I asked Richard Stallman this question: His answer was: Live cheaply. Eric S. Raymond answer was: Be independently wealthy. I have tried to reach billionaire philanthropists (Bill Gates, Steve Wozniak, Dean Kamen, Warren Buffet, and others) with the idea that there are very talented people around who have brilliant ideas (say for instance another Newton or Mozart) but are not financially independent to afford to work…
I think really wealthy people have two problems when it comes to this: (1) there are a lot of people out there who want money but can't deliver. (2) many of these wealthy people, like the guy I mentioned above, want to be actively involved in solving problems. He didn't want to give money to OpenSSL because his only role there would be giving them money. Instead, he wanted to create some organization with his name on it so that he could be seen to be doing something.
[0]: I don't remember exactly what his proposal was, but I remember thinking it sounded really bureaucratic and unlikely to have any real benefits in practice.