CALCULUS Understanding Its Concepts and Methods
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Joseph-Louis Lagrange (1736--1813) --- Historical Sketch
The luminary of this Sketch, Joseph Louis Lagrange, is described in Boyer's History of Mathematics as being "generally regarded as the keenest of mathematicians of the eighteenth century, only Euler being a close rival, ... . " See . There are those who might argue with this assessment, but none could deny that Lagrange was a remarkable and dominant mathematician of his time. Turnbull says in his little book, The Great Mathematicians, that Lagrange "would set to mathematics all the little themes on physical inquiries which his friends brought him, much as Schubert would set to music any stray rhyme that took his fancy." See .
Joseph-Louis Lagrange was born in 1736 to a wealthy French family of Turin, Italy, the first of his parents' eleven children; and he remains to this day a heroic figure in Turin, though he spent most of his life elsewhere.
In school, he was not at first attracted to mathematics, finding geometry rather dull. He preferred instead the study of classical Greek. He also studied astronomy and is today recognized as one of the founders of modern astronomy. At about age 17 he became enamored with mathematics. After some fits and starts in pursuing original ideas in his self-taught mathematics, it became clear that he was deeply talented in the subject. At age 19 he was appointed Professor of Mathematics at the Royal Artillery School in Turin. His interest in astronomy continued and he made important contributions to the field of celestial mechanics.
Lagrange was a member of the French Academy of Sciences which appointed him to head the Comité International des Poids et Mesures (International Committee of Weights and Measures) in 1790. He persuaded the Committee to adopt a metric system based on the number ten rather than on the number twelve.
The first mathematical discovery that Lagrange made was to notice that repeated differentiation of a product of two functions results in a Pascal Triangle pattern. He wrote a letter to Euler about this, only to find that it had already been discovered by Euler himself. Show the first four steps of the pattern Lagrange wrote about.
 A History of Mathematics, Second Ed., by Boyer and Merzbach, Wiley & Sons, 1991, p. 490
 The Great Mathematicians, by Herbert Westren Turnbull, Simon & Schuster, 1962, p. 117-8
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