Although Joseph Louis Lagrange was born in Turin, in the Italian kingdom of Piedmont, on January 25, 1736, he was of French ancestry. His father had planned for him to become a lawyer, but at school Joseph read a paper by Edmond Halley regarding the use of algebra in optics and was so intrigued he took up the study of mathematics.

Lagrange proved to be a mathematical prodigy; he was teaching geometry at the Royal Artillery School in Turin at the age of eighteen, and he established the Turin Academy of Sciences in 1758. In 1755 he came to the attention of mathematician Leonhard Euler to whom Lagrange sent an article he had written entitled "On the Calculus of Variations" (variations of orbits in celestial mechanics). Euler was in the process of addressing this topic himself, and he was so impressed that he withheld his own work, thus allowing Lagrange to publish...