A thought while riding the train today:
Are there only a limited number of mental strategies for solving a particular problem, and is it possible to build a system to calculate what those strategies are?
When someone says to "look at it from another angle," it's basically saying to use a different strategy to solve a problem.
I remember when I took Combinatorics at Pomona College, one of my professors, Shariar Shariari (perhaps one of my favorite of all time), was saying how solving Combinatorics problems is difficult because you don't really go in a progression like how you learn multiplication after adding--that is, each problem is a unique beast in itself.
Somehow, this reminds me of that and how there are various strategies for a single problem, but one would always seem to be so much more elegant. Anyone ever read Fermat's Enigma?
Would a computer be able to trace mental strategies for solving a particular problem?
Of course, it's a little bit more complex in that some strategies will have prerequisites of prior knowledge (maybe even of other strategies).