I am so confused as to why your standard seems to be so absurdly high to me.

The way in which I operationalize the originality / interest of research is "in 50 years, what will the best mathematicians think about it?" I think that this perspective is unusual amongst mathematicians as a group, but not among the greatest ones. I'd be interested in how it jibs with your own.

Anyway, I think that if one adopts this perspective and takes a careful look at current research using Bayesian reasoning, one is led to the conclusion that almost all of it will be considered to be irrelevant (confidence ~80%).

When I was in grad school, I observed people proving lots of theorems in low dimensional topology that were sort of interesting to me, but it's also my best guess that most of them will be viewed in hindsight as similar to how advanced Euclidean geometry theorems are today – along the lines of "that's sort of pretty, but not really worthy of serious attention."

Is it because I don't see how "superficially original" all of the work done in my field is? I lack perspective?

How old are you?

When I started grad school, I was blown away by how much the professors could do.

A few years out of grad school, I saw that a lot of the theorems were things that it was well known to experts that it was possible to prove by using certain techniques, and that proving them was in some sense a matter of the researchers dotting their i's and crossing their t's.

And in situations where something seemed strikingly original, the basic idea often turned out to be due to somebody other than the author of a paper (not to say that the author plagiarized – on the contrary, the author almost always acknowledged the source of the idea – but a lot of times people don't read the fine print well enough to notice).

For example, the Wikipedia page on Paul Vojta reads

In formulating a number of striking conjectures, he pointed out the possible existence of parallels between the Nevanlinna theory of complex analysis, and diophantine analysis. This was a novel contribution to the circle of ideas around the Mordell conjecture and abc conjecture, suggesting something of large importance to the integer solutions (affine space) aspect of diophantine equations. It has been taken up in his own work, and that of others.

I had the chance to speak with Vojta and ask how he discovered these things, and he said that his advisor Barry Mazur suggested that investigate possible parallels between Nevanlinna theory and diophantine analysis.

Similarly, even though Andrew Wiles' work on Fermat's Last Theorem does seem to be regarded by experts as highly original, the conceptual framework that he used had been developed by Barry Mazur, and I would guess (weakly – Idon't have an inside view – just extrapolating based on things that I've heard) that people with deep knowledge of the field would say that Mazur's contribution to the solution of Fermat's last theorem was more substantial than that of Wiles.

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.