Mathematician:Adrien-Marie Legendre


 * 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 Gauss and Abel.


 * 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 Gauss in 1798.

Nationality
French

History

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


 * Pioneered work on the distribution of primes and its application to number theory.
 * Conjectured that $$\pi \left({n}\right)$$ approaches $$\frac n {\ln \left({n}\right) - 1.08366}$$ 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.
 * Discovered the Diophantine Equation $$ax^2 + by^2 + cz^2 = 0$$ which is known as the Legendre Equation.

Theorems and Definitions

 * Legendre Symbol
 * Legendre's Constant
 * Legendre Transform
 * Factorial Divisible by Prime Power
 * Legendre Equation
 * Legendre's Differential Equation
 * 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 Euclid's 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