BERTRAND, JOSEPH(-LOUIS-FRANOIS)

born March 11, 1822, Paris, Fr. died April 5, 1900, Paris French 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. Bertrand graduated from the cole Polytechnique in 1839 with a doctorate in thermodynamics and continued his work in engineering at the cole Nationale Suprieure des Mines while teaching at the Collge Saint-Louis. He later also taught at the cole Normale Suprieure and the Collge de France. The author of several mathematical textbooks, Bertrand gave his name to curves with a linear relationship between first and second curvature. In 1899 Bertrand's research on infinitesimal analysis led to his important work, Calcul des probabilits (Calculus of Probabilities), which introduced a problem in continuous probabilities known as Bertrand's paradox. Bertrand was a member of the French Academy of Sciences and, in 1884, became a member of the Acadmie Franaise.