Mathematician:Adrien-Marie Legendre

1752 - 1833


 * French mathematician, focusing in the fields of statistics, abstract algebra, number theory, and mathematical 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: September 18, 1752
 * Died: January 10, 1833


 * 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 Polynomial
 * Legendre Transformation

Books and Papers

 * "Éléments de Géométrie" (1794), a reorganization of Euclid's "Elements" with simpler but just as rigorous proofs.
 * "Essai sur la Theorie des Nombres" (1798, 2 vols.), possibly the first treatise dedicated solely to number theory.
 * "Theorie des Nombres" (1830), an expanded version of "Essai sur la Theorie des Nombres", including work from the intervening years.