Adrien-Marie Legendre

One side of a priority dispute in which publication and claimed earlier use were not the same thing. Legendre first published the method of least squares in 1805. Gauss presented it with a probabilistic treatment in 1809 and claimed to have used it since 1795. The record is clearer when those two facts are kept separate. Legendre also made long-lasting contributions to number theory, Legendre polynomials, elliptic integrals, geodesy, and metric surveying. A portrait long reproduced as his was actually the politician Louis Legendre; in 2005 a caricature in an album from around 1820 was identified as a rare image of the mathematician. The episode is a lesson in source identification, not the unveiling of one definitive face.

This is a thought experiment about influence, not a verified historical fact.

Beginners choose a line that looks closest to scattered points; intermediate learners minimize the sum of squared residuals. Advanced learners derive normal equations and error models. Experts compare Legendre’s publication, Gauss’s claim of earlier use, and Gauss’s probabilistic justification as distinct pieces of evidence.