Adrien-Marie Legendre was born in Paris on 18 September 1752. At 274 years from his birth, his name remains attached to polynomials, an early form of quadratic reciprocity and a method for fitting data — not to a familiar public portrait.

He studied at the Collège Mazarin and taught at the École Militaire. Early work on projectile trajectories earned recognition from the Berlin Academy. His career was that of a state mathematician and textbook author, not the inventor of a single headline theorem.

In number theory he studied the distribution of primes and formulated an early version of the law of quadratic reciprocity. The complete proof came from Carl Friedrich Gauss. Priority should be split: Legendre published; Gauss finished the proof.

In 1805 he published the least-squares method for fitting observations. Gauss claimed he had used it earlier. The dispute remains open in the history of the subject; this article does not settle it.

The polynomials that bear his name appear in differential equations with spherical symmetry. His classification of elliptic integrals prepared the ground for Abel and Jacobi. The textbook “Éléments de géométrie” circulated in translation; he also worked on geodetic measurements between Paris and Greenwich.

The engraving often used as his portrait has been identified by historians as the politician Louis Legendre. The cover shows the Institut de France, formerly the Collège Mazarin where he studied, not that misidentified image.

The anniversary marks a modern-era scholar whose tools are still used in physics and statistics, not a laboratory hero popularised by the wrong face.

Image: Guilhem Vellut / Wikimedia Commons, CC BY 2.0. Institut de France (Collège des Quatre-Nations / Collège Mazarin), Paris, 13 June 2017. Not a portrait of Legendre; the commonly used engraving shows Louis Legendre. Cropped to 16:9.

Source consulted: Adrien-Marie Legendre | MacTutor History of Mathematics; Adrien-Marie Legendre | Encyclopaedia Britannica; Adrien-Marie Legendre | The Royal Society.