PRIMES: Ziv Scully's Story
PRIMES is an incredibly unique and uniquely incredible experience. I had wanted to do math research ever since I attended Canada/USA Mathcamp, which opened my eyes to the breadth and beauty of mathematics, but this interest was made real by PRIMES and my mentor. There are so many math problems, some of which are solved and some of which are not easily approached by someone like me who has a (relatively) limited mathematical background. Just finding an appropriate concept to study—let alone narrowing down to a particular problem—is probably the biggest obstacle between high school students and math research. At PRIMES, mentors and faculty suggest potential projects that they think are both interesting and possible, but this still leaves students with many options. My mentor, Yan, introduced me to the parallel chip-firing game, but it was ultimately my decision what aspects of the game to examine closely.
Note that a possible project need not be an easy project! Doing math research is difficult, especially when balancing it with everything else in the school year. However, it's very helpful to do research over a relatively long period of time; if you think about the problems often enough, ideas start swimming around on their own even when you're not focusing only on math. You are exploring the unknown, so there can be several weeks when it feels like you make minimal progress, but this makes it only more satisfying when you finally do find something new. My mentor suggested three specific questions about the parallel chip-firing game as targets. All of those questions remain unsolved, but we introduced a new tool for studying the game that opens up many new questions.
I recommend PRIMES to virtually anybody who loves math. Research is perhaps the most exciting thing about mathematics, but it's difficult to go at it alone with no prior experience. Having a mentor to suggest a possible problem, discuss ideas with and provide direction if those ideas run dry is what PRIMES offers, and it turned me from someone who was curious about research into someone who was capable of doing it. There are very few places where high school students have this type of opportunity. Try it!
Ziv Scully worked on the project Progress on the parallel chip-firing problem under the mentorship of Yan Zhang.