I would like $100k to work on the Collatz conjecture for 6 months. I have an idea that will probably fail, but if I had that money I would quit my job work my ass off for six months to flesh it out. But I have no credentials, no way to write a grant proposal, and even I wouldn't invest in myself. ....and yet if we did this sort of experiment 10000 times over, humanity might make some big breakthroughs because some of…
> I would like $100k to work on the Collatz conjecture for 6 months > I have no credentials Then why would you need $100k to work on mathematics?
it's to live off, and support dependents while doing something that would not bring in traditional forms of profit.
That's why it's usually called a grant, rather than an investment - because the granter isn't going to see a direct financial return (but would want to see a societal return such as knowledge or something cultural etc).