New Delhi, Nov. 27 -- World War II saw the full fury of air power in battle, first exercised by Axis forces and then by the Allies, culminating in American B-29 bombers dropping atomic bombs on Hiroshima and Nagasaki. But before that, as the US sent warplanes behind enemy lines in Europe, most were shot down by German tanks and air fighters. A pressing need was to armour these planes. But this made these craft heavy.

It was a classic optimization problem: How much of the plane should be armoured?

In came Abraham Wald, a mathematician working at the Statistical Research Group of Columbia University. His first task was to call in data, specifically on the surviving fighters' bullet holes, which was duly presented to him. On average, the p...