January 25, 1736: Joseph-Louis Lagrange is born
Joseph-Louis Lagrange (1736-1813)
Scientific contributions to: Astronomy, Mathematics
Known for: Analytical mechanics, Celestial mechanics, Mathematical analysis, Number theory
Giuseppe Luigi Lagrangia on his original name, Lagrange was an Italian-French mathematician who made great contributions to number theory and to analytic and celestial mechanics.
His interest in mathematics was aroused by the chance reading of a memoir by the English astronomer Edmond Halley. At 19 he was teaching mathematics at the artillery school of Turin. His early publications, on the propagation of sound and on the concept of maxima and minima (in calculus of variations), were well received; the Swiss mathematician Leonhard Euler praised Lagrange’s version of his theory of variations.
By 1761 Lagrange was already recognized as one of the greatest living mathematicians. In 1764 he was awarded a prize offered by the French Academy of Sciences for an essay on the libration of the Moon. In this essay he used the equations that now bear his name. His success encouraged the academy in 1766 to propose, as a problem, the theory of the motions of the satellites of Jupiter. The prize was again awarded to Lagrange, and he won the same distinction in 1772, 1774, and 1778. In 1766, on the recommendation of Euler and the French mathematician Jean d’Alembert, Lagrange went to Berlin to fill a post at the academy vacated by Euler, at the invitation of Frederick the Great, who expressed the wish of “the greatest king in Europe” to have “the greatest mathematician in Europe” at his court.
Lagrange stayed in Berlin until 1787. His productivity in those years was prodigious: he published papers on the three-body problem, which concerns the evolution of three particles mutually attracted according to Sir Isaac Newton’s law of gravity; differential equations; prime number theory; the fundamentally important number-theoretic equation that has been identified (incorrectly by Euler) with John Pell’s name; probability; mechanics; and the stability of the solar system. In his long paper “Réflexions sur la résolution algébrique des équations” (1770; “Reflections on the Algebraic Resolution of Equations”), he inaugurated a new period in algebra and inspired Évariste Galois to his group theory.
When Frederick died, Lagrange preferred to accept Louis XVI’s invitation to Paris. From the Louvre he published his classic “Mecanique Analytique”, a lucid synthesis of the hundred years of research in mechanics since Newton, based on his own calculus of variations, in which certain properties of a mechanistic system are inferred by considering the changes in a sum (or integral) that are due to conceptually possible (or virtual) displacements from the path that describes the actual history of the system. This led to independent coordinates that are necessary for the specifications of a system of a finite number of particles, or “generalized coordinates”. It also led to the so-called Lagrangian equations for a classical mechanical system in which the kinetic energy of the system is related to the generalized coordinates, the corresponding generalized forces, and the time.
When the École Centrale des Travaux Publics (later renamed the École Polytechnique) was opened in 1794, he became, with Gaspard Monge, its leading professor of mathematics. His lectures were published as “Théorie des fonctions analytiques” (”Theory of Analytic Functions”, 1797) and “Leçons sur le calcul des fonctions” (”Lessons on the Calculus of Functions”, 1804) and were the first textbooks on real analytic functions. In them Lagrange tried to substitute an algebraic foundation for the existing and problematic analytic foundation of calculus—although ultimately unsuccessful, his criticisms spurred others to develop the modern analytic foundation. Lagrange also continued to work on his “Mécanique analytique”, but the new edition appeared only after his death.
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Article: From “Lagrange, Joseph-Louis, comte de l’Empire”, Encyclopædia Britannica 2006 Ultimate Reference Suite DVD. Picture: Joseph-Louis Lagrange. Author: N/A. Year: N/A.
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