Dear Uncle Colin,
As I progress through my maths education, I notice that the people around me are getting smarter and smarter. How do I keep my head up when everyone is brighter than me?
I'm Mightily Put Off Seeing Their Outstanding Results
Hi, IMPOSTOR, and thanks for your message!
If it's any consolation, I know exactly how you feel. At school, I was generally the best mathematician in the room. At sixth form, there were people who knew stuff I didn't. At university, I was better-than-average (some of the people there weren't just on a different plane, but flying with an altogether different airline); by the time I got into my PhD programme, I was distinctly run-of-the-mill.
If you think about it for a moment, this is exactly how you'd expect things to go: everyone does GCSE, a much smaller proportion (of generally decent mathematicians) does A-level, only the most mathematically-inclined of those students go on to do a degree, and only a fraction of those with degrees take up doctoral studies: at each stage, one is mixing with better and better mathematicians.
The good news is, many of your classmates probably feel the same way as you do, intimidated by the stars at the top of the class. If you have a question, the chances are that several other people do too, and will be glad that you asked it - even if the stars roll their eyes.
The first thing is, don't see maths as a competition with anyone except yourself. It's a truism that maths is not a spectator sport - but it's also not a solo sport; you can work with others in your class, whether they're stars or not, to improve your skills. Don't fear the stars, learn from them! Don't hide from your peers, compare notes, share the things you understand and the things that they understand.
The biggest adjustment that helped me was letting go of (at least some of) my ego: sometimes, I was so hung up on trying to be, or appear to be, the smartest person in the room, I'd lose sight of things like 'learning the maths I needed to'. Nowadays, I revel in being among smart people (things like Big MathsJam and G4G are the highlights of my year) - that's when I'm going to be surprised and entertained and be able to share in the joy of learning maths.
Hope that helps!
- Uncle Colin