Credit for the development of least squares is given to Frederich Gauss, who had developed the foundation of the method by the age of eighteen, in 1795. However, the method was also developed independently by Adrien Legendre and Robert Adrain at slightly later dates.

The first recognized use of the term least squares was in Legendre’s appendix to Nouvelles méthodes pour la détermination des orbites des comètes, Sur la Méthode des moindres quarrés “On the method of least squares,” published in 1805. Legendre was the first mathematician to publish a work involving the method of least squares, despite Gauss having been using it for twenty years prior. The first proof of the method was published by Robert Adrain in his paper Research concerning the probabilities of errors which happen in making observations, published in 1808.

Adrain used none of the terms used by Legendre to describe the method, and indicated that he had absolutely no knowledge of his work on the subject. Another and more rigorous proof was given by Gauss in the 1809 paper Theoria motus corporum coelestium, his first published work on the subject coming almost thirty-five years after his first encounter with least squares. Least squares was developed independently by three different mathematicians within a short span of time, and each contributed important parts of the theory to general mathematical literature.

Early use of the method was almost exclusively limited to the study of celestial movement, where it provided a strong tool for locating and tracking objects where data on previous locations was limited or inaccurate.

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The Analyst, Vol. 4, No. 2 (Mar., 1877), pp. 33-36

Least Squares

On the History of the Principle of Least Squares