[mlLK]

If you have a ton of ideas and they're all, for the most part, general, vague, novel, and abstract, practice prototyping. Make it really dirty, don't over-think it, and keep a closed-mind while in the beginning stages of a project; IOW, don't pre-optimize your project by recursively worrying about other edge cases, write for a single case and get something on the screen.

Given your background, I'd scratch all these "big picture" or "overly ambitious" ideas and return to a domain you're more confident in, pick something (axiom, rule, theorem, etc.) specific, and see if you can express or simulate an example of the "thing" in action.