Little did I know that PUMaC would end up playing a huge role in my college experience. It is entirely run by Princeton undergraduate students, and during my sophomore and junior year at Princeton, I coordinated the 100+ volunteers and managed a lot of the logistical aspects of the competition.

How does the competition work?

Teams of 8 students compete in a power round (which is proof based and done in the week leading up to the competition), 2 individual rounds (students choose from algebra, geometry, combinatorics, and number theory), and a team round (which usually has some fun gimmick to tie it together). There are two divisions which teams can compete in - A and B - meant to give less experienced teams a chance of success. Individuals who excel in one of the individual tests are invited to take the individual finals, an extremely challenging proof based round, which puts them in the running for the individual awards (but doesn't count for team awards). In the afternoon when the individual finals and grading happens, there are lots of mini-events to keep the students occupied, like a puzzle hunt, board games, a math bowl competition, and a lecture by a prominent professor. The competition is aimed at high school students, but advanced middle schoolers occasionally attend.

One of my favorite aspects of the competition is that each team is assigned their own proctor and room. The proctor is a Princeton student, and often ends up talking with their team and answering questions about Princeton and college in general. To my knowledge, PUMaC is the only competition that does this - others have students in large lecture halls, or use parents and coaches as proctors. PUMaC's choice to do this makes a lot of extra work for the organizers and limits the size of the competition, but also makes for a better and more personal student experience.

While I was lucky to live in easy driving distance of Princeton, teams do come from all over the country (and even all over the world), to participate. They have also started offering a power competition which only involves the power round and does not require traveling to campus - teams submit their solutions by email.

In addition to the math itself, on-site competitions like PUMaC are valuable because (like math circles and camps) they bring students into an environment where being excited about math is the norm, give them opportunities to develop friendships with others who share their interests, expose them to aspects of math culture, and help to cement their identities as "math kids".