Where are you from and have you only recently moved to the UK?
Sounds like a good sign for creativity. It won't even occur to most kids to generalise results and I think that's where the talent lies rather than just the ability to do it
I used to generalise everything I found to save time. Annoyingly though, even when I showed the teachers I had reduced loads of things to algebraic formulae (hence reducing months work of work to simply punching in numbers) they just ignored me and got me to punch in numbers. Then months letter we'd get to a new topic and the cycle repeats! I also saw really quickly the importance of proof! Like, when we were given this massive list of "Circle Theorems", I remember managing to prove them all in the course of the lesson, remarking that most of them were the same! The worst part is that when a random kid in a random maths class says he hates doing maths and wants different work, society is programmed to ignore them because it has become a social stereotype! It's generally accepted that everyone hates maths and that anyone who says otherwise is a geek and so is interested in things that others find boring. The problem is that, by the time people are free of that kind of education, the ones who have actually discovered that is it fun are doing things too advanced for everyone else to understand and so it becomes something that isn't socially acceptable to talk about... which sucks!
If you stopped a random person in the street and asked them about black holes, magnetism, evolution, etc.. (assuming they don't just think you're a nutter) a large proportion of people will know the key principle and readily engage with you in a conversation that will lead to one or both of you learning something knew and being enriched. If you stopped someone in the street and asked them what the Riemann Hypothesis is or even what differentiation is... or even a bloody quadratic equation, a very very small proportion of people would know and, the worst part is, they would literally not give a ****!
Oh right, if that's how your school does it then that would be perfectly acceptance
No, I was just suggesting that, if you're going to pursue a maths degree with money in mind then I'd imagine you would be unlikely to motivate yourself to commit enough time to it to succeed at somewhere like Cambridge. But, by the sounds of things, it sounds like you are beginning to get motivated
My pleasure. Well, I am certainly considering it. The drawbacks are that it means pretty much giving up your life in pursuit of knowledge, or at least until you get a stable career as a professor or whatever and the other is that it's stupidly competitive and I would have no idea how I compare to other people seeking an academic career! I suppose all I want to do is explore ideas and share ideas. If an option arises that would enables me to do this in the best possible way, I will take it in an instant
I suppose the epitome of sharing ideas is lecturing and of exploring them is research so that certainly seems a good enough goal to set myself for the time being!
How about you? What things have you vaguely got in mind?