Adrien-Marie Legendre

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Adrien-Marie Legendre bigraphy, stories - Mathematician

Adrien-Marie Legendre : biography

September 18, 1752 – January 10, 1833

Adrien-Marie Legendre () (18 September 1752 – 10 January 1833) was a French mathematician. Legendre made numerous contributions to mathematics. Well-known and important concepts such as the Legendre polynomials and Legendre transformation are named after him.

Life

Adrien-Marie Legendre was born in Paris (or possibly, in Toulouse, depending on sources) on 18 September 1752 to a wealthy family. He was given an excellent education at the Collège Mazarin in Paris, defending his thesis in physics and mathematics in 1770. From 1775 to 1780 he taught at the École Militaire in Paris, and from 1795 at the École Normale, and was associated with the Bureau des longitudes. In 1782, he won the prize offered by the Berlin Academy for his treatise on projectiles in resistant media, which brought him to the attention of Lagrange.

In 1783 he became an adjoint of the Académie des Sciences, and an associé in 1785. In 1789 he was elected a Fellow of the Royal Society. During the French Revolution, in 1793, he lost his private fortune, but was able to put his affairs in order with the help of his wife, Marguerite-Claudine Couhin, whom he married in the same year. In 1795 he became one of the six members of the mathematics section of the reconstituted Académie des Sciences, named the Institut National des Sciences et des Arts, and later, in 1803, of the Geometry section as reorganized under Napoleon. In 1824, as a result of refusing to vote for the government candidate at the Institut National, Legendre was deprived by the Ministre de L’Intérieur of the ultraroyalist government, the comte de Corbière, of his pension from the École Militaire, where he had served from 1799 to 1815 as mathematics examiner for graduating artillery students. This was partially reinstated with the change in government in 1828 and in 1831 he was made an officer of the Légion d’Honneur.

He died in Paris on 9 January 1833, after a long and painful illness. Legendre’s widow made a cult of his memory, carefully preserving his belongings. Upon her death in 1856, she left their last country house to the village of Auteuil where the couple had lived and are buried.

His name is one of the 72 names inscribed on the Eiffel Tower.

Portrait debacle

For two centuries, until the recent discovery of the error in 2005, books, paintings and articles have incorrectly shown a side-view portrait of the obscure French politician Louis Legendre (1752–1797) as that of the mathematician Legendre. The error arose from the fact that the sketch was labelled simply "Legendre". The only known portrait of Legendre, recently unearthed, is found in the 1820 book Album de 73 portraits-charge aquarellés des membres de I’Institut, a book of caricatures of seventy-three members of the Institut de France in Paris by the French artist Julien-Leopold Boilly as shown below:Boilly, Julien-Leopold. (1820). Album de 73 portraits-charge aquarellés des membres de I’Institut ( #29). Biliotheque de l’Institut de France.

Honors

  • The Moon crater Legendre is named after him.
  • Main-belt asteroid 26950 Legendre is named after him.

Scientific activity

Most of his work was brought to perfection by others: his work on roots of polynomials inspired Galois theory; Abel’s work on elliptic functions was built on Legendre’s; some of Gauss’ work in statistics and number theory completed that of Legendre. He developed the least squares method, which has broad application in linear regression, signal processing, statistics, and curve fitting; this was published in 1806 as an appendix to his book on the paths of comets. Today, the term "least squares method" is used as a direct translation from the French "méthode des moindres carrés".

In 1830 he gave a proof of Fermat’s last theorem for exponent n = 5, which was also proven by Lejeune Dirichlet in 1828.

In number theory, he conjectured the quadratic reciprocity law, subsequently proved by Gauss; in connection to this, the Legendre symbol is named after him. He also did pioneering work on the distribution of primes, and on the application of analysis to number theory. His 1798 conjecture of the Prime number theorem was rigorously proved by Hadamard and de la Vallée-Poussin in 1896.