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 integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mat ...
,
differential geometry,
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 ...
,
economics
Economics () is the social science that studies the production, distribution, and consumption of goods and services.
Economics focuses on the behaviour and interactions of economic agents and how economies work. Microeconomics analyzes ...
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 th ...
.
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
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 ...
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 n ...
, 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 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 is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speakin ...
, now known as
Bertrand's Paradox. There is another paradox in
game theory 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 r ...
.
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
economics
Economics () is the social science that studies the production, distribution, and consumption of goods and services.
Economics focuses on the behaviour and interactions of economic agents and how economies work. Microeconomics analyzes ...
he reviewed the work on
oligopoly theory, specifically the
Cournot Competition Model (1838) of French mathematician
Antoine Augustin Cournot. 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
Thermodynamiquepoints 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.
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)
*
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)
See also
*
*
*
*
*
*
*
*
Bertrand curve
*
Further reading
*
References
External links
Bertrand, Joseph Louis Francois (1822–1900)*
*
Author profilein the database
zbMATH
zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Information Infrastruct ...
{{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