
The Gauss-Legendre algorithm was discovered by Carl Friedrich Gauss around 1800, though it wasn't published until much later in his collected works. The method combines two important mathematical concepts: the arithmetic-geometric mean, which Gauss extensively studied, and Legendre's relation, developed by Adrien-Marie Legendre. This algorithm represented a significant advancement in computing π, as it converges much faster than classical methods like Archimedes' approach or infinite series.