Jean Baptiste Joseph Fourier [L1 ], who flourished in Revolutionary and Napoleonic France, was a mathematician and public figure whose solution of certain "heat problems" essentially frames all of modern analysis (or at least so CL proposes). "Fourier analysis", as he appears to have understood it, deals with the decomposition of functions into their harmonic components, that is, expression as a sum of characteristic sinusoids or equivalent trigonometrics.
See also: Fast Fourier Transform