PRIMES: Dmitry Vaintrob's Story
I liked math since I was very young: my dad is a mathematician and a fun pastime in our family would be my dad giving me problems or answering my math questions.
While in high school, I did two research projects: one with Sergei Tabachnikov, one with Pavel Etingof. My mentors showed me that surprisingly, despite the fact that I knew very little (and felt like I knew nothing at all,) it was possible to work and make progress on real open problems. My mentors helped me do math that I would never have thought I was prepared for, and flesh out my ideas in rigorous proofs. It was kind of exhilarating.
I made a bit of progress on both projects I worked on. The topology project with Etingof turned out to give a much more general and neat result than we had initially expected, and the paper I wrote for it placed well in the Siemens and Intel scholarship competitions.
Doing math research sometimes feels very frustrating, especially when you feel you're underqualified. But when you're "in the zone," you feel like an artist who just discovered paper and paint.
Doing math research in high school is fun, and it helps to understand what math is really about. There are always two extremes in learning a subject either being too superficial, or getting too bogged down in details. When you use things you learned for research, you automatically tend towards the golden balance; everything else is just unusable. It's good to experience this as early as possible, I think. One piece of advice for student don't be embarrassed, and act stupider than you are. The problem of most mathematicians who never fully realize their talent is that they act smarter than they are.
Dmitry Vaintrob, the top prize in the 2006 Siemens competition and in the 2007 ISEF and the 3d place in the 2007 Intel STS.