Lagrange, Joseph Louis

Born Jan. 25, 1736, in Turin; died Apr. 10, 1813, in Paris. French mathematician and specialist in mechanics. Member of the Paris Academy of Sciences (1722).

The son of an impoverished official, Lagrange studied mathematics on his own. At the age of 19 he was already a professor at the artillery school in Turin. In 1759 he was elected a member of the Berlin Academy of Sciences and was its president from 1766 to 1787. He moved to Paris in 1787 and was appointed a professor at the Ecole Normale in 1795 and at the Ecole Polytechnique in 1797.

Lagrange’s most important works were devoted to the calculus of variations and to analytic and theoretical mechanics. Working from results obtained by L. Euler, he developed the principal concepts of the calculus of variations and proposed a general analytic method (the variational method) for solving variational problems. In his classical treatise Mécanique analytique (1788; Russian translation, vols. 1–2, 2nd ed., 1950), Lagrange proposed a “general formula,” the principle of virtual displacements, as the basis of all statics and a second “general formula,” which combines the virtual displacements principle and d’Alembert’s principle, as the basis of all dynamics (d’Alembert -Lagrange principle). The general formula of statics can be obtained as a particular case from the general formula for dynamics. Lagrange introduced generalized coordinates and provided the form for the equations of motion that bears his name.

Lagrange strove to establish “simple” and “universal” principles of mechanics. In doing this, he proceeded from concepts characteristic of 18th-century progressive scientists that only those principles can be true that correspond to objective reality.

Lagrange also made outstanding contributions to mathematical analysis (a formula for the remainder in a Taylor’s series, the finite increments formula, the theory of undetermined multipliers), number theory, algebra (symmetrical functions of the roots of an equation, the theory and applications of continued fractions), mathematical cartography, and astronomy, as well as to problems in differential equations (the theory of singular solutions, the method of variation of constants) and interpolation.