PRIMES: Christina Chen's Story
I was interested in mathematical research because I wanted to do something that was more advanced than simply problem solving. I wanted to exercise both my interest and willpower by solving problems that have not been solved before. I think that sometimes solving solved problems can seem somewhat limited because you know that a (reasonably) elegant solution exists and sometimes, even solving a difficult problem may be anticlimactic once you realize that many people have solved the problem before, maybe with more elegant approaches. Therefore, I imagined that I might derive a greater sense of accomplishment from research. I also anticipated that research would be a lot more difficult, and I was excited to see how I could confront all the setbacks and dead ends that seem common in research. In a way, I wanted to experience these feelings and try to obtain something valuable from them.
My mentor, Tanya Khovanova, has been extremely helpful in developing this interest. She has a knack for insights and varied suggestions that would excite me for a week until our next meeting. She is also willing to tell me whether parts of my explanations or my writings seemed mushy, so that when I correct them, I feel extremely thorough. The professor who suggested my project, Dan Klain, has also been immensely helpful. He always explained to me any technical details that I didnít understand, so my lack of previous knowledge did not significantly hinder my progress.
This was my first time at research, so I did not really expect anything significant. I was actually pretty scared that I would not achieve much. However, I did discover many interesting points and collected them in my paper.
Mathematical research is such a worthwhile and valuable experience. It is very different from problem solving because it does not have the security of a known solution. Sometimes, you are worried about not obtaining anything particularly useful or interesting. However, in the end, when you do, that feeling is empowering because you have determined something nobody ever has before. During the process, you both acquire new knowledge and the experience of confronting the inevitable setbacks of such a project, which can then be applied to other subjects.
PRIMES is definitely a good program for high school students who are interested in math and mathematical research. The combination of great mentors and interesting projects, as well as the luxury of an entire year of research, generates a unique experience that promotes a lot of learning and amazing discoveries.
Christina Chen worked on the project Hiding behind and hiding inside under the mentorship of Tanya Khovanova. In September 2011 she published her research paper, Volume bounds for shadow covering, in co-authorship with her mentor and Prof. Daniel Klain, on arXiv.org.