Joseph Louis Lagrange (1736—1813) was born in 1736, in Turin, Italy. He spent the early part of his life in Turin. While there he was involved in carrying out research work in calculus of variations and mechanics.
In 1766, Lagrange was invited by the Prussian king, Frederick II, to fill the position vacated by Euler in Berlin. Frederick the Great proclaimed in his appointment that “the greatest king in Europe” ought to have “the greatest mathematician in Europe.” In 1787, after the death of Frederick II, he went to Paris, accepting an invitation from Louis XVI. In 1797, he accepted a position at the newly formed École Polytechnique in Paris. He was made a count by Napoleon and remained at the École Polytechnique till his death. He died in 1813.
Throughout his life, Lagrange did work of fundamental importance. He made numerous contributions to many branches of mathematics, including number theory, the theory of equations, differential equations, celestial mechanics, and fluid mechanics. In 1770, he proved the famous Lagrange’s theorem in group theory.
He is responsible for the work leading to Galois theory. In his paper, “Réflexion sur la théorie algébriques des équations,” Lagrange carefully analyzed the various known methods to solve a polynomial equation of degree ≤ 4 by means of radicals. He was interested in finding a general method of solution for polynomials of higher degree. He was unable to find a general solution, but in his paper he introduced several key ideas on the permutations of roots which finally led Abel and Galois to develop the necessary theory to answer the question. Lagrange’s work on the solution of polynomial equations is one of the sources from which modern group theory evolved.