Adrien-Marie Legendre

Adrien-Marie Legendre (1752–1833) was a French mathematician whose work shaped number theory, geometry, and mathematical physics. He developed influential methods including least squares and the theory of elliptic functions.

Method of least squares: A statistical method that estimates unknown quantities by minimizing the sum of squared residuals. Legendre published an early systematic account of this method in 1805.
Quadratic reciprocity: A theorem describing when one integer is a square modulo another prime. Legendre formulated a proof of this central theorem, later completed rigorously by Gauss.
Carl Friedrich Gauss: A German mathematician whose work ranged across number theory, astronomy, and geodesy. Gauss independently developed least squares and supplied a rigorous proof of quadratic reciprocity.
Éléments de géométrie: Legendre’s influential 1794 geometry textbook, widely used in Europe and the United States. Its repeated editions carried his approach to geometry across generations.
Legendre symbol: A function that records whether an integer is a quadratic residue modulo an odd prime. This notation made his work on quadratic residues a lasting tool in number theory.
Geodesy: The science of measuring Earth’s shape, orientation, and gravitational field. Earth-measurement problems motivated Legendre’s work on ellipsoids and least squares.
Joseph-Louis Lagrange: An Italian-French mathematician whose work transformed analysis, mechanics, and number theory. Lagrange and Legendre belonged to the generation that reshaped French mathematics.
Nouvelles méthodes pour la détermination des orbites des comètes: Legendre’s 1805 work presenting a systematic method of least squares. The book applied error-minimizing calculations to astronomical observations.
Legendre polynomials: A sequence of orthogonal polynomials that solves Legendre’s differential equation. Their role in potential theory extends Legendre’s mathematical-physics research.
Ellipsoid: A three-dimensional surface formed by stretching or compressing a sphere along its axes. Legendre studied ellipsoids as models of Earth in mathematical geodesy.

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