# PRIMES: Kavish Gandhi's Story

A long time ago in a galaxy pretty close to here, I was born. Although I was not Force-sensitive and the Jedi Academy turned down my application on the grounds that they did not “accept people that lived in the real world,” I soon discovered something far greater than the Jedi Order: mathematics. I first encountered math in the form of addition, division, subtraction, and multiplication, and I soon was hooked; how one could manipulate all of those confusing symbols to solve a problem was wondrous to me. Going into middle school and high school, I had not been exposed to many different areas of mathematics; for the most part, my outside-of-school mathematics experience had been limited to competitions. For a while, I thought that math came in the form that you see in mathematics competitions; ready-made problems that almost invariably have elegant solutions and, of course, always have an intended approach. Competitions fascinated me, and, for a while, were enough to quench my thirst for new, interesting mathematics.

Then I found PRIMES. At first, I was skeptical that I, a high school student, could do research that interested real mathematics professors. After a long application process, I was thrilled to be accepted into the program and soon realized that not only could I do research, I was able to think about mathematics in a completely different way. With competitions, you often use pre-developed and pre-memorized techniques; however, with research, there is no set technique or cookie-cutter approach. Often, we found ourselves inventing our own techniques or manipulating known techniques to solve the problems that we encountered. And, often, the problems yielded solutions that we were not expecting and led us to new and interesting areas of research. PRIMES really opened my eyes to the essence of mathematics: not solving problems, but exploring problems. You may find results, but mathematics is not only about the results; it’s about how you got there.

I think the most rewarding thing about research is the feeling that you get when discovering something new. When you solve a competition problem, you know that there is already a designated solution, even with proof-based competitions. However, with research, people really do not know where their research will lead outside of speculation, and therefore you really are on the cutting-edge. This mystery, this idea that what you’re doing could lead almost anywhere, is amazing.

In sum, I think that PRIMES has been an invaluable experience for me, and most definitely would be an exceptional experience for any high school student interested in mathematics. There is no doubt that it is hard; research does not come easily or quickly, but rather requires hours upon hours of struggle. However, doing research is something that every mathematically-inclined student should be exposed to, and the PRIMES program does an extraordinary job of introducing and enveloping you in the research experience. I cannot laud it highly enough; the mentors are outstanding, the projects are great, the support is exceptional, the experience is phenomenal. Oh, and remember to never trust a Sith lord, and may the Math be with you.

**Kavish Gandhi**, together with
Noah Golowich,
worked on the project
Inequalities and partition regularity of linear homogenous
equations under the
mentorship of Laszlo Lovasz.

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