Mathematician:Joseph Louis Lagrange

Born Giuseppe Lodovico Lagrangia.

He did the following:
 * Author of Réflexions sur la résolution algébrique des equations (1770), a complete restudy of all the known methods of solving the cubic and quartic equations.
 * Proposed a prime number as the universally adopted number base. Thus every systematic fraction would be reducible and represent the number in a unique way.
 * Established some very general theorems on whether a number is prime from examining its digits.
 * Tried in vain to prove Fermat's Last Theorem.
 * One of the few exceptions of his time who was doubtful that a polynomial equation of degree greater than four was capable of a formal solution by means of radicals.
 * Gave an insufficient proof of the Fundamental Theorem of Algebra.

He also proved Wilson's Theorem.

Nationality
Italian-born, but also considered to be French, living mainly in France and Prussia.

History

 * Born: 25 January 1736, Turin, Italy
 * Died: 10 April 1813, Paris, France.

Theorems and Definitions

 * Lagrange's Theorem (Number Theory)
 * Lagrange's Identity
 * Lagrange's Four Square Theorem
 * Proved Wilson's Theorem


 * Lagrange's Theorem (Group Theory) was named after him, although he did not prove the general form. What he actually proved was that if a polynomial in $n$ variables has its variables permuted in all $n!$ ways, the number of different polynomials that are obtained is always a divisor of $n!$.

Books and Papers

 * 1770: Réflexions sur la résolution algébrique des equations: a complete restudy of all the known methods of solving the cubic and quartic equations.
 * 1797: Théorie des fonctions analytiques
 * 1798: Résolution des équations numériques: Includes a method of approximating to the real roots of an equation by means of continued fractions.
 * 1800: Leçons sur le calcul des fonctions

Also see

 * : Chapter $\text{X}$
 * : Introduction
 * : Chapter $\text {A}.22$