ProofWiki:Mathematicians/Joseph Louis Lagrange
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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.
Contents |
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 Formula
- 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
- John J. O'Connor and Edmund F. Robertson: "Joseph Louis Lagrange": MacTutor History of Mathematics archive
- Eric Temple Bell: Men of Mathematics (1937): Chapter $\text{X}$
- Allan Clark: Elements of Abstract Algebra (1971)... (previous)... (next): Introduction
- George F. Simmons: Calculus Gems (1992): Chapter $\text {A}.22$
