Usually I do not decide what problems to solve. They just come to me and I try to solve them. I have tried to solve some big problems, but that has never worked out for me.
The "problems" that I solve, or try to solve, come mostly from the following sources: academic colleagues asking questions, natural questions that arise during math seminars, finding the optimal way to reach some goal specified by one of my bosses, finding ways to fix or understand ad hock methods invented by my coworkers, natural questions that occur to me while reading astronomy, math, AI, or economics articles, and lastly, answering mathematical or AI questions about games just because I love games and game theory.
Sometimes problems or questions will remain in my head for years before being solved. Many are never solved, but they are fun to think about.
It is very rare that one of my solutions affects more than 100 people.
The "problems" that I solve, or try to solve, come mostly from the following sources: academic colleagues asking questions, natural questions that arise during math seminars, finding the optimal way to reach some goal specified by one of my bosses, finding ways to fix or understand ad hock methods invented by my coworkers, natural questions that occur to me while reading astronomy, math, AI, or economics articles, and lastly, answering mathematical or AI questions about games just because I love games and game theory.
Sometimes problems or questions will remain in my head for years before being solved. Many are never solved, but they are fun to think about.
It is very rare that one of my solutions affects more than 100 people.