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:

* DoSimpleThings to satisfy one UserStory.
* DoSimpleThings to satisfy the next UserStory.
* RefactorMercilessly to merge the two solutions into a reuse-based 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
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CategoryMath CategoryProblemSolvingStrategy