I mean, that's the heart of it right there. You're netting $200k+ but you wouldn't set aside six months expenses and take a sabbatical to work on your idea. So why would someone else?
Because different people have different marginal utilities of money. It's not implausible that there is someone (or a group of people) out there who is interested in seeing the Collatz conjecture proven, who places less value on the $100k than koheripbal does.
What you fail to understand is that when you net 200k$, you are rich. There's a moral issue to ask other to fund your rich lifestyle to allow you work on something and on top of that, taking all the fame in case of success.
It's ok to be on the top 1% by the benefits of you work. However, it's hard to justify asking others to finance your stay on the top 1% for charity.
I don't disagree with you -- $200k is a lot, especially by global standards. But I encourage you to check the Form 990s filed with the IRS by your favorite 501 charity, and see how much is spent on e.g. executive salaries. This kind of compensation is not uncommon.
$200K is not a lot if you live in a high cost location like SF on NYC, are senior in your IT career, and have a family. In IT it's below average, and the commenter here is saying he'd be taking a pay cut to do this.
He's an expensive grant, but he's probably got more potential to solve a problem than the average PhD student.
Because different people have different marginal utilities of money. It's not implausible that there is someone (or a group of people) out there who is interested in seeing the Collatz conjecture proven, who places less value on the $100k than koheripbal does.