In December 1807, a French mathematician named Joseph Fourier presented a memoir to the Paris Academy of Sciences claiming that any reasonable signal — any sound, any temperature distribution, any periodic process — could be written as a sum of sines and cosines. Lagrange, who had spent decades on trigonometric series, objected so forcefully that publication was blocked . The manuscript sat for fifteen years before it appeared in book form as Théorie analytique de la chaleur in 1822 . Fourier was trying to model heat flow in a metal bar.

Two centuries later, every JPEG image, every MP3 track, every Wi-Fi packet, and every MRI scan in routine clinical use leans on the same idea. Fourier did not aim at any of that.…