Fourier, the son of a tailor from Auxerre in France, was educated at the local military school and later at the Ecole Normale in Paris. He held posts at both the Ecole Normale and the Ecole Polytechnique where he was a very effective and influential teacher. In 1798 he accompanied Napoleon on the invasion of Egypt and later contributed to and oversaw the publication of the Description de l'Egypte (1808–25), a massive compilation of the cultural and scientific materials brought back from the expedition.

Fourier's most important mathematical work is contained in his Théorie analytique de la chaleur (1822; The Analytical Theory of Heat), a pioneering analysis of the conduction of heat in solid bodies in terms of infinite trigonometric series, now known as Fourier series. Fourier was led to consider these series when attempting to solve certain boundary-value problems in physics and his interest was always in the physical applications of mathematics rather than in its development for its own sake. His work continues to be extremely important in many areas of mathematical physics, but it has also been developed and generalized to yield a whole new branch of mathematical analysis, namely, the theory of harmonic analysis.