PRIMES: Travis Schedler's Story
My first serious experience with research mathematics was as a high schooler, when I attended the Research Science Institute (RSI) at MIT. This program, on which PRIMES is partially based, paired me with a graduate student mentor, Sasha Soloviev. We ended up obtaining our research problem from Prof. Etingof, and my work on the problem turned into a collaborative one with Etingof and Soloviev. This was extremely exciting and opened up a whole new world for me, where it was possible to observe and prove completely new phenomena. While the phenomena were quite concrete and observable via the computer, it was totally unclear how to prove it, and the elegant methods we ended up using, based on elementary group theory, amazed me. Ever since then, I have been addicted to mathematical problems, particularly those of an algebraic nature that admit nonobvious but often quite elementary and deep solutions.
My mentors, Etingof and Soloviev, were integral to my success and to developing my interest in research mathematics. Even now, the world of research mathematics is often a murky one to explore, and it is unclear which paths to take. Etingof and Soloviev's guidance, in terms of posing the problem, steering towards the solution, and helping me learn mathematics and the proper way to think about research problems, was essential. As a high school student, if not also as an undergraduate or graduate student, it is difficult to find one's way in research mathematics and discover its joy without guidance. Furthermore, for me it is always much more exciting to explore research problems in communication or collaboration with other mathematicians. Even though I attended a top magnet high school, there was no opportunity to discuss mathematics with active researchers there, and my experience with Etingof and Soloviev was incredibly eye-opening.
Aside from obtaining very interesting mathematical results, a taste of mathematical research, and learning a great deal, I entered my project into the Westinghouse Science Talent Search (now Intel) and placed fifth in the nation, often a near guarantee of admission to top colleges; I also published a joint article with Etingof and Soloviev in the prestigious Duke Mathematical Journal. This publication has paid many dividends over the years, both in terms of interesting contact with other researchers expanding on our results, and probably even in terms of obtaining admission and/or jobs.
It is hard to describe in words the feeling of doing mathematical research. It is more than merely satisfying and exciting. Learning mathematics in school or from books, in its distilled and perfected form, it is hard to understand its origin. Usually, these results have an empirical origin, either by working out many examples, trying to solve applied problems, or simply by trial and error of different possible approaches. This origin is generally hidden, as only the most efficient route is presented in class. However, by carrying out original research, one gains a new appreciation for the subject and its many mysteries, how remarkable the well-established results taught in school really are, and how they might have been obtained. One experiences firsthand, rather than secondhand, discovery.
I firmly believe that any high schooler who likes mathematics and is curious about its true nature, or is interested in exploring what life is like on its frontiers, could scarcely do better than to attend the PRIMES program. It is certain to be very exciting and eye-opening, and one is certain to gain lasting and valuable friendships and mentors along the way. Above all, it is great fun! And, of course, it can provide valuable life experience, whether a head start on a career in mathematical or scientific research, or simply valuable analytical and personal skills applicable in any future endeavors. Finally, the experience and resulting accomplishments are quite likely to be helpful in college admissions and beyond.
Travis Schedler, the 5th place in the 1997 Westinghouse competition for a project done at the RSI under the guidance of Pavel Etingof and Alexander Soloviev.