The Analytic Theory of Heat
In 1822, Fourier published his work on the flow of heat in Théorie analytique de la chaleur ( The analytical theory ).Fourier claimed that any function of one variable, whether continuous or discontinuous, can be expanded into a series of sines of multiples of the variable. This result is not correct without additional conditions, but Fourier's observation that some discontinuous functions are the sum of infinite series was a breakthrough. This work provides the basis for what is now known as the Fourier transform.
Real roots of polynomial
This work contains much original material, in particular, Fourier's theorem on real roots of polynomials , published 1820.
Description of the greenhouse effect
Fourier suggested that the Earth's atmosphere might act as an insulator of some kind. It is widely recognized as the first proposal for what is now known as the greenhouse effect (although Fourier never called it that).
One of his best-known phrases is: p>
„The profound study of nature is the most fertile source of mathematical discoveries.“