During WWII, the Royal Air Force called upon a mathematician to improve their bombers. Specifically, they wanted to reduce the chances of them being shot down.
Bombers are relatively slow moving targets escorted by smaller fighters to protect them from air attacks. But antiaircraft fire would occasionally knock them down.
So a reasonable solution was to put metal armor on the bottoms.But putting metal armor all over the bottom would add too much weight.
So this mathematician examines the bottoms of all the bombers which had been in combat. Most had at least some damage to their undersides, clustered about seemingly at random over the bottoms. After examining all the locations the bombers had received damage, he made a recommendation.
What was it?