Yale students performed historically well in this year’s William Lowell Putnam Mathematical Competition, according to results released last week by the Mathematical Association of America, the competition’s organizers.

Twenty Yalies placed in the top 500 students in the competition, the fifth highest number of students in the top 500 of any institution that competed this year. Only Carnegie Mellon University, the Massachusetts Institute of Technology, Princeton and the University of Waterloo had more students in the top 500. Last year, Yale had only seven students in the top 500 — the 11th highest total in the nation.

According to Patrick Devlin, a mathematics professor and team coach for Yale, the number of Yale students in the top 500 is the highest in at least 20 years. This year’s total is almost three times larger than the average over the last two decades and 30 percent higher than the University’s previous record in that same interval.

“This is really exciting. It’s indicative of exciting new growth,” Devlin said. “It was a very pleasant surprise.”

The Putnam Competition is widely regarded as one of the most difficult mathematics competitions in the world. This year’s competition was taken by 4,638 students, of whom 1,145 achieved a score of zero out of a possible 120 points, and only 1,274 students scored more than 10 points. The competition consists of a six-hour exam, taken by undergraduates across the United States and Canada in two three-hour segments. The exam takes place once a year on the first Saturday in December. The test covers numerous areas of mathematics, from linear algebra and combinatorics to calculus.

The successful results this year reflect an anomalously high turnout for the exam last December, likely a University record, according to Devlin. The 92 students who took the exam comprised 1.6 percent of Yale’s undergraduate population — a turnout five times larger than Yale’s average attendance over the last two decades.

Devlin emphasized that, given the difficulty of the exam, having large numbers of students participate in a “communal effort” is critical to doing well overall.

A quarter of the 20 Yale students in the top 500 were first years — a disproportionately large representation compared to sophomores and juniors.

Yale’s highest scorer this year, Harish Vemuri ’21, participated in mathematics competitions in high school and attended the United States of America Mathematical Olympiad, a highly selective mathematics contest used to determine the United States’ mathematics team at the International Mathematical Olympiad. For his results in this year’s Putnam competition, Vemuri earned an honorable mention from the Mathematical Association of America.

“I did a lot of math competitions in high school; [the Putnam] was kind of the same thing. … I took [the competition] seriously, and it was nice to get a good score,” Vemuri said. “I like the problems [on math competitions] a lot more than [classroom math]. My only concern is that it is timed, you have to do it really quickly. And that’s kind of annoying, but the problems are nice.”

Along with the other first years in the top 500, Vermuri took Devlin’s “Vector Calculus and Linear Algebra I” course last semester, a class in which Putnam problems often appear on homework assignments.

Each college designates three people to represent the school in the Putnam. These students’ scores determine the university’s team score. In this category, Yale placed 20th in the United States. Devlin, however, pointed to the top 500 statistic as more indicative of how well a school performs in a given year than the team statistic.

This year’s competition featured a newly introduced Putnam seminar organized by Devlin, with the help of Yale math professors Andrew Casson and Ross Berkowitz, and the Yale Undergraduate Mathematics Society, under its co-president from last term, Aaron Berger ’18, who was Yale’s highest scorer last year.

The current co-president of the Yale Undergraduate Mathematics Society, Charles Kenney ’19, pointed to Devlin as an important force behind the improvement in the scores.

“Math at Yale is looking up. It’s really the community element that made this difference between this year and previous years,” he said. “The position of teacher for [‘Vector Calculus and Linear Algebra I’] is kind of like [that of] ‘Defense Against the Dark Arts’ in Harry Potter, it changes almost every year. … [The teacher] makes a huge difference, having a really young, enthusiastic, kind person who cares about keeping students in that class and keeping students excited about math.”

**Keshav Raghavan** | keshav.raghavan@yale.edu