French mathematician and educator remembered for his elegant applications of differential equations (differential equation) to analytical mechanics, particularly in thermodynamics, and for his work on statistical probability (probability theory) and the theory of curves and surfaces.

The nephew of the mathematician Jean-Marie-Constant Duhamel (Duhamel, Jean-Marie-Constant), Bertrand was also related by marriage to the mathematicians Paul Appell, Émile Borel (Borel, Émile), Charles Hermite (Hermite, Charles), and Émile Picard (Picard, Charles-Émile). Bertrand graduated from the École Polytechnique in 1839 with a doctorate in thermodynamics and continued his work in engineering at the École Nationale Supérieure des Mines while teaching at the Collège Saint-Louis. He later also taught at the École Normale Supérieure, the École Polytechnique, and the Collège de France (France, Collège de).

In 1889 Bertrand's research on infinitesimal analysis led to his important work, Calcul des probabilités (calculus) (“Calculus of Probabilities”), which introduced the problem known as Bertrand's paradox concerning the probability (probability theory) that a “random chord” of a circle will be shorter than its radius. His name is also associated with Bertrand curves in differential geometry.

The author of several mathematical textbooks, Bertrand also wrote the books D'Alembert (1889) and Pascal (1891), as well as a number of biographical essays. He was the editor of Journal des Savants (1865–1900) and contributed many popular articles on the history of science. In 1856 he was elected to the French Academy of Sciences (Sciences, Academy of), where as sécrétaire pérpetuel, a position he held from 1874 until his death, his influence in promoting mathematics and mathematicians was strongly felt. In 1884 he became a member of the literary French Academy.