Question

I think that the question itself is entirely misleading. It tacitly assumes as if mathematics could be separated into two parts: mathematical results and their proofs. Mathematics is nothing other than the proofs of mathematical results. Mathematical statements lacks any value, they are neither good nor bad. From the mathematical point of view, it is entirely immaterial whether the answer to a mathematical question like `Is there an even integer greater than two that is not the sum of two primes?' is yes or no. Mathematicians simply do not interested in the right answer. What they would like to do is to solve the problem. That is the main difference between natural sciences or engineering on the one hand, and mathematics on the other. A physicist would like to know the right answer to his question and he does not interested in the way it is obtained. An engineer needs a tool that he can use in the course of his work. He does not interested in the way a useful device works. Mathematics is nothing other than a specific set consisting of different solutions to different problems and, of course, some unsolved problems waiting to be solved. Proofs are not important for mathematics, they constitute the body of knowledge we call mathematics.