Gaspard Monge (1746-1818): Application of Geometry to Analysis

Abstract

Two centuries after the death of the mathematician Gaspard Monge, his main results are presented, for the period preceding his political and organizational commitment during the French Revolution and the Napoleonic era in Italy and Egypt. After an examination of the fortune of his works in Russia, Monge’s main contributions to the theory of partial differential equations of the first order, to the solution of the minimal surface equation (with his pupil Meusnier) and to the first study of the optimal transport problem (Monge-Ampère equation) are underlined. These subjects are well developed in the current mathematical research in analysis and in differential geometry.