Mathematician:Joseph Louis Lagrange

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Italian-born French mathematician who made big advances in the fields of the calculus of variations and analytical mechanics.

Contributed to number theory and algebra.

Extended a lot of the fields established by Euler, and in turn laid down the groundwork for later explorations by Gauss and Abel.

Played a leading part in establishing the metric system of weights and measures.

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.
  • Demonstrated in $1794$ that $\pi^2$ is irrational.
  • Proved Wilson's Theorem.


Italian-born, of mixed Italian and French parentage, living mainly in France and Prussia.


  • Born: 25 January 1736, Turin, Italy
  • 1755: Appointed Professor at Royal Artillery School at Turin
  • 1766: Moved to Berlin to take over position of Euler, who had moved to St. Petersburg
  • 1786: Moved to Paris after death of Frederick the Great
  • Died: 10 April 1813, Paris, France.

Theorems and Definitions

  • 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 $n!$.

Results named for Joseph Louis Lagrange can be found here.

Definitions of concepts named for Joseph Louis Lagrange can be found here.


  • 1770: Réflexions sur la résolution algébrique des equations: a complete restudy of all the known methods of solving the cubic and quartic equations.
  • 1788: Mécanique Analytique
  • 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

Critical View

The "generalized coordinates" of our mechanics of today were conceived and installed by Lagrange, and this was an achievement of unmatchable magnitude.
-- Salomon Bochner

Also known as

Some sources render his name as Joseph-Louis Lagrange.

He was born Giuseppe Lodovico Lagrangia, or Giuseppe Ludovico de la Grange Tournier.

He is also reported as Giuseppe Luigi Lagrange, and also Giuseppe Luigi Lagrangia.