Benoit Mandelbrot is one of the most celebrated mathematicians of the 20th Century. At the age of 14/15, Mandelbrot found himself as a Jew in Nazi-occupied France, marked for death. A French Resistance leader, David Feuerwerker, made provisions to keep him alive and hide him, but The Battle of Britain was raging. Supposedly, although Wikipedia will not confirm this outright, The Battle of Britain inspired him to begin trying to solve one of the most lingering applied math problems of all time: How long is the coast of Britain?
He would eventually solve this question by answering that the length was technically infinite, and revolutionize mathematical thinking and formalize the study of Fractals doing so. Fractals have been really important in the development of modern computer hardware and semiconductors among other things. It’s a strange story.