D-Day and the Mathematics of Tides

The success of D-Day on June 6, 1944 depended critically on mathematics. The landing required a specific combination: low tide (to expose beach obstacles), enough light for bombardment, and a rising tide to float landing craft off the beach. British mathematician Arthur Doodson — who had built the world's first tide-prediction machine in 1919 — provided precise tide tables for Normandy. He decomposed tides into 114 harmonic constituents using Fourier analysis, effectively performing a harmonic analysis of the ocean. Mathematics helped liberate Europe.