I think it would be interesting to have a clarity on how many of the world's greatest problem solvers were positive people and had a positive mindset and outlook of the world. I predict that most of them were like me - negatively inclined - just much, much smarter and more skilled than me. I predict that they didn't have "faith" that there would be a solution, they had work ethic to solve the problem. Ton continually focus on the negative, until they were able to find a solution that negated the negative.
I absolutely agree. A positive thinker is unlikely to solve a problem. They can feed themselves when they're hungry. For them, this could be considered a major problem-solving skill. :) Seeing a problem, identifying the negative, and creating solutions requires significant skill. There are also limited individuals. These qualities make them geniuses.
People whose biggest challenge is getting out of bed in the morning. We reduce ourselves to pretty incapable people, very easily.