Adrien-Marie Legendre – Biography of Adrien-Marie Legendre

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Adrien-Marie Legendre He was born on September 18, 1752, in Paris, France. He was a mathematician whose distinguished work on elliptical integrals provided basic analytical tools for mathematical physics.

Little is known about the early life of Legendre, except that his family wealth allowed him to study physics and mathematics, beginning in 1770, at the Collège Mazarin (Collège des Quatre-Nations) in Paris and that, at least until the French Revolution, he did not have to work. But nevertheless, Legendre He taught mathematics at the École Militaire de Paris from 1775 to 1780.

In 1782 he won an award offered by the Berlin Academy of Sciences for his effort to “determine the curve described by cannon balls and bombs, taking into account air resistance, and give rules to obtain the ranges corresponding to the different initial velocities and to different projection angles“.

The following year he presented a research on celestial mechanics to the French Academy of Sciences and was soon rewarded with membership. In 1787 he joined the French team, led by Jacques-Dominique Cassini and Pierre Mechain, in geodetic measurements carried out in conjunction with the Royal Greenwich Observatory in London. At this time he also became a member of the British Royal Society. In 1791 he was appointed together with Cassini and Mechain to a special committee to develop the metric system and, in particular, to carry out the measurements necessary to determine the standard meter. He also worked on projects to produce logarithmic and trigonometric tables.

The Academy of Sciences was forced to close in 1793 during the French Revolution, and Legendre he lost his family wealth during the upheaval. However, he got married at this time. The following year he published Elements of géométrie (Elements of Geometry), a reorganization and simplification of the propositions of Euclid’s Elements that was widely adopted in Europe, despite the fact that it was full of fallacious attempts to defend the parallel postulate. Legendre He also gave a simple proof that p is irrational, as well as the first proof that p2 is irrational, and conjectured that p is not the root of any finite degree algebraic equation with rational coefficients (i.e., p is a transcendental number) .

His Eléments was even more pedagogically influential in the United States, undergoing numerous translations beginning in 1819; one of those translations went through 33 editions. The French Academy of Sciences reopened in 1795 as the National Institute of Sciences and Arts, and Legendre settled in the math section. When Napoleon Bonaparte reorganized the institute in 1803, Legendre remained in the new geometry section. In 1824 he refused to endorse the government candidate for the Institut and lost his pension from the École Militaire, where he had served from 1799 to 1815 as an examiner in mathematics for graduate artillery students.

His Nouvelles methods for the determination of orbites des comètes (1806; “New methods for the determination of the orbits of the comet”) contains the first integral treatment of the method of least squares, although the priority for its discovery is shared with his German rival Carl Friedrich Gauss.
In 1786, Legendre investigated elliptical integrals. In your most important work, Traite des fonctions elliptiques (1825-37; “Treatise on Elliptic Functions”), reduced elliptic integrals to three standard forms now known by name. He also compiled tables of the values ​​of his elliptic integrals and showed how they can be used to solve important problems in mechanics and dynamics. Shortly after their work appeared, the independent discoveries of Niels Abel and Carl Jacobi completely revolutionized the subject of elliptical integrals.
Legendre published his own investigations on number theory as well as those of his predecessors, in a systematic form under the title Théorie des names, 2 vol. (1830) This work included his imperfect proof of the law of quadratic reciprocity. The law was considered by Gauss, the greatest mathematician of the time, as the most important general result in number theory since the work of Pierre de Fermat in the seventeenth century. Gauss also gave the first rigorous test of the law.