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.