This Math Professor Loves a Good Problem

Article Content

This story originally appeared in the fall 2026 issue of UC San Diego Magazine as “Across and Down.”

David Quarfoot, PhD ’15, associate professor of mathematics at UC San Diego, loves a good problem. You can tell by the words he uses when describing one: Elegant. Beautiful. Authentic. For a mathematician, that's not unusual. For a cruciverbalist, or someone who constructs crossword puzzles, it starts to feel like a personal philosophy. Quarfoot is both, with more than 40 puzzles published in The New York Times to prove it.

Quarfoot came to puzzles the way most do, as a solver. But ideas for themes and clues kept surfacing, and eventually, he decided to try building them himself. It turns out the mathematical skills transfer more cleanly than you might expect.

“If you've gone deep enough into mathematics, you’ve developed an ability to get excited about challenges you can’t immediately solve,” he says. “You develop a willingness to sit with something and let it take an hour, or a day.”

That frame of mind, he’ll tell you, applies equally to developing a crossword grid. The creative side is finding the spark — noticing, say, that Belgian waffles, French fries and Canadian bacon all contain country names and building outward from there. The technical side is pure math, a probabilistic exercise in which every letter placed opens up or eliminates possibilities. Load a corner with z’s and q’s, and you've painted yourself into one. Choose your words wisely, and the whole thing falls into place.

It isn’t so different from Quarfoot’s mathematical research, which examines the nature of problems themselves — what makes them good, what purposes they serve and how better problems might quietly transform education.

“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,” he says. “An easy way to change education is just to put better problems in front of students.”

For the latest issue of UC San Diego Magazine, Quarfoot is doing just that — but for readers — one square at a time.

View the answers to Professor Quarfoot's latest crossword puzzle created just for UC San Diego Magazine.