[ashley95]

I think we also have to be honest and admit that, yes, indeed, there is less novel maths for all of us to be doing. The pioneers came first and discovered a lot of low hanging fruit. There were a lot of geniuses that mined the rest and reached higher in the tree. Now even the smartest mathematicians are left solving abstract puzzles with little utility in the real world. (Don't get me wrong, it's very fun, and sometimes useful too.)

After my PhD in applied mathematics, I decided to leave the field, partly because I feel it really has advanced so far that new discoveries do little to move the needle in the real world. There's enough smart people who obsess over nothing else but maths that I can go and do more practical stuff...

[_alternator_]

Is this not just a perspective issue? The fields we learn about in school are the ones that are in some sense mature, that have been cashed.

When I was in grad school, we learned about wavelets, but we did research on convex optimization for statistics. The first was an accomplishment of the last generation of mathematicians, and it would be hard to publish something groundbreaking. But nobody had really considered sparsity inducing optimization, so that was our problem.

In many ways, the situation is somewhat better for applied mathematicians because the problem space is wider. Ingrid Daubechies was an applied mathematician, and her work on wavelets was an outgrowth of work that originated in the petroleum exploration community. Wild how these connections get made.