Lagrange, Joseph-Louis (1736–1813)

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LAGRANGE, JOSEPH-LOUIS (1736–1813)

LAGRANGE, JOSEPH-LOUIS (1736–1813), French mathematician. Lagrange, a leading mathematician of the Enlightenment, contributed to a wide range of fields and played a leading role in the establishment of the metric system. Born in Turin to a French family of high officials in the service of the dukes of Savoy, Lagrange was destined for a career in the law. While in his teens he was introduced to the study of advanced mathematics when he read a treatise on calculus by the English astronomer royal Edmond Halley (1656–1742). Lagrange's remarkable mathematical abilities were quickly recognized, and in 1755, at the age of nineteen, he was appointed professor of mathematics at the artillery school of Turin. He spent the next eleven years in his native city and established his reputation as one of the leading mathematicians in Europe. In 1766 Lagrange left Turin to become the director of the mathematics section at the Berlin Academy, taking over from Leonhard Euler (1707–1783), who had recently returned to St. Petersburg. In 1787, following the death of his patron Frederick II of Prussia (ruled 1740–1786), Lagrange moved to Paris as "veteran" member of the Paris Academy of Sciences. He remained there until his death, and during the tumultuous years that followed, he managed to stay apart from the political fray that absorbed many of his colleagues.

By the age of twenty Lagrange had already made one of his most important contributions to mathematics, the calculus of variations, which he developed along with Euler. Unlike the ordinary calculus, which analyzes the point characteristics of specific functions, the calculus of variations deals with the extremum characteristics of functions as a whole. The work quickly attracted the attention of Pierre-Louis Moreau de Maupertuis (1698–1759), president of the Berlin Academy, who used it to support his "principle of least action" against numerous critics.

Lagrange successfully applied his calculus of variations to many scientific fields. In 1759 he sided with Euler against Jean Le Rond d'Alembert (1717–1783) in the controversy on the proper mathematical representation of vibrating strings. In the late 1760s and the early 1770s Lagrange took part in several prize competitions sponsored by the Paris Academy on questions in celestial mechanics. He won the grand prize several times with essays on the orbit and rotation of the Moon, the trajectories of comets, the orbital perturbations of the moons of Jupiter, and the three body problem in general. After publishing on these and other topics in solid and fluid mechanics throughout his career, he summarized his work in Mécanique analytique in 1788. There he proposed to establish mechanics as a series of general formulas whose development would yield the necessary equations for the solution of each specific problem. Lagrange also contributed substantially to debates on the foundations of calculus, promoting a purely algebraic understanding of the subject as against the geometric views of colleagues such as d'Alembert.

In 1790 the French Constituent Assembly established the Committee on Weights and Measures and made Lagrange its chairman. In this position Lagrange was largely responsible for the adoption and diffusion of the decimal metric system. During the 1790s he taught at the newly established École Polytechnique, and in his later years he worked on revising and republishing his works. During the empire he came under the patronage of Napoléon I, who made Lagrange a count of the empire, a senator, and a grand officer of the Legion of Honor. On his death in 1813 Lagrange was entombed in the Pantheon.

See also Alembert, Jean Le Rond d' ; Astronomy ; Enlightenment ; Euler, Leonhard ; Mathematics ; Weights and Measures .

BIBLIOGRAPHY

Primary Source

Lagrange, Joseph-Louis. Analytical Mechanics. Translated and edited by Auguste Boissonnade and Victor N. Vagliente. Dordrecht, Boston, and London, 1997. Translation of Mécanique analytique, nouvelle édition (1811).