Comment by hodgehog11

Yes and no. I think we have vastly underestimated the extent of the search space for math problems. I also think we underestimate the degree to which our worldview influences the directions with which we attempt proofs. Problems are derived from constructions that we can relate to, often physically. Consequently, the technique in the solution often involves a construction that is similarly physical in its form. I think measure theory is a prime example of this, and it effectively unlocked solutions to a lot of long-standing statistical problems.