# PRIMES: Saarik Kalia's Story

I can't really remember a time when I hadn't been interested in math. I remember playing all the math computer games that my dad would buy me when I was little. I guess even back then, though I hadn't actually done any serious math competitions, I had already begun to build up a love for it. I think middle school was really where my love of math flourished. I did all the math contests and went way ahead in the math curriculum, but I think the most important thing I learned was that math is more than just memorizing the Pythagorean Theorem or the quadratic formula and being able to plug in the parameters to get your answer. Math is about ingenuity. It's about seeing past all the numbers and seeing something much deeper underlying the problem you're working on. And it's a lot more about creativity than I think a lot of people give it credit for.

If you have taken a liking to math competitions because you've realized that maybe what you learn in school doesn't really get at that underlying beauty in mathematics, then I think you're on the right track to truly appreciating math. But there's even one further step than math competitions, and I think that's research. After a while, you might find that all the contest math problems come down to seeing the same patterns and using the same strategies that were essentially laid out for you to find. In research though, everything's different because there's no one behind a desk making sure there's a nice answer at the end of the problem, and it's a whole different experience finding an answer that nature has hidden away (and one that you weren't even sure existed) than one that a guy in the AMC office hid in choice A, B, C, D, or E.

As a PRIMES student for two years now, I can say that this research really is spectacular. In my first year, I can honestly say I wasn't too fond of my original project. I looked at the problem and I couldn't see that underlying beauty behind all mathematical phenomena. I investigated further into my problem and I still felt like I couldn't find that beauty. I suppose sometimes that's just how research is. Sometimes you are presented a question that has no nice answer or that no matter how hard you look, you just can't see that answer. But I think that's good because that makes the sensation when you do see a nice answer to a problem you're presented with far more meaningful. Over that summer, I explored much deeper in one direction of the project, and by the time December came, though the paper I had published had little to do with my original prompt, it exhibited that beauty which I had been hoping for all along. And that's the great thing about research. It is your own, and you can go in whichever direction your intuition leads you.

My project this past year has been great as well, and it's given me a whole different experience because this time I was working with a partner. I think when we first saw our project this year, we were both completely baffled, for one thing, just by trying to understand the project, but even more importantly, trying to conceive of some way that we could possibly make any progress on it. I think if I showed myself in January all the progress we've made on the project by now, he would be shocked that that work could have been our own. That just goes to show that even after doing research for one year, you'll still be surprised at what you can accomplish. Working with a partner has been great too. Having a second head to run your thoughts by is immensely helpful. It forces you to check every counterexample. It forces you to figure out how to properly explain what you're trying to say. And it gives you a new perspective and a new way of looking at everything you do.

All in all, PRIMES has had a tremendous impact on my high school experience. I don't know where I would be right now if I had never applied. PRIMES has convinced me with almost certainty that I want to make a career out of research. It has given me a way to turn my love of learning and my love of math into a way of life that I can carry on long after I finish school. They say if you love what you do, you never work a day in your life. I think if I do end up in a career in research and it's anything like my experience at PRIMES, I won't ever have to work a day in my life.

Saarik Kalia, together with Michael Zanger-Tishler, worked on the project Schmidt games and a family of anormal numbers under the mentorship of Tue Ly.

Email us: primes@math.mit.edu