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Lagrange, Joseph Louis, Comte

mechanics mathematics integer square

(Count) [lagrãzh] (1736–1813) French mathematician: revolutionized mechanics.

Born of a French father and Italian mother in Turin, Lagrange saw the family wealth frittered away when he was a teenager. He took to mathematics early and became a professor at the Royal Artillery School in Turin at 19. He moved in 1766 to succeed as Director of the Berlin Academy of Sciences. In 1797 he was in Paris as professor of mathematics at the École Polytechnique. His first wife died young; when he was 56 he married a teenage girl, remaining happily married until his death. He was a highly productive mathematician but his health broke down as a result of overwork and he suffered periodically from intense spells of depression; he virtually gave up mathematics by his late 40s. He was modest and widely liked.

The great book for which he is known, Analytical Mechanics, was started when he was 19, but despite early progress was only finished and published when he was 52. It developed mechanics, and used a powerful combination of the calculus of variations and the calculus of four-dimensional space to treat mechanical problems generally. The book does not use geometric methods as did (there are no diagrams!).

Lagrange made contributions to the gravitational three-body problem and to number theory; he proved some of unproven theorems and solved the ancient problem of finding an integer x such that ( nx 2 + 1) is a square where n is another integer (not a square).

Lagrange worked with on weights and measures, and in effect was the father of the metric system. Napoleon thought very highly of him.

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