Jean Baptiste Joseph Fourier ( March 21 , 1768 - May 16 , 1830 ) was a French mathematician and physicist who is best known for starting the investigation of Fourier series and their use to problems of heat flow . Jean Baptiste Joseph Fourier ( 21 March 1768 -- 16 May 1830 ) was a French mathematician and physicist best known for initiating the investigation of Fourier series and their applications to problems of heat transfer and vibrations .