Joseph Louis, Comte Lagrange 1, was Tourangean by descent, Italian by birth, German by adoption, and Parisian by choice. He began his teaching as professor of mathematics in the artillery school at Turin (1755) when only nineteen years of age, succeeded Euler (1766) as mathematical director in the Berlin Academy, and was called to Paris (1787), where he became a member of the Academie des Sciences and, somewhat later (1795 ), was professor of mathematics at the newly founded Ecole Normale and (1797) at the Ecole Polytechnique. Under Napoleon he was made a senator and a count, and was awarded other honors appropriate to his genius.
Lagrange was not one of the infant prodigies in mathematics. Indeed, it is said that he showed no interest in the subject until he was seventeen; but from that time on he made such marvelous progress that in a few years he became recognized as the gre atest living scholar in his science. When he was twenty-three years old he published two memoirs 2 which at once attracted attention. Euler wrote (October 2, 1759) an enthus iastic letter to him about the problem of isoperimetry which is here solved and on which the great Swiss mathematician had long been working, and d'Alembert was equally apprec iative of its importance. It is here that we find the beginning of the calculus of variations, and it is here that Lagrange took the first step toward Berlin and Paris, although it was not until 1766 that Frederick the Great wrote that "the greatest king in Europe" wanted "the greatest mathematician of Europe" at his court. As a result of this letter, Lagrange went to Berlin and remained there more than twenty years. At about the time that Frederick was urging him to go to Berlin he solved Fermat's pro blem relating to the equation nx^2 + 1 = y^2, n being integral and not a square 3, an intellectual feat that added greatly to his reputation. He now began a series of investi gations on partial differential equations, numerical equations, the theory of numbers, the calculus of variations, and the application of mathematics to physical problems, and made some progress in the theory of elliptic functions. To one of his memoirs (1773) may be traced the first important step in the theory of invariants, and in another there is evidence that the notion of a group was in his mind. At this time, too, he composed his monumental work on analytic mechanics 4, although this was not published until a year after he left Berlin.
The death of Frederick (1787) brought many changes to Prussia. Lagrange, whose frail constitution had never found the climate of Berlin salutary, and whose sensitive nature now found the intellectual atmosphere far from agreeable, decided to accept th e invitation of Louis XVI to take up his residence in Paris. It was about the time of the agitation for the metric system, and Lagrange was made president of the commission to carry out the work. The value of such an undertaking could appeal even to a S ans-culotte, and so, although all foreigners were banished from France, the Committee of Public Safety expressly excepted Lagrange from the decree. Nevertheless the fate of Lavoisier and Bailly, both of whom met their death by the guillotine, led Lagrang e to decide on leaving France. He spoke bitterly to Delambre of the death of Lavoisier, saying that the mob had removed in an instant a head that it would take a century to reproduce. Prussia knew his genius and seriously wanted him back; Paris knew his name and vaguely wished him to remain. The Prussia of that day wished to be scientific; the Paris of that day merely wished to be thought so. But just as Lagrange was reaching a decision, new forces were created in France, and these forces were more po tent than any fear of the guillotine, than any discouragement at the acts of the revolutionary leaders, or than any call of the successor of Frederick. France had decided to establish a school with the humble name of Ecole Normale, and a little later she established a second one, the Ecole Polytechnique, and to each school Lagrange was called and to each he gave a mathematical impetus that it has never lost. In the first he saw a chance to found the training of teachers on the most thorough scholarship, and no similar institution either before or since that time has so thoroughly recognized the value of this principle, and none has ever stood so high in the esteem of the world. Similarly, in the Ecole Polytechnique he saw the opportunity for basing the technical work on a foundation of the highest type of mathematical skill, and this institution, like the other, has ever since been a constant inspiration to the world of science. It was at the Ecole Normale that he gave those lectures on algebra and ar ithmetic 5 that he had to temper to the revolutionary demand before he could bring the work up to the standard that permitted him to present the calculus of functions6. It was at the Ecole Polytechnique that he lectured on analytic functions 7, setting forth in new fa shion the differential and integral calculus and the calculus of fluxions. Here, too, he expounded his noteworthy work on numerical higher equations8.
It is probably that his work more profoundly influenced later mathematical research than did that of any of his contemporaries, although it was an era of giants in this field.
(Smith, pp. 482-486.)