View source for Biography:Joseph Bertrand

{{Short description|French mathematician}}
{{for multi|the basketball player|Joseph Bertrand (basketball)|the Olympic swimmer|Joseph Bertrand (swimmer)}}
{{Infobox scientist
| name              = Joseph Louis François Bertrand
| image             = Bertrand.jpg
| birth_date        = {{birth date |1822|3|11|df=y}}
| birth_place       = [[Place:Paris|Paris, France]]
| death_date        = {{death date and age |1900|4|5 |1822|3|11|df=y}}
| death_place       = Paris, France
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| fields            = [[Mathematics]]
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'''Joseph Louis François Bertrand''' ({{IPA-fr|ʒozɛf lwi fʁɑ̃swa bɛʁtʁɑ̃}}; 11 March 1822 – 5 April 1900) was a French [[Biography:Mathematician|mathematician]] whose work emphasized [[Number theory|number theory]], [[Differential geometry|differential geometry]], [[Probability theory|probability theory]], [[Finance:Economics|economics]] and [[Physics:Thermodynamics|thermodynamics]].<ref>[https://archive.org/details/logesacadmiq00bertuoft Éloge historique de Joseph Bertrand par Gaston Darboux (1902)]</ref>

==Biography==

Joseph Bertrand was the son of physician Alexandre Jacques François Bertrand and the brother of archaeologist Alexandre Bertrand. His father died when Joseph was only nine years old; by that time he had learned a substantial amount of mathematics and could speak Latin fluently.
At eleven years old he attended the course of the École Polytechnique as an auditor. From age eleven to seventeen, he obtained two bachelor's degrees, a license and a PhD with a thesis concerning the mathematical theory of electricity, and was admitted to the 1839 entrance examination of the École Polytechnique. Bertrand was a professor at the École Polytechnique and Collège de France, and was a member of the Paris Academy of Sciences of which he was the permanent secretary for twenty-six years.

He conjectured, in 1845, that there is at least one prime number between ''n'' and 2''n''&nbsp;−&nbsp;2 for every ''n''&nbsp;>&nbsp;3. [[Biography:Pafnuty Chebyshev|Chebyshev]] proved this conjecture, now termed [[Bertrand's postulate]], in 1850. He was also famous for two paradoxes of [[Probability|probability]], known now as [[Bertrand paradox (probability)|Bertrand's Paradox]] and the Paradox of [[Bertrand's box paradox|Bertrand's box]]. There is another paradox concerning [[Game theory|game theory]] that is named for him, known as the [[Finance:Bertrand paradox (economics)|Bertrand Paradox]]. In 1849, he was the first to define real numbers using what is now termed a [[Dedekind cut]].<ref>{{cite book|last=Bertrand|first=Joseph|title=Trait'e d'Arithmetique |url = https://gallica.bnf.fr/ark:/12148/bpt6k77735p/f209.image.r=%22joseph%20bertrand%22 |year=1849|at=page 203|quote=An incommensurable number can be defined only by indicating how the magnitude it expresses can be formed by means of unity. In what follows, we suppose that this definition consists of indicating which are the commensurable numbers smaller or larger than it ....}}</ref><ref>{{cite book |last=Spalt |first=Detlef |title=Eine kurze Geschichte der Analysis|year=2019|publisher=Springer|doi=10.1007/978-3-662-57816-2|isbn=978-3-662-57815-5 |s2cid=186745152 }}</ref>

Bertrand translated into French [[Biography:Carl Friedrich Gauss|Carl Friedrich Gauss]]'s work concerning the theory of errors and the method of least squares.

Concerning [[Finance:Economics|economics]], he reviewed the work on [[Finance:Oligopoly|oligopoly]] theory, specifically the [[Finance:Cournot competition|Cournot Competition Model]] (1838) of French mathematician [[Biography:Antoine Augustin Cournot|Antoine Augustin Cournot]]. His [[Finance:Bertrand competition|Bertrand Competition Model]] (1883) argued that Cournot had reached a very misleading conclusion, and he reworked it using prices rather than quantities as the strategic variables, thus showing that the [[Finance:Economic equilibrium|equilibrium]] price was simply the competitive price.

His book [http://gallica.bnf.fr/notice?N=FRBNF30098024 Thermodynamique] states in Chapter XII, that thermodynamic entropy and temperature are only defined for [[Physics:Reversible process (thermodynamics)|reversible process]]es. He was one of the first people to state this publicly.

In 1858 he was elected a foreign member of the Royal Swedish Academy of Sciences.

==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)
* ''[https://gallica.bnf.fr/ark:/12148/bpt6k99724x.texteImage Thermodynamique]'' (Paris : Gauthier-Villars, 1887)
* ''[http://gallica.bnf.fr/ark:/12148/bpt6k996041 Méthode des moindres carrés]'' (Mallet-Bachelier, 1855) (translation of [[Biography:Carl Friedrich Gauss|Gauss]]'s work on [[Least squares|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/ark:/12148/bpt6k99602b Calcul des probabilités ]'' (Paris : Gauthier-Villars et fils, 1889)<ref>{{cite journal|author=Davis, Ellery W.|title=Review: ''Calcul des Probabilités'', par J. Bertrand|journal=Bull. Amer. Math. Soc.|year=1891|volume=1|issue=1|pages=16–25|url=https://www.ams.org/journals/bull/1891-01-01/S0002-9904-1891-00020-6/S0002-9904-1891-00020-6.pdf|doi=10.1090/s0002-9904-1891-00020-6|doi-access=free}}</ref>
* ''[http://gallica.bnf.fr/notice?N=FRBNF30097972 Arago et sa vie scientifique]'' (Paris : J. Hetzel, 1865) (biography of Arago)
* ''[http://gallica.bnf.fr/ark:/12148/bpt6k681143 Blaise Pascal]'' (Paris : C. Lévy, 1891) (biography)
* ''[http://gallica.bnf.fr/ark:/12148/bpt6k777319 Les fondateurs de l'astronomie moderne: Copernic, Tycho Brahé, Képler, Galilée, Newton]'' (Paris: J. Hetzel, 1865) (biographies)

==See also==

* {{annotated link|Bertrand paradox (probability)}}
* {{annotated link|Finance:Bertrand paradox (economics)}}
* {{annotated link|Bertrand's box paradox}}
* {{annotated link|Bertrand's postulate}}
* {{annotated link|Physics:Bertrand's theorem}}
* {{annotated link|Bertrand's ballot theorem}}
* {{annotated link|Bertrand–Edgeworth model}}
* [[Differentiable curve#Bertrand curve|Bertrand curve]]
* {{annotated link|Buckingham π theorem}}

==Further reading==
*{{DSB
|first=D.J.
|last=Struik
|title=Bertrand, Joseph Louis Francois
|volume=2
|pages=87–89
}}

==References==
{{Reflist}}

==External links==
*[http://scienceworld.wolfram.com/biography/Bertrand.html Bertrand, Joseph Louis Francois (1822–1900)]
*[https://web.archive.org/web/20040404032538/http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Bertrand.html Joseph Louis François Bertrand] (archived 4 April 2004)
*[https://web.archive.org/web/20160303171340/http://www-gap.dcs.st-and.ac.uk/~history/References/Bertrand.html References for Joseph Bertrand] (archived 3 March 2016)
* [http://www-history.mcs.st-andrews.ac.uk/Biographies/Bertrand.html Joseph Louis François Bertrand]
* {{Gutenberg author |id=6114| name=Joseph Bertrand}}
* {{Internet Archive author |sname=Joseph Bertrand}}
* [https://zbmath.org/authors/?q=ai:bertrand.joseph-louis-francois Author profile] in the database [[Zentralblatt MATH|zbMATH]]



{{DEFAULTSORT:Bertrand, Joseph Louis Francois}}
[[Category:Differential geometers]]
[[Category:Number theorists]]
[[Category:Probability theorists]]

{{Sourceattribution|Joseph Bertrand}}