I think that creativity needs to be carefully defined to have a real discussion about how much it contributes to very high achievement. I have a feeling that a lot of very high achievers may have a heavy dose of intuition, which I don't think of as coextensive with creativity although they seem to overlap a bit. I guess, for me, creative thinking and intuition both fall under what I often see described as "divergent thinking", as they both give startling results, but they're not the same in the way they operate, and I don't think they're necessarily possessed in equal measure by a particular person. I think of creativity as more generative, and intuition as more reflective.
I think of creativity, in the context of problem-solving, along the lines of broadening potential inputs or searches for solutions to a problem, and intuition essentially along the lines of pattern matching, but so subtle that it can seem like black magic. Intuition may be part of what's generally considered the creative process some of the time, such as suggesting initial areas of potentially valuable research, etc.
There must be lots of highly gifted researchers out there, who brainstorm with the best of them, yet never become renowned because they never stumble upon the pathway to a great discovery; but intuition can remove the need for luck. If my concept is true, then some of the world's great scientists may have had tremendous gifts in other areas, though not world-beating intution, but still got lucky. Others would be guided by a vision of something like the theory of relativity, and due to their other gifts would be able to see the idea through to fruition. Still other brilliant minds might strongly intuit insights that they can't prove in the end, though they know them to be true; a conjecture like Fermat's Last Theorem would be a good example.
I've read that mentorship can be important for a developing genius, although it is obviously not necessary in all cases. Perhaps intuition can be taught in part.
