Depends on the surface area of unbroken ground. I understand there are quite a few marginal areas in mathematics where you can come up with novel approaches that will be quite impressive to the other five people working on that specific sub-sub-sub-area, but not necessarily that much to mathematics at large. Also, contemporary mathematicians whose names are actually recognizable by popular science literate non-mathematicians are a very small group even compared to the sort of top researchers who are working with the sort stuff the apocryphal wisdom about needing to be in your 20s seems to apply to.
Though I'd also like to see more arguments about how above 30 mathematicians can do all sorts of useful stuff when you don't get fixated on paradigm-upending world-class results, and what sort of stuff this is.
Series: How to Purchase AI Risk Reduction
Here is yet another way to purchase AI risk reduction...
Much of the work needed for Friendly AI and improved algorithmic decision theories requires researchers to invent new math. That's why the Singularity Institute's recruiting efforts have been aimed a talent in math and computer science. Specifically, we're looking for young talent in math and compsci, because young talent is (1) more open to considering radical ideas like AI risk, (2) not yet entrenched in careers and status games, and (3) better at inventing new math (due to cognitive decline with age).
So how can the Singularity Institute reach out to young math/compsci talent? Perhaps surprisingly, Harry Potter and the Methods of Rationality is one of the best tools we have for this. It is read by a surprisingly large proportion of people in math and CS departments. Here are some other projects we have in the works:
Here are some things we could be doing if we had sufficient funding: