“The visual is central to all levels of mathematics,” said Witheley, delivering his opinions one day to a small amphitheather of schoolteachers at a mathematics conference at York University. “It changes the question you ask, it changes the methods you use, it changes the answers, and it changes the way mathematicians communicate and teach. What you see is central to how you reason and problem solve.”
One of his vignettes recounted a problem during the Second World War, when the British were losing too many aircraft. Mathematician and statistical theorist Abraham Wald worked on the problem of how to save more planes ; he was trying to determine where extra armor plates would be most beneficial. His first instinct was to add armor to the most damaged areas of returning planes, but after analyzing the visual data – the patterns of bullet holes on returning aircraft – Wald reached the opposite conclusion. He conducted his analysis by drawing and outline of a plane and cumulatively marking all the places where returning planes had been shot, which left almost the entire image covered, except two crucial locations. Wald then correctly surmised that the planes lost in battle had been hit in the unmarked areas – the cockpit and the tail engine – indicating it was those areas that needed more armor.
Soibhan Roberts (2006), King of Infinite Space : Donald Coxeter, The Man who Saved Geometry