Maths is, I believe, unique as a discipline in that it displays a distinct set of discrete difficulty steps the further into it you go. The first step is encoun

Maths is, I believe, unique as a discipline in that it displays a distinct set of discrete difficulty steps the further into it you go. The first step is encountered at school: many students find they may be OK with basic arithmetic but anything conceptual like algebra is beyond them. A second step is encountered at college/university: someone who is perfectly good at school-level mathematics can find themselves totally at sea within literally week 1 of a degree course. And someone who copes fine with this level may in turn find that the more rarefied and demanding level demanded by a very top university is beyond them (source: this was my own experience - fine at degree level at an 'ordinary' university having flamed out spectacularly in an Oxbridge interview, demonstrating absolutely that I'd have been totally out of my depth there). Then, there are those few who push through even that level with enough ability to become productive and innovative academics. When you start with a population for whom even arithmetic can be a challenge, it's not too surprising that only a miniscule priesthood emerge from the other side.