During the Second World War, the Army Air Corps came to a mathematician named Abraham Wald with a pressing question. Officers had surveyed returning bombers after each mission, tabulating the number of bullet holes on each section of the planes. How much more armor, they wanted to know, should go on the fuselage, where the greatest number of bullet holes were found, versus on the engine, where the fewest appeared?
They got an answer, but it wasn’t the one they expected. Put the armor where you find the fewest holes, Wald told them. There are so few holes on the engine nacelles, he explained, because the planes hit there simply never make it home to get counted.
It’s a wonderful illustration of the power of mathematical reasoning. Jordan Ellenberg, a University of Wisconsin—Madison mathematician, recounted the story on Tuesday at the Aspen Ideas Festival.
But the story also illustrates the quandary facing educators and policymakers as they consider the role of mathematics in the 21st century. Wald, after all, didn’t turn to calculus, or trigonometry, or geometry to obtain his answer. Nor, for that matter, do most Americans use the abstract techniques they master in their classrooms when they draw on quantitative reasoning and mathematical skills in their daily lives.