January 25, 2010
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Joseph-Louis Lagrange (25 January 1736 – 10 April 1813), born Giuseppe Lodovico (Luigi) Lagrangia, was an Italian-born mathematician and astronomer, who lived part of his life in Prussia and part in France, making significant contributions to all fields of analysis, to number theory, and to classical and celestial mechanics. On the recommendation of Euler and D'Alembert, in 1766 Lagrange succeeded Euler as the director of mathematics at the Prussian Academy of Sciences in Berlin, where he stayed for over twenty years, producing a large body of work and winning several prizes of the French Academy of Sciences. Lagrange's treatise on analytical mechanics (Mécanique Analytique, 4. ed., 2 vols. Paris: Gauthier-Villars et fils, 1888-89), written in Berlin and first published in 1788, offered the most comprehensive treatment of classical mechanics since Newton and formed a basis for the development of mathematical physics in the nineteenth century. In 1787, at age 51, he moved from Berlin to France and became a member of the French Academy, and he remained in France until the end of his life. Therefore, Lagrange is alternatively considered a French and an Italian scientist. Lagrange survived the French Revolution and became the first professor of analysis at the École Polytechnique upon its opening in 1794. Napoleon named Lagrange to the Legion of Honour and made him a Count of the Empire in 1808. He is buried in the Panthéon.

His father, who had charge of the Kingdom of Sardinia's military chest, was of good social position and wealthy, but before his son grew up he had lost most of his property in speculations, and young Lagrange had to rely on his own abilities for his position. He was educated at the college of Turin, but it was not until he was seventeen that he showed any taste for mathematics. Alone and unaided he threw himself into mathematical studies; at the end of a year's incessant toil he was already an accomplished mathematician, and was made a lecturer in the artillery school.

Lagrange is one of the founders of calculus of variations. He wrote several letters to Leonhard Euler between 1754 and 1756 describing his results. He outlined his "δ-algorithm", leading to the Euler–Lagrange equations of variational calculus and considerably simplifying Euler's earlier analysis.

In 1758, with the aid of his pupils, Lagrange established a society, which was subsequently incorporated as the Turin Academy of Sciences, and most of his early writings are to be found in the five volumes of its transactions, usually known as the Miscellanea Taurinensia. The next work he produced was in 1764 on the libration of the Moon, and an explanation as to why the same face was always turned to the earth, a problem which he treated by the aid of virtual work.

Already in 1756 Euler, with support from Maupertuis, made an attempt to bring Lagrange to the Berlin Academy. Later, D'Alambert interfered on Lagrange's behalf withFrederick of Prussia and wrote to Lagrange asking him to leave Turin for a considerably more prestigious position in Berlin. Lagrange turned down both offers, responding in 1765 that

It seems to me that Berlin would not be at all suitable for me while M.Euler is there.

In 1766 Euler left Berlin for Saint Petersburg, and Frederick wrote to Lagrange expressing the wish of "the greatest king in Europe" to have "the greatest mathematician in Europe" resident at his court. Lagrange was finally persuaded and he spent the next twenty years in Prussia, where he produced not only the long series of papers published in the Berlin and Turin transactions, but his monumental work, the Mécanique analytique. His residence at Berlin commenced with an unfortunate mistake. Finding most of his colleagues married, and assured by their wives that it was the only way to be happy, he married; his wife soon died, but the union was not a happy one.

In 1786, Frederick died, and Lagrange, who had found the climate of Berlin trying, gladly accepted the offer of Louis XVI to migrate to Paris. He received similar invitations from Spain and Naples. He became a member of the French Academy of Sciences, which later became part of the National Institute. At the beginning of his residence in Paris he was seized with an attack of the melancholy. Curiosity as to the results of the French revolution first stirred him out of his lethargy, a curiosity which soon turned to alarm as the revolution developed. It was about the same time, 1792, that the unaccountable sadness of his life and his timidity moved the compassion of a young girl who insisted on marrying him, and proved a devoted wife to whom he became warmly attached. Although the decree of October 1793 that ordered all foreigners to leave France specifically exempted him by name, he was preparing to escape when he was offered the presidency of the commission for the reform of weights and measures. The choice of the units finally selected was largely due to him, and it was mainly owing to his influence that the decimal subdivision was accepted by the commission of 1799. In 1795, Lagrange was one of the founding members of the Bureau des Longitudes.

In 1795, Lagrange was appointed to a mathematical chair at the newly-established École normale, which enjoyed only a brief existence of four months. Lagrange was appointed professor of the École Polytechnique in 1794; and his lectures there are described by mathematicians who had the good fortune to be able to attend them, as almost perfect both in form and matter. On the other hand, Fourier, who attended his lectures in 1795, wrote:

His voice is very feeble, at least in that he does not become heated; he has a very pronounced Italian accent and pronounces the s like z … The students, of whom the majority are incapable of appreciating him, give him little welcome, but the professors make amends for it.

In 1810, Lagrange commenced a thorough revision of the Mécanique analytique, but he was able to complete only about two-thirds of it before his death in 1813. He was buried that same year in the Panthéon in Paris. The French inscription on his tomb there reads:

JOSEPH LOUIS LAGRANGE. Senator. Count of the Empire. Grand Officer of the Legion of Honour. Grand Cross of the Imperial Order of Réunion. Member of the Instit
ute and the Bureau of Longitude. Born in Turin on 25 January 1736. Died in Paris on 10 April 1813.