Concerning competitions
“Professional mathematics is not a sport.”
Attending the Stanford Math Circle probably won’t help you to become a gold medalist at the International Mathematical Olympiad. If that’s your only goal, then you should probably spend all your free time at the Art of Problem Solving website, and skip the Stanford Math Circle altogether. But before you go, we hope you’ll pause to ask yourself whether you’ve really chosen the right goal — because many great mathematicians don’t think you have.
A striking example is Andrew Wiles, prover of Fermat’s Last Theorem. Wiles stresses that “creating new mathematics is a quite different occupation from solving problems in a contest. Why is this? Because you don’t know for sure what you are trying to prove or indeed whether it is true.” Wiles insists that a very large part of a serious mathematician’s work involves choosing the right questions to investigate. Some questions lead deep into the heart of things, while others lead nowhere at all — and, since life is short, it makes a huge difference which of them you spend your time on. But in a contest, you spend as much time as you can on all the questions, which have already been chosen for you.
That’s just not how things go here at the Stanford Math Circle. We spend a lot of our time grappling with the same raw mathematical phenomena that led the great historical masters to their key insights and discoveries. A very large part of our work involves choosing the right questions to investigate. And, just like the great historical masters, we cooperate much more than we compete — because most problems really worth solving are far too hard for even the most talented individual to solve without help.