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 ...

The authors do not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and have disclosed no relevant affiliations beyond their ...

On his website andertoons.com, illustrator Mark Anderson has a cartoon in which a boy is handing his teacher an assignment. “To show how well I understand fractions,” he says, “I only did half of my ...