Proof

Proof is what makes maths different - things that have been proven in maths will always hold true! Instead of looking to learn more things that you are going to have to study again at A-Level, why not try something really challenging: PROOF.

Below you will find an interactive book that sets out some problems to investigate. Some of these ideas have been proven and some remain open questions.

I am not going to try to direct you towards which problems to try first (presumably the authors of the book thought about this). Scroll through the book and pick a problem that interests you - the easier ones should be nearer the beginning of the book!

This may well be the first time that you have been presented with maths that you can't find a solution to but that's okay! Several of these problems remain unproven, even by expert mathematicians. These are supposed to be difficult and you will learn something from the attempt.