Mathematician:Adrien-Marie Legendre

Mathematician

 * French mathematician, focusing in the fields of statistics, abstract algebra, number theory and analysis.


 * Has a moon crater named after him.


 * His work formed the basis for work by many others, including and.


 * Gave an early proof of Fermat's Last Theorem for $n = 5$.


 * Attempted a proof of the Law of Quadratic Reciprocity in $1785$, but it was flawed. It was eventually proven by in $1798$.
 * Pioneered work on the distribution of primes and its application to number theory.


 * Conjectured that $\pi \left({n}\right)$ approaches $\dfrac n {\ln \left({n}\right) - 1.08366}$ as $n \to \infty$, which is very close to correct. In this context, $1.08366$ is known as Legendre's constant.


 * Known for the Legendre Transform, which is commonly used to go from the Lagrangian to the Hamiltonian Function in Classical Mechanics.


 * Developed the Least Squares Method for linear regression.


 * Investigated the Diophantine Equation $a x^2 + b y^2 + c z^2 = 0$ which is known as the Legendre Equation.


 * Introduced the notation $\Gamma \left({z}\right)$ as the Gamma function.

Nationality
French

History

 * Born: 18 Sept 1752, Paris (or possibly Toulouse), France
 * Died: 10 Jan 1833, Paris, France

Theorems and Definitions

 * Legendre Symbol
 * Legendre's Constant
 * Legendre Transform
 * Factorial Divisible by Prime Power
 * Legendre Equation
 * Legendre's Differential Equation
 * Legendre's Duplication Formula
 * Legendre Polynomial

Books and Papers

 * 1782: Recherches sur la trajectoire des projectiles dans les milieux résistants
 * 1784: Recherches sur la figure des planètes which contains the Legendre polynomials
 * 1785: Recherches d'analyse indéterminée
 * 1787: Mémoire sur les opérations trigonométriques dont les résultats dépendent de la figure de la terre
 * 1794: Éléments de Géométrie, a reorganization of with simpler but just as rigorous proofs.
 * 1798: Essai sur la Théorie des Nombres, 2 volumes, possibly the first treatise dedicated solely to number theory.
 * 1808: Théorie des Nombres, a second edition of Essai sur la Théorie des Nombres
 * 1811: Exercices du Calcul Intégral, Volume 1
 * 1817: Exercices du Calcul Intégral, Volume 2
 * 1819: Exercices du Calcul Intégral, Volume 3
 * 1825: Traité des Fonctions Elliptiques, Volume 1
 * 1826: Traité des Fonctions Elliptiques, Volume 2
 * 1830: Traité des Fonctions Elliptiques, Volume 3
 * 1830: Théorie des Nombres, an expanded version of Essai sur la Théorie des Nombres, including work from the intervening years