Good Problems

David Quarfoot, PhD '15
David Quarfoot, PhD ’15 has created more than 40 crossword puzzles for The New York Times.

Math Professor David Quarfoot, PhD ’15, loves problems. You can tell by the words he uses to describe them: “elegant” and “beautiful” and “authentic.” Quarfoot chooses his words carefully, a habit picked up from his hobby making crossword puzzles for The New York Times.

“I got into them at first as a solver, like most people,” he says. But he soon had ideas for themes and clues he wanted to see, so he tried his hand at making them. Quarfoot has since created more than 40 puzzles for the Times, and when asked, he believes his background in math helps the creation process. “If you’ve gone deep enough into mathematics, you’ve developed an ability to get excited about challenges you can’t immediately solve,” Quarfoot says. “You’ve developed a resilience and can say, ‘Maybe I won’t figure this out in 10 minutes. Maybe it will take an hour to think of this word.’ That frame of mind can be applied to other disciplines, of course, and goes for both creating or solving puzzles.”

Puzzles and problems go hand in hand for Quarfoot, and they have a remarkable relation to his academic pursuits. In addition to his teaching, Quarfoot’s research concerns the nature of problems—articulating different qualities and types, the purposes they may serve and simply, what might make them good or bad.

“There are many ways to define a problem as ‘good’—a problem can be good because it helps a student understand an idea, or have greater creativity or build a skill that would serve them well in life. I’ve always believed that an easy way to change education is to just put better problems in front of students. Unlike broad curriculum requirements and other enforced standards, teachers really do have control over the kinds of problems they give. And if we understand what it means to give better problems, it could improve education overall.”

As a puzzle creator, Quarfoot often incorporates creative characters—he’s used directional arrows before, and may feature a number on occasion (hint, hint). He also enjoys themed puzzles—in which the longer entries are all related with the same clue. We asked him for one especially for Tritons, and he didn’t hold back. “Using the Times scale of difficulty, starting with Monday and getting harder through the week, I’d call this a Wednesday.”