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“Profound study of nature is the most fertile source of mathematical discoveries.”

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Joseph Fourier livre The Analytical Theory of Heat

Source: The Analytical Theory of Heat (1878), Ch. 1, p. 7

“The principles of the theory are derived, as are those of rational mechanics, from a very small number of primary facts”

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Joseph Fourier livre The Analytical Theory of Heat

Source: The Analytical Theory of Heat (1878), Ch. 1, p. 6
Contexte: If we consider further the manifold relations of this mathematical theory to civil uses and the technical arts, we shall recognize completely the extent of its applications. It is evident that it includes an entire series of distinct phenomena, and that the study of it cannot be omitted without losing a notable part of the science of nature.
The principles of the theory are derived, as are those of rational mechanics, from a very small number of primary facts, the causes of which are not considered by geometers, but which they admit as the results of common observations confirmed by all experiment.

“The analytical equations, unknown to the ancient geometers, which Descartes was the first to introduce into the study of curves and surfaces, are not restricted to the properties of figures, and to those properties which are the object of rational mechanics; they extend to all general phenomena. There cannot be a language more universal and more simple, more free from errors and from obscurities, that is to say more worthy to express the invariable relations of natural things.
Considered from this point of view, mathematical analysis is as extensive as nature itself; it defines all perceptible relations, measures times, spaces, forces, temperatures; this difficult science is formed slowly, but it preserves every principle which it has once acquired; it grows and strengthens itself incessantly in the midst of the many variations and errors of the human mind.
Its chief attribute is clearness; it has no marks to express confused notions. It brings together phenomena the most diverse, and discovers the hidden analogies which unite them.”

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Joseph Fourier livre The Analytical Theory of Heat

Preliminary Discourse, p.7 Note: often quoted as Mathematics [or mathematical analysis] compares the most diverse phenomena and discovers the secret analogies that unite them.
The Analytical Theory of Heat (1878)