# Legendre, Adrien Marie

### From Enlightenment Revolution

**Legendre, Adrien Marie** (1752-1833): French Mathematician.

Born into a comfortable Parisian family, Legendre taught mathematics at the École Militaire in Paris from 1775 to 1780, won the Berlin Academy prize in 1782, was elected to the French Academy of Sciences in 1783 and named professor at the École Normale in 1795.

The early part of his career involved work on spheroids and geodesy, including the “Recherches sur la figure des planètes” (1784) where Legendre polynomials first appeared. His *Elements of Geometry* (1794)— a re-writing of Euclid —was immensely popular and went through several editions and translations. His work on elliptic integrals began in 1786, building on earlier work by Euler, Leonhard, Lagrange, Joseph Louis and John Landen, and culminated in his *Treatise on Elliptic Functions* (1825-1832). In a supplement to the last edition, Legendre called attention to revolutionary work on modern elliptic functions (the inverses of elliptic integrals) by Niels Henrik Abel and Carl Gustav Jacob Jacobi. His *New Methods for the Determination of Comet Orbits* (1806) contained the first published application of the method of least squares, which •Carl Friedrich Gauss would attribute to himself in 1809. In his *Theory of Numbers* (1808-1830) he published a proof of the law of quadratic reciprocity, widely regarded as the most important advance in number theory since Pierre Fermat.

Today, Legendre’s name is associated primarily with the second-order differential equation that bears his name: . Its solutions form the aptly named set of Legendre polynomials.

Further Reading:

Jean Itard, “Legendre, Adrien Marie.” *Dictionary of Scientific Biography*, vol. 8: 135-143.

**Ziad Elmarsafy**

University of York