Background

Joseph Louis François Bertrand was born on March 11, 1822, in Paris, France, the son of Alexandre Jacques François Bertrand and Marie Caroline Belin. His father, Alexandre, had studied at the École Polytechnique where he had become friends with Jean-Marie Duhamel who later married Alexandre Bertrand's sister. Alexandre was a writer of popular science books but sadly he died young and after this tragic event Joseph, who was nine years old, went to live with Duhamel and his wife. Of course, this sad event did have the beneficial effect that Joseph was guided by Duhamel.

Education

At the age of eleven, Joseph Bertrand was allowed to attend classes at the École Polytechnique. In 1838, at sixteen, Bertrand took the degrees of bachelor of arts and bachelor of science, and at seventeen he received the doctor of science degree with a thesis in thermomechanics.

The same year (1839) Bertrand officially entered the École Polytechnique and also published his first paper on the mathematical theory of electricity. After two years of study there he entered the École des Mines (now Mines ParisTech) in 1841.

Career

In 1841 Bertrand became a professor of elementary mathematics at the Collège Saint-Louis (now Lycée Saint-Louis), a position that he filled until 1848. In May 1842 he and his brother, returning to Paris from a visit to their friends the Aclocques at Versailles, were nearly killed in a railroad accident which left a scar on Bertrand’s face.

In 1844, Bertrand also became répétiteur d'analyse at the École Polytechnique. Three years later he became examinateur d’admission at this school and suppléant of the physicist Jean-Baptiste Biot at the Collège de France.

In 1848, during the revolution, Bertrand served as a captain in the national guard. He published much during these years — in mathematical physics, in mathematical analysis, and in dilierential geometry. The first of Bertrand’s many textbooks, the Traité d’arithmétique, appeared in Paris in 1849 and was followed by the Traité élémentaire d’algèbre (1850); both were written for secondary schools. They were followed by textbooks for college instruction. Bertrand always knew how to fascinate his readers and his lecture audiences, and his books had a wide appeal because of content and style. In 1853 he edited and annotated the third edition of J. L. Lagrange’s Mécanique analytique. From the many publications in this period, one, Mémoire sur le nombre de valeurs ..., introduces the so-called problem of Bertrand: to find the subgroups of the symmetric groups of lowest possible index. Another publication, Mémoire sur la théorie des courbes à double courbure (1850), discusses curves with the property that a linear relation exists between first and second curvature; these are known as curves of Bertrand.

In 1852 Bertrand became professor of special mathematics at the Lycée Napoléon (now Lycée Henry IV). He also taught at the École Normale Supérieure. In 1856 he replaced Jacques Charles François Sturm as professor of analysis at the École Polytechnique, where he became the colleague of Duhamel. He then left secondary education to pursue his academic career. In 1862 he succeeded Biot at the Collège de France. Bertrand held his position at the École Polytechnique until 1895, that at the Collège de France until his death.

During the Commune of 1871, Bertrand’s Paris house was burned, and many of his manuscripts were lost, among them those of the third volume of his textbook on calculus and his book on thermodynamics. He was able to rewrite and publish the latter as Thermodynamique. Afterward he lived at Sèvres and then at Viroflay. At his home, Bertrand enjoyed being the center of a lively intellectual circle.

Bertrand’s publications, apart from his textbooks, cover many fields of mathematics. Although his work lacks the fundamental character of that of the great mathematicians of his period, his often elegant studies on the theory of curves and surfaces, of differential equations and their application to analytical mechanics, of probability, and of the theory of errors were widely read. Many of his articles are devoted to subjects in theoretical physics, including capillarity, theory of sound, electricity, hydrodynamics, and even the flight of birds. In 1889 Bertrand’s research on infinitesimal analysis led to his important work, Calcul des probabilités, which introduced the problem known as Bertrand’s paradox concerning the probability that a "random chord" of a circle will be shorter than its radius. His name is also associated with Bertrand curves in differential geometry.

From 1865 until his death Bertrand edited the Journal des savants. For this periodical, as for the Revue des deux mondes, he wrote articles of a popular nature, many dealing with the history of science. This interest in history of science appears also in the many éloges he wrote as secrétaire perpétuel of the Academy, among which are biographies of Poncelet, Élie de Beaumont, Lamé, Lcverrier, Charles Dupin, Foucault, Poinsot, Chasles, Cauchy, and F. F. Tisserand. He also wrote papers on Viète, Fresnel, Lavoisier, and Comte, and books on d’Alembert and Pascal.

Bertrand spent the later part of his life in the midst of his large family, surrounded by his friends, who were many and distinguished. Joseph Bertrand died on April 5, 1900, in Paris, Ile-de-France, France.

Achievements

• Joseph Louis François Bertrand was a mathematician and educator remembered for his elegant applications of differential equations to analytical mechanics, particularly in thermodynamics, and for his work on statistical probability and the theory of curves and surfaces.

Works

More photos

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  • Traite D'Arithmetique 1849
  • Traite D'Algebre 1850
  • Calcul des probabilités 1888
  • D'Alembert 1889

Views

Quotations: "The roulette wheel has neither conscience nor memory."

"The first successes were such that one might suppose all the difficulties of science overcome in advance, and believe that the mathematician, without being longer occupied in the elaboration of pure mathematics, could turn his thoughts exclusively to the study of natural laws."

Membership

In addition, Joseph Bertrand was a member of the Royal Society, the Russian Academy of Sciences (then Saint Petersburg Academy of Sciences), the Lincean Academy and the Academy of Sciences of Turin.

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  In 1854 Joseph Bertrand was elected to the French Academy of Sciences.

  French Academy of Sciences , France

  1854

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  In 1858 Joseph Bertrand was elected a foreign member of the Royal Swedish Academy of Sciences.

  Royal Swedish Academy of Sciences , Sweden

  1858

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  On December 4, 1884, Joseph Bertrand replaced the chemist Jean-Baptiste Dumas in the Académie Française.

  Académie française , France

  1884

Personality

Physical Characteristics: Joseph Bertrand got a scar on his face after railroad accident.

Connections

In 1844, Joseph Bertrand married Louise Céline Acloque, by whom he had several children.

Father:

Alexandre Jacques François Bertrand

Mother:

Marie Caroline Belin

Brother:

Alexandre Louis Joseph Bertrand

Alexandre Louis Joseph Bertrand was a French archaeologist and a curator of the Gallo-Roman museum in Saint-Germain-en-Laye.

Sister:

Louise Pauline Arsène Hermite (Bertrand)

late wife:

Louise Céline Acloque

Son:

Marcel-Alexandre Bertrand

Marcel-Alexandre Bertrand was a French stratigrapher and structural geologist, who is noted for his geologic surveys of the Provence region of southeastern France and the Jura and Alps mountain ranges.

Daughter:

Gabrielle Jane Bertrand

Daughter:

Berthe Lucie Bertrand

Son:

Joseph Désiré Bertrand

Son:

Léon Gratien Bertrand