Joseph Louis Lagrange Biography

Although Joseph Louis Lagrange was born in Turin, in the Italian kingdom of Piedmont, on January 25, 1736, he was of French ancestry. His father had planned for him to become a lawyer, but at school Joseph read a paper by Edmond Halley regarding the use of algebra in optics and was so intrigued he took up the study of mathematics.

Lagrange proved to be a mathematical prodigy; he was teaching geometry at the Royal Artillery School in Turin at the age of eighteen, and he established the Turin Academy of Sciences in 1758. In 1755 he came to the attention of mathematician Leonhard Euler to whom Lagrange sent an article he had written entitled "On the Calculus of Variations" (variations of orbits in celestial mechanics). Euler was in the process of addressing this topic himself, and he was so impressed that he withheld his own work, thus allowing Lagrange to publish first, and he had Lagrange admitted to the Berlin Academy.

In 1764, Lagrange won a prize from the Paris Academy for his work on the libration (wobble) of the Moon, and began to apply himself toward developing a systematization of mechanics. This had been started by Galileo, but Lagrange was able to establish several general equations for describing motion in mechanical systems. He published his book Méchanique Analytique in 1788 and was pleased to note it did not have a single geometric diagram in it.

Euler moved to St. Petersburg in 1766, and Lagrange succeeded him as Director of the mathematics section at the Berlin Academy. Based on Lagrange's calculus of variations, it summarized research in mechanics since the time of Isaac Newton, transformed mechanics into a division of mathematical analysis and made use of differential equations.

Lagrange next investigated a problem that had not been resolved by Newton. Newton's theory of universal gravitation dealt superbly with the interactions between two objects but, as everyone knew, there were many objects in the solar system. To be sure, the Sun contains 98 percent of the solar system's mass, but there were perturbations in the orbits of the other less massive members that could no longer be ignored or explained.

Lagrange worked on multiple-body systems, such as the Sun-Earth-Moon system, or Jupiter and its four known moons. His calculations established regions where it was possible for a small body to remain in equilibrium if it and the two other objects formed an equilateral triangle. These regions, now called the Lagrangian points, follow the same orbit as the larger object, but either lead or trail it by 60 degrees. It was over one hundred years later that the "Trojan asteroids," a swarm of asteroid s that lead and trail within 60 degrees of Jupiter, were discovered. One of the Lagrangian points involving the Earth-Moon system has been suggested as an ideal location for establishing a large permanent space colony.

After his patron Frederick the Great died, Lagrange moved to Paris at the invitation of King Louis XVI in 1787, where he remained through the upheaval of the French Revolution. In 1793 he was appointed to a commission to create a new system of weights and measures which resulted in the creation of the metric system. Also on the commission were his friends Pierre Laplace and chemist Antoine-Laurent Lavoisier. In 1797 he was appointed Professor of Mathematics at the new École Normale where he instigated a new concept; the thorough training of teachers.

In a book published in 1797, he tried to establish the calculus without using infinitesimals or Newton's limits. While he failed at this, his search for foundations and generalizations inspired Augustin-Louis Cauchy, Niels Henrik Abel, and Karl Weierstrass (1815-1897) in the following century.

He was honored by Napoleon who named him to the Legion of Honor and created him a Count of the Empire in 1808. Lagrange died in Paris on April 10, 1813.