Harvard math students chase hard problems for the pure joy of solving

Easton Singer '26 walked out of a six-hour math competition on a Saturday in November with orchestra rehearsal waiting and graduate school applications still unsigned. He'd voluntarily spent his reading period on the William Lowell Putnam Mathematical Competition — the most prestigious math contest for undergraduates in North America — not because he had to, but because he wanted to.

"I take it just because it's fun," Singer said. "It's the best chance to do math problems."

That sentence captures something real about how the best problem-solvers actually work. The Putnam isn't a resume line for most who attempt it. It's a puzzle box that attracts people who find genuine pleasure in the hunt.

The exam itself is genuinely brutal. Twelve questions, ten points each, a perfect 120 is nearly mythical — achieved only five times since 1938. Last year, just five students worldwide scored 80 or above. Fewer than 1% of competitors even reached half points. Yet roughly 4,000 undergraduates sit for it annually, most knowing the odds are stacked against them.

"It just feels good when you solve the hard problems," said Andrew Gu '26, who has twice placed in the Putnam's top 16. "In some problems, discovering the little trick that they put in there just feels magical."

That word — magical — matters. It's the feeling of a mechanism clicking into place, of seeing the hidden structure beneath chaos. It's not about beating others. It's about the problem itself finally yielding.

A deliberate choice against the grind

Historically, Harvard dominated the Putnam team rankings. But in recent years, MIT has claimed 69 of the top 100 spots and swept the entire top five "Putnam Fellows" five years running. The difference isn't aptitude — it's approach.

MIT runs official prep workshops and dedicated training classes. Harvard's Department of Mathematics has made the opposite choice. Beyond registration and advertising, the department hosts one event: a "Putnam Postmortem" to review solutions afterward.

"I think it makes sense to de-emphasize competition mathematics," explained Professor Noam Elkies, himself a three-time Putnam Fellow from his undergraduate years at Columbia. "As one progresses from grade-school math to college and beyond, one moves further from the domain of competition problems that are guaranteed to be solvable within an hour or so under the constraints of a closed-book exam."

It's a philosophy that trusts students to find their own motivation. Cindy Jimenez, the undergraduate program coordinator for mathematics, noted the irony: "It's worthy to note how well Harvard does despite the lack of departmental-organized practices and training, especially against large universities that hold Putnam workshops and classes."

After the exam, the Science Center hall filled with laughter and animated conversation as students compared solutions. "It was really cool seeing other methods people use, because there are so many different ways to get the same answer," said Matteo Salloum '28. "It's very illuminating, because math is very collaborative."

That's the real insight. Competition math, stripped of the institutional pressure, becomes what it was always meant to be: a shared language for people who think in patterns and love the moment when a pattern finally reveals itself. Singer left the exam content with his effort, then rushed off to piano rehearsal for the Harvard College Opera.

Six problems solved. One Saturday well spent. No regrets.