One of my favourite stories, which is really about the importance of looking at things the right way!
During the Second World War, the British government wanted to figure out how to better protect their planes. They did a survey of the bullet holes on the planes that had returned

On the basis of the where the damage was maximum, they decided where to put extra armour.
One man, a Hungarian Jew mathematician named Abraham Wald, disagreed. His theory was that planes with bullet holes in the other places never made it back.

While there were holes in specific places in the examined planes, all these planes had made it back, so it was clearly not that dangerous. So he recommended exactly the opposite, the undamaged places should be the most heavily armoured. His insight saved thousands of lives!