Lately I've been feeling particularly incompetent mathematically, to the point that I question how much of a future I have in the subject. Therefore I quite often wonder what mathematical ability is all about, and I look forward to hearing if your perspective gels with my own.

More later, but just a brief remark – I think that one issue is that the top ~200 mathematicians are of such high intellectual caliber that they've plucked all of the low hanging fruit and that as a result mathematicians outside of that group have a really hard time doing research that's both interesting and original. (The standard that I have in mind here is high, but I think that as one gains perspective one starts to see that superficially original research is often much less so than it looks.) I know many brilliant people who have only done so once over an entire career.

Outside of pure math, the situation is very different – it seems to me that there's a lot of room for "normal" mathematically talented people to do highly original work. Note for example that the Gale-Shapley theorem was considered significant enough so that Gale and Shapley were awarded a Nobel prize in economics for it, even though it's something that a lot of mathematicians could have figured out in a few days (!!!). I think that my speed dating project is such an example, though I haven't been presenting it in a way that's made it clear why.

Of course, if you're really committed to pure math in particular, my observation isn't so helpful, but my later posts might be.