When Ayush Tibrewal ’26 and William Ning ’26 meet for weekly Putnam Seminars, the discussions are as much about camaraderie as they are about cracking problems. 

Yalies, including Tibrewal and Ning, prepare to tackle the William Lowell Putnam Mathematical Competition — one of the most prestigious and notoriously challenging exams in collegiate mathematics, held annually in December. The math department supports participants through fall seminars designed to sharpen problem-solving skills while fostering a collaborative spirit.

“The Putnam is a test of problem-solving and creativity, not just mathematics,” Tibrewal wrote. “It’s about finding joy in solving hard problems, no matter the score.”

The Putnam challenges students across North America to solve 12 exceptionally tough proof-based problems over six hours. With a median score often hovering around two out of 120, the exam is both a formidable challenge and a rare opportunity to compete in collegiate-level mathematics. 

The Putnam’s difficulty sets it apart from other math competitions. Unlike high school contests, which focus more on computational skills, the Putnam emphasizes proof-based reasoning. 

Andrew Yarmola, a faculty member who helps organize the seminars, explained that the problems require insight and creativity rather than mastery of advanced theorems.

“Most research mathematicians would need hours to solve these problems, but Putnam participants have only six,” Yarmola wrote.

Ning added that another challenge of the Putnam is that the problems are “unlike anything you’ve seen before” and a successful solution often involves stringing together simple but unintuitive steps.

Weekly seminars help students practice with past problems while introducing key strategies. These sessions are also a space for building community.

“The moment when a group of students cracks a problem together is always inspiring,” Yarmola wrote.

For some, the Putnam is an important academic milestone, offering recognition and opportunities for those who excel. However, many participants approach it because of their sheer love of math.

“Even solving one problem is impressive,” wrote Yarmola. “It’s not about points—it’s about the engagement.”

Beyond the Putnam, the math department continues to nurture students’ problem-solving skills with events like the Barge Competition in the spring. This internal contest focuses on easier problems, making it a stepping stone for those interested in taking the Putnam in future years.

The collaborative environment also fosters lighter moments. Yarmola recalls one memorable seminar when a group of students cheered as a participant spent 20 minutes flipping a marker until it landed upright.

“Ultimately, the Putnam is about having fun, practicing, and never giving up,” Yarmola wrote. “It’s a way to remember that math is not just challenging—it’s also beautiful.”

The 85th Putnam Competition will be held on Saturday, Dec. 7.