# PRIMES: Nihal Gowravaram's Story

Like many other PRIMES students, I've always had an affinity for math. As a young child, I always loved playing around with numbers and discovering new things. But, as I grew older, this exploration was replaced by something more concrete: competitions. Initially, I embraced competitions, as it gave me the chance to challenge myself beyond the classroom curriculum and form friendships with other competitors. But, as time went on, I grew unsatisfied. Though math competitions were integral in developing my skills, I felt that math could not be confined to doing "x" problems in "y" minutes. I wished to rekindle the sense of exploration towards math that I had when I was younger: my answer was PRIMES.

At first, I was skeptical; how could I, a high school sophomore, conduct mathematical research? Soon, however, PRIMES made me realize that this goal was not out of sight. Working with my brilliant mentor Dr. Joel Brewster Lewis, I began an extensive study of pattern avoidance, a branch of combinatorics, with my research partner Ravi Jagadeesan. Though at first I was intimidated by some of the background reading, with reassurance from my mentor, I continued to persist onwards, reading a single paper dozens of times for hours or even days. Similarly, PRIMES taught me patience. Through math competitions, I had always expected to get an immediate "Aha" moment to lead me to the correct solution/answer. Yet, math research problems are not engineered like competition problems, and so, I initially found myself frustrated. However, I soon learned to grow patient, as the process of mathematical inquiry itself grew to satisfy me, and that eventual "Aha" moment was all the more satisfying.

Thus, upon writing our paper, I had an immense feeling of satisfaction, not only because I had written a paper and conducted original math research, but also because I had rediscovered my childhood interest in math as a process of discovery. PRIMES has provided me with a new outlook on mathematics and has fostered my desire to continue with math research. Thank you, PRIMES!

If you're a high school student who loves math, applying to PRIMES will be the best decision of your life.

**Nihal Gowravaram**,
together with Ravi Jagadeesan,
worked on the project
Beyond alternating permutations: Pattern avoidance in Young
diagrams and tableaux
under the mentorship of Dr. Joel Lewis.

**Email us:**
primes@math.mit.edu