Adrien-Marie Legendre

Adrien-Marie Legendre (1752–1833) was a French mathematician who quietly shaped huge swathes of maths — number theory, geometry, the method of least squares — yet spent much of his career being gently steamrolled by more famous rivals. For two centuries nobody even knew what he looked like: the only portrait everyone used turned out to be a completely different man!

The enduring idea

Legendre invented a beautifully compact bit of notation, the Legendre symbol, which packs the question "is this number a perfect square modulo a prime?" into a tidy \pm 1. That symbol is the natural language for one of the deepest gems in all of number theory, the law of quadratic reciprocity. His name also lives on in Legendre polynomials and the Legendre transform used across physics.

For 200 years the "portrait of Legendre" in textbooks showed a stern-looking gentleman — until a historian realised it was actually a French politician named Louis Legendre, no relation. The only genuine likeness is a cheeky watercolour caricature, so the great geometer is best known by a cartoon. He had rotten luck with credit, too: Gauss casually mentioned discovering least squares and quadratic reciprocity, both of which Legendre had published, leaving Legendre fuming for years.