Mathematical Problem Solving...

I've been looking at problem solving heuristics for mathematical problem solving. It still seems to be 'dark magic' despite the current research into mathemtical learning taking place in universities today. If you search the web you'll find little more than rehashes of Polya's original work.
The areas I feel haven't been considered stem around making internal representations of problems and altering/mainpulating those internal presentations in a way a mathematician might. We need to start building a way of recording the internal vocalbulary used by mathematicians (and physicists, biologists etc). I'm not saying this is easy, but the majority of papers I read are information poor, vague notions about some classroom experiment performed on bunch of under 16's which make great reading for curriculum teachers but offer no value whatsoever to those who actually want to figure out how 'it' is done. I'd say the really difficult progression in math is from undergraduate to graduate maths when the obfuscation of motivation behind the ever increasing number of theorems and at the same time the formality of argument reach ever increasing levels.
We want to know what goes on in the mind of an Atiyah when he first sees a new bit of mathematics to learn?
How does he approach reading, problems etc?
What kind of mental map do they keep of the interconnections and categories of problems and mathematics they have encountered?
How about samples of their original notebooks? Textbooks hide to much for those who want to teach themselves the reality behind the origin of theorems and conjectures (though see John Mason at the OU).
How do they represent directions and goals? How do they react to difficulties and problems?
This is not an organised list but just a tumble of ideas no-one has seemed to ask.
The answers of course must be quite detailed - we want to see videos of them in action so we can spot patterns in what they do. Learning from the masters by osmosis is still a viable option if you ask me - we just need to utilise digital technology a little more.