Moreover, if one selects a problem, works on it in isolation for a few years and finally solves it, there is a danger, unless the problem is very famous, that it will no longer be regarded as all that significant.
Timothy GowersIt is obvious that mathematics needs both sorts of mathematicians, theory-builders and problem-solvers.
Timothy GowersWhat a mathematical proof actually does is show that certain conclusions, such as the irrationality of , follow from certain premises, such as the principle of mathematical induction. The validity of these premises is an entirely independent matter which can safely be left to philosophers.
Timothy Gowers