It's actually pretty easy to imagine when you consider the problem of selecting which 100K mathematicians will receive this beneficence. The first few thousand would be straightforward, but they're presumably all the ones who have tenure and can already spend the next 10 years working on whatever they want.

After that, how do you separate the promising mathematicians from the lazy and the crackpots?

This is the same problem that a "Manhattan Project" to cure cancer or what have you always runs into: It's easy to see where to get value from the first dollar, but the 30 billionth dollar likely costs more than a dollar just to figure out how to productively spend it!

"Fortunately", experimental particle physics doesn't have this problem, since you can always use that next dollar to build a bigger collider.

With 100k grants to give, I think you'd want quite a few crackpots, and maybe even some lazy mathematicians. Those could be the types who come up with a game changing result.

100K mathematicians is a lot, but Wikipedia says there are 9267 people with Erdös number of 2, which is a huge mark of distinction: the median Erdös number in Fields medal laureates is 3.

I say, start a program with the Erdös-2 people and as it develops let these hire Erdös-3 folks.

this isn’t sustainable though, as people with smaller Erdös numbers will die out and larger ones will be too common.

so we should probably allow the smaller Erdös numbers to be inherited through primogeniture, to make sure we still have an identifiable class of good mathematicians to give money to.