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Fourier wished to know when the Earth began:
Fourier was much more a scientist by inclination than a mathematician. But he was intrigued by the study of conductive heat flow. Why? Fourier conjectured, as did the Comte de Buffon (Georges Louis Leclerc) before him, that the Earth had been formed from molten material flung out from the Sun. They felt that if they could calculate the time taken for the Earth to cool to today's temperature, they would know the age of the Earth!
The calculations would be complex and time-consuming. So a motivated Fourier developed time-saving mathematical algorithms (known now as Fast Fourier Transforms, or FFTs) to aid his solving this mystery of when the earth began. His interest in mathematics was not for its own sake but as a means to an end.
This was dangerous work, as religious teaching at the time was that Earth was created in 4004 BC. Newton was estimating Earth's age at 50,000 years. Buffon decided Earth must be at least 75,000 old. Fourier's much-more-accurate calculations, though, yielded a planetary age of 100 million years. Modern science puts Earth's age only about 50 times greater than Fourier's number, calculated circa 1820! But to be fair to Fourier, there's no way he could have guessed that radioactivity is keeping the earth hot.
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Reference: This information was found in, but not quoted from, John Gribbin's 2002 Random House book The Scientists: A History of Science Told Through the Lives of Its Greatest Inventors.
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