Joseph Louis François Bertrand

Joseph Louis François Bertrand ( born March 11, 1822 in Paris, † April 5, 1900 ) was a French mathematician and educator.

Life

Bertrand was known for his elegant applications of differential equations in the field of analytical mechanics, especially of thermodynamics, as well as for his work on statistical probability, the theory of curves and surface theory.

Bertrand grew after the early death of his father to the husband of his sister Jean -Marie Duhamel and had this early contact with mathematics. Later, the mathematician Charles Hermite married ( he married Bertrand's sister ), Paul appeal and Emile Picard in Bertrand's family, so that his house an intellectual meeting place. Bertrand was already talking with 9 years of Latin fluently and was admitted at age 11 to lectures at the École polytechnique. There he was given at the earliest opportunity with 16 years of an academic degree and a doctorate on thermodynamics one year later in 1839 and published his first work. In the same year he studied formally at the École Polytechnique and then at the Ecole des Mines. 1841 to 1849 he was a high school teacher of mathematics at the Lycée Saint- Louis. During this time he was seriously injured in 1842 in a train accident and suffered permanent facial injuries. In the 1848 revolution, he was captain of the National Guard. In 1844 he was a tutor at the École Polytechnique and from 1856 as the successor of Charles -François Sturm professor there. From 1852 he was a teacher at the Lycée Henri IV and taught at the École normale supérieure. In 1849, he was the successor of Jean -Baptiste Biot at the Collège de France, where he taught until an interruption from 1878 to 1886, as well as at the same time at the École Polytechnique.

In 1845 he suspected that for every n ≥ 1, at least one prime p with n

In economics, he developed the theory of oligopoly on ( Bertrand competition), in particular the competitive model of Augustin Cournot.

From him comes Bertrand's paradox in probability, contained in his book Calcul des probabilites of 1888, in which, incidentally, he did not mention Tschebyschoff. The book served Henri Poincaré as the starting point of his own textbook in 1896.

Bertrand was known in his time as a writer of textbooks, as textbooks on arithmetic and elementary algebra (1850), Analysis ( in two volumes in 1864, 1870), Thermodynamics (1887 ), Electrodynamics ( 1890). He also wrote biographies of Blaise Pascal, and of astronomers such as Kepler.

In 1856 he became a member of the Paris Academy of Sciences, whose permanent secretary he was from 1874. He was also a Grand Officer of the Legion of Honor and a member of the Accademia dei Lincei.

Bertrand had been married since 1844 and had three sons, of whom Marcel Bertrand a well-known geologist was.

Works

• Traité de calcul de calcul intégral et différentiel (Paris: Gauthier -Villars, 1864-1870 )
• Rapport sur ​​les progrès les plus récents de l' analysis mathématique (Paris: Imprimerie Imperiale, 1867)
• Traité d' arithmétique (L. Hachette, 1849)
• Thermodynamique (Paris: Gauthier -Villars, 1887)
• Translation of Gauss: Méthode of moindres scarves ( Mallet- Bachelier, 1855)
• Leçons sur la théorie de l' Electricité mathématique / professées au Collège de France (Paris: Gauthier -Villars et fils, 1890)
• Calcul des probabilites (Paris: Gauthier -Villars et fils, 1889)
• Blaise Pascal (Paris: C. Lévy, 1891)
• Les fondateurs de l' modern astronomy: Copernic, Brahé Tycho, Kepler, a Galileo, Newton (Paris: J. Hetzel, 1865)
• L' Académie des sciences et les académiciens de 1666 a 1793 (Paris: J. Hetzel, 1869)