Mathematician:Joseph Louis Lagrange

Mathematician

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:

• 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.
• Completed the solution of the partial differential equation which defines the form of a vibrating string.
• Between $1772$ and $1785$ he also addressed the partial differential equation of the first order.
• Established the general solution of the linear equation, and classified the various kinds of non-linear equation.

Nationality

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

History

• 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 Formula
• Lagrange's Four Square Theorem
• Lagrange's Identity
• Lagrange Interpolation Formula
• Lagrange's Method of Multipliers
• Lagrange's Theorem (Number Theory)

• Euler-Lagrange Equation (with Leonhard Paul Euler)
• Lagrange-Charpit Method (with Paul Charpit)
• Lagrange Basis Polynomial
• Lagrange Form of Remainder of Taylor Series
• Lagrange Number
• Lagrangian

• Proved Wilson's Theorem, which as a result is sometimes referred by some sources as the Wilson-Lagrange 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 $n!$.

Results named for Joseph Louis Lagrange can be found here.

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

Publications

• 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.

Some prepend his title Comte.

Some sources give his surname as LaGrange.

Sources

• John J. O'Connor and Edmund F. Robertson: "Joseph Louis Lagrange": MacTutor History of Mathematics archive

• 1937: Eric Temple Bell: Men of Mathematics: Chapter $\text{X}$
• 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Introduction
• 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Chapter $2$: Subgroups and Cosets: $\S 40$
• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): A List of Mathematicians in Chronological Sequence
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Lagrange, Joseph Louis, Comte de (1736-1813)
• 1991: David Wells: Curious and Interesting Geometry ... (previous) ... (next): A Chronological List Of Mathematicians
• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.22$: Lagrange ($\text {1736}$ – $\text {1813}$)
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): A List of Mathematicians in Chronological Sequence
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Lagrange, Joseph Louis, Comte (1736-1813)
• 2004: Ian Stewart: Galois Theory (3rd ed.) ... (previous) ... (next): Historical Introduction: Polynomial Equations
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Lagrange, Joseph Louis, Comte (1736-1813)
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Lagrange, Joseph-Louis (1736-1813)