Joseph Louis François Bertrand

Joseph Louis François Bertrand (March 11, 1822 – April 5, 1900, born and died in Paris) was a French mathematician who worked in the fields of number theory, differential geometry, probability theory, and thermodynamics.

Bertrand was a professor at the École Polytechnique and Collège de France. He was a member of the Paris Academy of Sciences and was its permanent secretary for twenty-six years. He was the son of physician Alexandre Jacques François Bertrand and the brother of archaeologist Alexandre Bertrand.

He conjectured, in 1845, that there is at least one prime between "n" and 2"n" − 2 for every "n" > 3. Chebyshev proved this conjecture, now called Bertrand's postulate, in 1850. He is also famous for a paradox in the field of probability, now known as Bertrand's Paradox. There is another paradox in game theory that is named for him, called the Bertrand Paradox.

Bertrand translated into French Carl Friedrich Gauss's work on the theory of errors and the method of least squares.

In the field of economics he reviewed the work on Oligopoly Theory, specifically Cournot competition model produced by the French mathematician and economist Augustin Cournot. The model of Bertrand competition argued that Cournot had reached a misleading conclusion; reworking Cournot's duopoly model using prices rather than quantities as the strategic variables thus showing that the equilibrium price was simply the competitive price - a striking conclusion largely ignored until recently.

Works by Bertrand

* " [http://gallica.bnf.fr/notice?N=FRBNF30098036 Traité de calcul différentiel et de calcul intégral] " (Paris : Gauthier-Villars, 1864-1870) (2 volumes treatise on calculus)
* " [http://gallica.bnf.fr/notice?N=FRBNF30098020 Rapport sur les progrès les plus récents de l'analyse mathématique] " (Paris: Imprimerie Impériale, 1867) (report on recent progress in mathematical analysis)
* " [http://gallica.bnf.fr/notice?N=FRBNF30098025 Traité d'arithmétique] " (L. Hachette, 1849) (arithmetics)
* " [http://gallica.bnf.fr/notice?N=FRBNF30098024 Thermodynamique] " (Paris : Gauthier-Villars, 1887)
* " [http://gallica.bnf.fr/notice?N=FRBNF37259333 Méthode des moindres carrés] " (Mallet-Bachelier, 1855) (translation of Gauss's work on least squares)
* " [http://gallica.bnf.fr/notice?N=FRBNF30098013 Leçons sur la théorie mathématique de l'électricité / professées au Collège de France] " (Paris : Gauthier-Villars et fils, 1890)
* " [http://gallica.bnf.fr/notice?N=FRBNF30097974 Calcul des probabilités ] " ( Paris : Gauthier-Villars et fils, 1889)
* " [http://gallica.bnf.fr/notice?N=FRBNF30097972 Arago et sa vie scientique] " (Paris : J. Hetzel, 1865) (biography of Arago)
* " [http://gallica.bnf.fr/notice?N=FRBNF30097973 Blaise Pascal] " (Paris : C. Lévy, 1891) (biography)
* " [http://gallica.bnf.fr/notice?N=FRBNF30097982 Les fondateurs de l'astronomie moderne: Copernic, Tycho Brahé, Képler, Galilée, Newton] " (Paris: J. Hetzel, 1865) (biographies)

ee also

* Bertrand's paradox (probability)
* Bertrand paradox (economics)
* Bertrand's box paradox
* Bertrand's theorem

Further reading

DSB
first=D.J.
last=Struik
title=Bertrand, Joseph Louis Francois
volume=2
pages=87-89

External links

* [http://scienceworld.wolfram.com/biography/Bertrand.html Bertrand, Joseph Louis Francois (1822–1900)]
* [http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Bertrand.html Joseph Louis François Bertrand]
* [http://www-gap.dcs.st-and.ac.uk/~history/References/Bertrand.html References for Joseph Bertrand]
*gutenberg author | id=Joseph_Bertrand | name=Joseph Bertrand
* [http://www-history.mcs.st-andrews.ac.uk/Biographies/Bertrand.html Joseph Louis François Bertrand]