How did you learn the mathematical formula for pi? It was likely the way I learned it. I was told to commit the value pi = 3.14 to memory along with the formula to calculate the area of a circle.

A year after he started his Ph.D. in mathematics at McGill University, Matt Bowen had a problem. “I took my qualifying exams and did absolutely horribly on them,” he said. Bowen was sure that his ...