Will a study of the mathematical proof of a (data structure and algorithm based) problem, when posed as a proposition, highlight peculiar properties of the problem which may help in designing an optimal algorithm?
I think that proofs should yield interesting insights, and therefore can be used in designing algorithms. Since the program is expected to return a true response for every input, proof must be, in some way, built into the program. Is there any text I can refer to in this regard which will help in real problem solving?