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.

I think this is, theoretically, one of the promises of communism. When I was in Cuba, I went to a local theater production of Don Quixote. It was free, and no one got any money from it, yet it was professional-level quality. In good times at least, under comminism, people have the freedom to explore their passions, because the state takes care of all their essential needs. Sadly, communism rarely leads to good times, and I can tell you for certian that none of my Cuban friends would say that the state adequately provides for their needs most of the time. It's a nice idea, at least.

In such a case he'd need to pay more money and spend even more time - when all he wants to do is work on this one particular problem.