Problem-solving pros: Three math majors get results at Putnam competition

Spending long hours in a room solving fantastically difficult math problems doesn’t seem like an award-winning plan for the weekend.

Unless you’re a math major.

A trio of mathematical sciences majors received non-zero scores at the 2021 William Lowell Putnam Mathematical Competition, the preeminent undergraduate mathematics competition in the United States and Canada. More than 4,000 students participate during the first Saturday in December, spending a total of six hours solving a dozen problems.

There are cash prizes for the top five teams and the top five students, but solving a problem —any problem — is an honor in itself.

Overall, the six-member Binghamton University team placed 54th out of 427 participating institutions. Junior Ashton Keith scored on five of the problems and received an honorable mention; he was ranked 89th out of 2,975 student participants. Sophomore Levi Axelrod solved two problems and first-year student Eric Wang, one.

If that doesn’t seem impressive, consider this.

“The median score in the competition has been zero many times,” Axelrod said. “More than half the people don’t get a single point on a single problem.”

Last year’s competition was conducted online due to the pandemic. This year, it was held in person, with all six team members working silently on problems in a proctored room.

The process is straightforward, Wang said: Students receive a paper with six questions, which they solve for the next three hours. After a lengthy break, they return for a second round of the same.

“It sounds like a lot of time, but the test moves faster when you’re lost in thought,” he said. “Six hours sounds like a lot of time for 12 questions, but I used all six hours and only managed to really think about three of the questions. And of those three questions I only got points on one of them.”

The right answer isn’t enough on its own. To get credit for an answer, the competitors need to provide a mathematical proof. Axelrod should know: During last year’s competition, he realized that the answer was between two and three; the constant e fits the bill, and often shows up in similar circumstances. He jotted down e — correctly.

“But I didn’t have enough proof, so I didn’t get any points for it. It was kind of a long shot,” he said.

Wang first learned about the Putnam competition in high school and asked his professors about registering once he started at Binghamton. The competition appeals to people who enjoy the problem-solving and competitive side of the field; he has been participating in some form of competitive math since the sixth grade, he said.

Axelrod also got an early start; in grade school, he looked forward to extra-credit problems on math tests that required him to think about a concept in a creative and unexpected way. Likewise, the Putnam competition is also a series of puzzles.

“There’s a bug that math majors catch. Once you have a good enough understanding of math, where you don’t feel like you’re drowning in it, the really interesting problems start feeling like solving puzzles,” Axelrod explained.

“You’re solving puzzles the entire time and you kind of get into the zone,” Keith added. “And if you do actually solve one, it’s extremely satisfying.”

The Mathematical Sciences Department offers support to students looking to expand their problem-solving skills. Associate Professor Alexander Borisov has been meeting informally with students to solve past competition problems, for example, while Professor and Chair Marcin Mazur organizes a Problem of the Week for the enjoyment of math faculty and students. There’s the Math Club, too, headed by advisor and adjunct lecturer David Biddle.

Wang, Keith and Axelrod already have this year’s Putnam competition penciled in on their calendar.

“I mean, I have nothing to do that weekend,” Keith joked.