# PRIMES: Raj Raina's Story

In 5th grade, my teacher posed an interesting question to my math class. He mentioned how, in order to get from one place to another, you first have to travel half the distance. Once halfway there, you have to travel half of the remaining distance, then half of that remaining distance, and so on. His question was how, then, do we get from one place to another if we have to go through this seemingly infinite process? This paradox was, of course, way above our heads, and most of the class disregarded it - not me. I spent hours at home trying to come up with a reasonable answer to the question; days went by with me questioning how I could have possibly traveled to my last location or the location before that. Of course, at the time, I had neither the knowledge nor the intuition to come up with the answer using the concept of infinite converging series, but that was not important. The important part was the fascination I felt when I tried to solve the problem - the feeling of wonder and enthusiasm that absorbed me into the problem and refused to let my attention free. The PRIMES program was the first time I had such a compelling interest towards mathematics since that event back in 5th grade.

When I first heard that I was selected for PRIMES-USA, I was a bit intimidated; how could I, a student who had so little experience in math research, possibly contribute anything relevant to the world of mathematics? My fear was quickly dismissed as my mentor Andrey guided me through the beautifully complex world of Ramsey Theory. Together, we made progress on branches of Ramsey Theory that had largely been undiscovered. Although the work was certainly difficult, it was even more rewarding; the moment when you solve something that no one else had considered, when you find some order in the apparent chaos of math, when you put your brick into the wall of mathematical contributions, is undoubtedly an unparalleled feeling.

I am reminded of a quote that stuck with me from Dr. Pavel Etingof at the annual PRIMES conference: "in the eyes of a mathematics problem, all are equal." This quote is the embodiment of the PRIMES experience. Although I certainly had little experience with the topic going in - far less than others in the field - the intense drive and enthusiasm that PRIMES fostered in me led me to do things I would have never thought possible. PRIMES catalyzed a rekindling for my love of mathematics, as I am sure it did for everyone else in the program.

Raj Raina worked on the project Minimum degrees of minimal Ramsey graphs under the mentorship of Andrey Grinshpun.

Email us: primes@math.mit.edu