The commissions in the scientific corps of the army were reserved for those of good birth, and being thus ineligible, he accepted a military lectureship on mathematics.

Fourier accompanied Napoleon Bonaparte on his Egyptian expedition in 1798, as scientific adviser, and was appointed secretary of the Institut d'Égypte.

In 1801,[4] Napoleon appointed Fourier Prefect (Governor) of the Department of Isère in Grenoble, where he oversaw road construction and other projects.

Fourier was buried in the Père Lachaise Cemetery in Paris, a tomb decorated with an Egyptian motif to reflect his position as secretary of the Cairo Institute, and his collation of Description de l'Égypte.

Though this result is not correct without additional conditions, Fourier's observation that some discontinuous functions are the sum of infinite series was a breakthrough.

Fourier left an unfinished work on determining and locating real roots of polynomials, which was edited by Claude-Louis Navier and published in 1831.

[15] In the 1820s, Fourier calculated that an object the size of the Earth, and at its distance from the Sun, should be considerably colder than the planet actually is if warmed by only the effects of incoming solar radiation.

[17] However, in the end, because of the large 33-degree difference between his calculations and observations, Fourier mistakenly believed that there is a significant contribution of radiation from interstellar space.

[19][20] In his articles, Fourier referred to an experiment by Horace Bénédict de Saussure, who lined a vase with blackened cork.

Fourier noted that if gases in the atmosphere could form a stable barrier like the glass panes they would have a similar effect on planetary temperatures.

[21] Fourier noted that the actual mechanisms that determine the temperatures of the atmosphere included convection, which was not present in de Saussure's experimental device.