G. Polya wrote in HTSI that "Mathematics presented with rigor is a systematic deductive science but mathematics in the making is an experimental inductive science." In this sense, the study of math problems and HOW to do them informs all scientific problem solving.
G. Polya put together a guide for solving math problems which is paraphrased under the Plans of Attack section of this website.
Outside the box
PROBLEM: Lay out 9 matches to make 4 equal triangles. Now remove 3 matches and still have 4 equal triangles.
PROBLEM: Measure the height of a tall building using a barometer. Neils Bohr’s answers.