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.
The courses offered in high school—and even more so those in college—help students master domains of knowledge that only a small minority of them may ever use to practical effect, even if that knowledge may enrich their lives and broaden their understanding. A curriculum more focused on proportions, quantitative analysis, logic, and statistics might be better tailored to their career goals and needs. But that curriculum would also deny those students the opportunity to explore much of the mathematical world.
Is math just a ticket to a good job, or is it the key to unlocking a secret world of beauty?
There’s no question that math can be useful. “The jobs of the 21st century rely on a highly quantitative-skilled workforce,” said Steven Strogatz, a professor of applied mathematics at Cornell. “If you want to go into high tech, or modern medicine, or finance, you’ll need to know a lot of math. And if you systematically turn yourself off from math, you won’t have those opportunities.”
There is also broader utility to knowing more-fundamental math, Strogatz added, as a means of developing critical thinking and problem solving. “A well-informed citizenry needs to know when politicians are lying, and needs to be able to evaluate risk,” he said. These sorts of skills, though, don’t require learning the quadratic equation. They might suggest reorienting the curriculum away from more-abstract fields of math, and toward practical applications.
But reducing math to its practical utility, Strogatz cautioned, sells it short. “Math is fantastic and beautiful,” he said. “If you miss out on the content of math ... your life is not as rich as it could be.”