My experience is that there are three levels of maths ability among people who breezed A-level, or at least passed it well enough to do university maths: - fun

My experience is that there are three levels of maths ability among people who breezed A-level, or at least passed it well enough to do university maths: - fundamentally does not grok University-level maths at all; - gets "ordinary" university maths (ie redbrick and "below"), but would not be able to cope with Oxbridge level; - Oxbridge level There are stark step-jumps between these three, and exam results are not a good indicator of which one an individual actually falls into. In particular, I believe you can be a good jobbing middle-level mathematician by learning the relevant stuff, providing you have the basic aptitude for it, but you need a real gift to be able to cope with the top level, and that's something that an exam format cannot elicit. Speaking personally, I did an interview at Cambridge, which served the excellent function - for both parties - of determining that I was not in the top group.