Joseph Louis François Bertrand
Encyclopedia
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
who worked in the fields of number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
, differential geometry, probability theory
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
, economics
Economics
Economics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...
and thermodynamics
Thermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...
.
Bertrand was a professor at the École Polytechnique
École Polytechnique
The École Polytechnique is a state-run institution of higher education and research in Palaiseau, Essonne, France, near Paris. Polytechnique is renowned for its four year undergraduate/graduate Master's program...
and Collège de France
Collège de France
The Collège de France is a higher education and research establishment located in Paris, France, in the 5th arrondissement, or Latin Quarter, across the street from the historical campus of La Sorbonne at the intersection of Rue Saint-Jacques and Rue des Écoles...
. 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
Alexandre Jacques François Bertrand
Alexandre Jacques François Bertrand was a French physician and mesmerist who was a native of Rennes. He was the father of archaeologist Alexandre Bertrand and mathematician Joseph Bertrand...
and the brother of archaeologist Alexandre Bertrand
Alexandre Bertrand
Alexandre Louis Joseph Bertrand was a French archaeologist who was a native of Rennes. He was the son of physician Alexandre Jacques François Bertrand and elder brother to mathematician Joseph Louis François Bertrand .Bertrand studied at Ecole Normale Superieure de la rue d'Ulm, and after a...
. 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.
He conjectured, in 1845, that there is at least one prime between n and 2n − 2 for every n > 3. Chebyshev
Pafnuty Chebyshev
Pafnuty Lvovich Chebyshev was a Russian mathematician. His name can be alternatively transliterated as Chebychev, Chebysheff, Chebyshov, Tschebyshev, Tchebycheff, or Tschebyscheff .-Early years:One of nine children, Chebyshev was born in the village of Okatovo in the district of Borovsk,...
proved this conjecture, now called Bertrand's postulate, in 1850. He is also famous for a paradox in the field of probability
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
, now known as Bertrand's Paradox
Bertrand's paradox (probability)
The Bertrand paradox is a problem within the classical interpretation of probability theory. Joseph Bertrand introduced it in his work Calcul des probabilités as an example to show that probabilities may not be well defined if the mechanism or method that produces the random variable is not...
. There is another paradox in game theory
Game theory
Game theory is a mathematical method for analyzing calculated circumstances, such as in games, where a person’s success is based upon the choices of others...
that is named for him, called the Bertrand Paradox
Bertrand paradox (economics)
In economics and commerce, the Bertrand paradox—named after its creator, Joseph Bertrand—describes a situation in which two players reach a state of Nash equilibrium where both firms charge a price equal to marginal cost. The paradox is that in reality, it usually takes a large number of firms to...
.
Bertrand translated into French Carl Friedrich Gauss
Carl Friedrich Gauss
Johann Carl Friedrich Gauss was a German mathematician and scientist who contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, geophysics, electrostatics, astronomy and optics.Sometimes referred to as the Princeps mathematicorum...
's work on the theory of errors and the method of least squares.
In the field of economics
Economics
Economics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...
he reviewed the work on Oligopoly
Oligopoly
An oligopoly is a market form in which a market or industry is dominated by a small number of sellers . The word is derived, by analogy with "monopoly", from the Greek ὀλίγοι "few" + πόλειν "to sell". Because there are few sellers, each oligopolist is likely to be aware of the actions of the others...
Theory, specifically Cournot competition
Cournot competition
Cournot competition is an economic model used to describe an industry structure in which companies compete on the amount of output they will produce, which they decide on independently of each other and at the same time. It is named after Antoine Augustin Cournot who was inspired by observing...
model produced by the French mathematician and economist Augustin Cournot
Antoine Augustin Cournot
Antoine Augustin Cournot was a French philosopher and mathematician.Antoine Augustin Cournot was born at Gray, Haute-Saone. In 1821 he entered one of the most prestigious Grande École, the École Normale Supérieure, and in 1829 he had earned a doctoral degree in mathematics, with mechanics as his...
. The model of Bertrand competition
Bertrand competition
Bertrand competition is a model of competition used in economics, named after Joseph Louis François Bertrand . It describes interactions among firms that set prices and their customers that choose quantities at that price....
argued that Cournot had reached a very misleading conclusion; reworking Cournot's duopoly
Duopoly
A true duopoly is a specific type of oligopoly where only two producers exist in one market. In reality, this definition is generally used where only two firms have dominant control over a market...
model using prices rather than quantities as the strategic variables thus showing that the equilibrium
Economic equilibrium
In economics, economic equilibrium is a state of the world where economic forces are balanced and in the absence of external influences the values of economic variables will not change. It is the point at which quantity demanded and quantity supplied are equal...
price was simply the competitive price.
In 1858, he was elected a foreign member of the Royal Swedish Academy of Sciences
Royal Swedish Academy of Sciences
The Royal Swedish Academy of Sciences or Kungliga Vetenskapsakademien is one of the Royal Academies of Sweden. The Academy is an independent, non-governmental scientific organization which acts to promote the sciences, primarily the natural sciences and mathematics.The Academy was founded on 2...
.
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 GaussCarl Friedrich GaussJohann Carl Friedrich Gauss was a German mathematician and scientist who contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, geophysics, electrostatics, astronomy and optics.Sometimes referred to as the Princeps mathematicorum...
's work on least squaresLeast squaresThe method of least squares is a standard approach to the approximate solution of overdetermined systems, i.e., sets of equations in which there are more equations than unknowns. "Least squares" means that the overall solution minimizes the sum of the squares of the errors made in solving every...
) - 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's paradox (probability)Bertrand's paradox (probability)The Bertrand paradox is a problem within the classical interpretation of probability theory. Joseph Bertrand introduced it in his work Calcul des probabilités as an example to show that probabilities may not be well defined if the mechanism or method that produces the random variable is not...
- Bertrand paradox (economics)Bertrand paradox (economics)In economics and commerce, the Bertrand paradox—named after its creator, Joseph Bertrand—describes a situation in which two players reach a state of Nash equilibrium where both firms charge a price equal to marginal cost. The paradox is that in reality, it usually takes a large number of firms to...
- Bertrand's box paradoxBertrand's box paradoxBertrand's box paradox is a classic paradox of elementary probability theory. It was first posed by Joseph Bertrand in his Calcul des probabilités, published in 1889.There are three boxes:# a box containing two gold coins,...
- Bertrand's theorem
- Bertrand's ballot theorem