PRIMES: Saarik Kalia's Story


I canít really remember a time when I hadnít 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 hadnít 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. Itís about seeing past all the numbers and seeing something much deeper underlying the problem youíre working on. And itís 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 youíve realized that maybe what you learn in school doesnít really get at that underlying beauty in mathematics, then I think youíre on the right track to truly appreciating math. But thereís even one further step than math competitions, and I think thatís 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, everythingís different because thereís no one behind a desk making sure thereís a nice answer at the end of the problem, and itís a whole different experience finding an answer that nature has hidden away (and one that you werenít 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 wasnít too fond of my original project. I looked at the problem and I couldnít see that underlying beauty behind all mathematical phenomena. I investigated further into my problem and I still felt like I couldnít find that beauty. I suppose sometimes thatís 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 canít see that answer. But I think thatís good because that makes the sensation when you do see a nice answer to a problem youíre 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 thatís 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 itís 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 weíve 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, youíll 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 youíre 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 donít 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 itís anything like my experience at PRIMES, I wonít 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.




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