Joseph Louis François Bertrand (; 11 March 1822 – 5 April 1900) was a French

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

who worked in the fields of

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777� ...

differential geometry Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multili ...

probability theory Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set o ...

economics Economics () is the social science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services. Economics focuses on the behaviour and intera ...

and

thermodynamics Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of the ...

Biography

Joseph Bertrand was the son of physician Alexandre Jacques François Bertrand and the brother of archaeologist

Alexandre Bertrand Alexandre Louis Joseph Bertrand (11 June 1820 – 1902) was a French archaeologist born in Rennes. Life He was the son of physician Alexandre Jacques François Bertrand (1795-1831) and elder brother to mathematician Joseph Louis Franço ...

. His father died when Joseph was only nine years old, but that did not stand in his way of learning and understanding algebraic and elementary geometric concepts, and he also could speak Latin fluently, all when he was of the same age of nine. At eleven years old he attended the course of the

École Polytechnique École may refer to: * an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée) * École (river), a tributary of the Seine flowing in région Île-de-France * École, Savoi ...

as an auditor (open courses). From age eleven to seventeen, he obtained two bachelor's degrees, a license and a PhD with a thesis on the mathematical theory of electricity and is admitted first to the 1839 entrance examination of the École Polytechnique. Bertrand was a professor at the

and

Collège de France The Collège de France (), formerly known as the ''Collège Royal'' or as the ''Collège impérial'' founded in 1530 by François I, is a higher education and research establishment (''grand établissement'') in France. It is located in Paris ne ...

, and was a member of the

Paris Academy of Sciences The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research. It was at th ...

where he was its permanent secretary for twenty-six years. He conjectured, in 1845, that there is at least one prime between ''n'' and 2''n'' − 2 for every ''n'' > 3.

Chebyshev Pafnuty Lvovich Chebyshev ( rus, Пафну́тий Льво́вич Чебышёв, p=pɐfˈnutʲɪj ˈlʲvovʲɪtɕ tɕɪbɨˈʂof) ( – ) was a Russian mathematician and considered to be the founding father of Russian mathematics. Chebyshe ...

proved this conjecture, now called

Bertrand's postulate In number theory, Bertrand's postulate is a theorem stating that for any integer n > 3, there always exists at least one prime number p with :n < p < 2n - 2. A less restrictive formulation is: for every

n > 1

, there is always ...

, in 1850. He was also famous for a paradox in the field of

probability Probability is the branch of mathematics concerning numerical descriptions of how likely an Event (probability theory), event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and ...

, now known as Bertrand's Paradox. There is another paradox in

game theory Game theory is the study of mathematical models of strategic interactions among rational agents. Myerson, Roger B. (1991). ''Game Theory: Analysis of Conflict,'' Harvard University Press, p.&nbs1 Chapter-preview links, ppvii–xi It has appli ...

that is named after him, called the Bertrand Paradox. In 1849, he was the first to define real numbers using what is now called a

Dedekind cut In mathematics, Dedekind cuts, named after German mathematician Richard Dedekind but previously considered by Joseph Bertrand, are а method of construction of the real numbers from the rational numbers. A Dedekind cut is a partition of the rat ...

. Bertrand translated into French

Carl Friedrich Gauss Johann Carl Friedrich Gauss (; german: Gauß ; la, Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes refer ...

's work on the

theory of errors In statistics, propagation of uncertainty (or propagation of error) is the effect of variables' uncertainties (or errors, more specifically random errors) on the uncertainty of a function based on them. When the variables are the values of exp ...

and the

method of least squares The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems (sets of equations in which there are more equations than unknowns) by minimizing the sum of the squares of the res ...

. In the field of

he reviewed the work on

oligopoly An oligopoly (from Greek ὀλίγος, ''oligos'' "few" and πωλεῖν, ''polein'' "to sell") is a market structure in which a market or industry is dominated by a small number of large sellers or producers. Oligopolies often result from ...

theory, specifically the Cournot Competition Model (1838) of French mathematician

Antoine Augustin Cournot Antoine Augustin Cournot (; 28 August 180131 March 1877) was a French philosopher and mathematician who also contributed to the development of economics. Biography Antoine Augustin Cournot was born at Gray, Haute-Saône. In 1821 he entered o ...

. His 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 equilibrium price was simply the competitive price. His boo
Thermodynamique
points out in Chapter XII, that thermodynamic entropy and temperature are only defined for reversible processes. He was one of the first people to point this out. In 1858 he was elected a foreign member of the

Royal Swedish Academy of Sciences The Royal Swedish Academy of Sciences ( sv, Kungliga Vetenskapsakademien) is one of the Swedish Royal Academies, royal academies of Sweden. Founded on 2 June 1739, it is an independent, non-governmental scientific organization that takes special ...

Works by Bertrand

*
Traité de calcul différentiel et de calcul intégral
' (Paris : Gauthier-Villars, 1864–1870) (2 volumes treatise on calculus) *
Rapport sur les progrès les plus récents de l'analyse mathématique
' (Paris: Imprimerie Impériale, 1867) (report on recent progress in mathematical analysis) *
Traité d'arithmétique
' (L. Hachette, 1849) (arithmetics) *
Thermodynamique
' (Paris : Gauthier-Villars, 1887) *
Méthode des moindres carrés
' (Mallet-Bachelier, 1855) (translation of

Gauss Johann Carl Friedrich Gauss (; german: Gauß ; la, Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes refer ...

's work on

least squares The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems (sets of equations in which there are more equations than unknowns) by minimizing the sum of the squares of the res ...

) *
Leçons sur la théorie mathématique de l'électricité / professées au Collège de France
' (Paris : Gauthier-Villars et fils, 1890) *
Calcul des probabilités
' (Paris : Gauthier-Villars et fils, 1889) *
Arago et sa vie scientifique
' (Paris : J. Hetzel, 1865) (biography of Arago) *
Blaise Pascal
' (Paris : C. Lévy, 1891) (biography) *
Les fondateurs de l'astronomie moderne: Copernic, Tycho Brahé, Képler, Galilée, Newton
' (Paris: J. Hetzel, 1865) (biographies)

References

External links

Bertrand, Joseph Louis Francois (1822–1900)

* *
Author profile
in the database

zbMATH zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure mathematics, pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Informa ...

{{DEFAULTSORT:Bertrand, Joseph Louis Francois 1822 births 1900 deaths Scientists from Paris 19th-century French mathematicians 19th-century French economists Differential geometers Number theorists Probability theorists Members of the Académie Française Members of the French Academy of Sciences Corresponding members of the Saint Petersburg Academy of Sciences École Polytechnique alumni Collège de France faculty Foreign Members of the Royal Society Members of the Royal Swedish Academy of Sciences Honorary members of the Saint Petersburg Academy of Sciences Lycée Saint-Louis alumni

Biography

Works by Bertrand

See also

Further reading

References

External links