Joseph Louis François Bertrand | |
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| Born | (1822-03-11)11 March 1822 |
| Died | 5 April 1900(1900-04-05) (aged 78) Paris, France |
| Scientific career | |
| Fields | Mathematics |
Joseph Louis François Bertrand (French pronunciation:[ʒozɛflwifʁɑ̃swabɛʁtʁɑ̃]; 11 March 1822 – 5 April 1900) was a Frenchmathematician whose work emphasizednumber theory,differential geometry,probability theory,economics andthermodynamics.[1]
Joseph Bertrand was the son of physicianAlexandre Jacques François Bertrand and the brother of archaeologistAlexandre 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 theÉcole 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 theÉcole Polytechnique andCollège de France, and was a member of theParis 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 betweenn and 2n − 2 for everyn > 3.Chebyshev proved this conjecture, now termedBertrand's postulate, in 1850. He was also famous for two paradoxes ofprobability, known now asBertrand's Paradox and the Paradox ofBertrand's box. There is another paradox concerninggame theory that is named for him, known as theBertrand Paradox. In 1849, he was the first to define real numbers using what is now termed aDedekind cut.[2][3]
Bertrand translated into FrenchCarl Friedrich Gauss's work concerning thetheory of errors and themethod of least squares.
Concerningeconomics, he reviewed the work onoligopoly theory, specifically theCournot Competition Model (1838) of French mathematicianAntoine Augustin Cournot. HisBertrand 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 theequilibrium price was simply the competitive price.
His bookThermodynamique states in Chapter XII, that thermodynamic entropy and temperature are only defined forreversible processes. He was one of the first people to state this publicly.
In 1858 he was elected a foreign member of theRoyal Swedish Academy of Sciences.
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 ....
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