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## LAGRANGE, J.L.(1736-1813)

 The two greatest mathematicians of the eighteenth century were Euler and Joseph Louis Lagrange(1737-1813), and which of the two was the greater is a matter of debate that often reflects the differing mathematical sensitivities of the debaters.  Lagrange was born is Turin, Italy, into a formerly prosperous family of French and Italian backgrounds; he was the youngest of eleven children and the only one to survive beyond infancy. He was educated in Turinand, as a young man, served as professor of mathematics at the military academy there.     In 1766, when Euler left Berlin, Frederick the Great wrote to Lagrange that "the greatest king in Europe." wished to have at his court "the greatest mathematician of Europe." Lagrange accepted the invitation and for twenty years held the post vacated by Euler.  A few years after leaving Berlin, in spite of the chaotic political situation in France, Lagrange accepted a professorship at the newly established Ecole Normale, and then at the Ecole Polytechnique.  The first of these schools was short-lived, but the second on became famous in the history of mathematics, inasmuch as many of the great mathematicians of modern France wrer trained there and many held professorships there.  Lagrange did much to develop the high degree of scholarship in mathematics that has become associated with the Ecole Polytechnique.     Later in life, lagrange was subject to great fits of loneliness and despondency.  He was rescued from these, when he was fifty-six, by a young girl nearly forty years his junior.  She was the daughter of his friend, the astronomer Lemonnier.  She was so touched by Lagrange's ungappiness hat she insisted on marrying him.  Lagrange subnitted, and the marriage turned out ideal.  She probed to be a very devoted and competent companion, and succeeded in drawing her husband out and reawakening his desire to live.  Of all his prizes in the world, Lagrange claimed, with honesty and simplicity, the one he most Valued was his tender and devoed young wife.     The attempt, which was far from successful, was made in 1797in his great publication Theorie des fonctions analytiques conternant les principes du calcul differentiel. The cardinal idea here was the representation of a function f(x) by a Taylor's series.  The derivatices f'(x), f"(x),.... were then defined as the coefficients of h, $h2$/2!,... in the Taylor expansion of f(x + h)in terms of f.  The notation f'(x), f"(x),..., very commonly used today, is due to Lagrange.     Napoleon Bonaparte, who hobnobbed with a number of the great mathematicians of France, summed up his estimate of lagrange by saying, "Lagrange is the lofty pyramid of the mathematical sciences.