The differential equations of the propagation of heat express the most general conditions, and reduce the physical questions to problems of pure analysis, and this is the proper object of theory.

Heat, like gravity, penetrates every substance of the universe, its rays occupy all parts of space. The object of our work is to set forth the mathematical laws which this element obeys. The theory of heat will hereafter form one of the most important branches of general physics.

*Analytical Theory of Heat*

The profound study of nature is the most fertile source of mathematical discoveries.

Quoted in M Kline, *Mathematical thought from ancient to modern times* (New York, 1972).

Mathematical Analysis is as extensive as nature herself.

Mathematics compares the most diverse phenomena and discovers the secret analogies that unite them.