On July 18 at the Program in Mathematics for Young Scientists (PROMYS) math camp, Jordan Ellenberg gave the 2024 Arnold Ross lecture. The audience was talented teens and their undergraduate counselors. The Arnold Ross lecture was named after Arnold Ross for his many contributions to the development of mathematical talent, including outreach programs at Ohio State that survive to this day.

In a vigorous hour, Ellenberg introduced the “cap set problem,” a popular question in combinatorics which is related to large subsets of integers containing no three terms in arithmetic progression, and to the card game Set.

He engaged the audience, asking them to work together on a simpler example so they could get a feel for the problem. Most everyone called out the same answer – “4!” – to Ellenberg’s delight.

Sixteen-year-old Lisa from California summed it up. “I thought the way Jordan related a simple yet well-known game of Set to a fundamental problem in number theory reflected a core value of PROMYS: Think deeply about simple things.”

Not coincidentally, “To think deeply about simple things” was a motto of Arnold Ross.