , —, , , —, —, , , and appear by courtesy of the Royal Institution. Helen Gardner and Robin J.
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