The wonderful Math Babe has some really great advice for a student who’s worried she isn’t ‘good at math’ because she isn’t fast at math. Replace talk of math with talk of philosophy and this makes some damn good advice for philosophy as well.
Ignore your surroundings, ignore the math competitions, and especially ignore the annoying kids who care about doing fast math. They will slowly recede as you go to college and as high school algebra gives way to college algebra and then Galois Theory. As the math gets awesomer, the speed gets slower.
And in terms of your identity, let yourself fancy yourself a mathematician, or an astronaut, or an engineer, or whatever, because you don’t have to know exactly what it’ll be yet. But promise me you’ll take some math major courses, some real ones like Galois Theory (take Galois Theory!) and for goodness sakes don’t close off any options because of some false definition of “good at math” or because some dude (or possibly dudette) needs to care about knowing everything quickly. Believe me, as you know more you will realize more and more how little you know.
One last thing. Math is not a competitive sport. It’s one of the only existing truly crowd-sourced projects of society, and that makes it highly collaborative and community-oriented, even if the awards and prizes and media narratives about “precocious geniuses” would have you believing the opposite. And once again, it’s been around a long time and is patient to be added to by you when you have the love and time and will to do so.
I know a lot of great philosophers who are fast philosophers. I know a lot of great philosophers who are slow philosophers. And I know a whole spectrum in between. But it frustrates the hell out of me when I hear it said of a philosopher that he – almost invariably he – is ‘just so fast!’ like it’s some intellectual virtue I should care about.