Here's how you solve a hard math problem:
- Solve for an easy special case. For geometry, start with a 2 dimension space.
- Solve for a harder special case, such as a 3 dimension space.
- Refactor the solutions together to apply to the general case, such as an n-dimensional space.
I believe this is explained in George Polya's HowToSolveIt.--ApoorvaMuralidhara
This applies directly to how ExtremeProgramming generates design:
See
FeynmanAlgorithm to hear someone bragging they are too smart to have to do it like that.
And all too often, you do the exact opposite:
- generalize the problem
- trivially solve the generalized version
- bring the solution back to the special case
CategoryMath CategoryProblemSolvingStrategy