"Art is not a mirror held up to reality but a hammer with which to shape it."
Mathematics is not a deductive science—that's a cliché. When you try to prove a theorem, you don't just list the hypotheses and then start to reason. What you do is trial and error, experimentation, guesswork.
The young do not know enough to be prudent, and therefore they attempt the impossible, and achieve it, generation after generation.