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.
My mother was an atheist. She used to say that there was good news and bad news about hell. The good news is, hell is just the product of a morbid human imagination. The bad news is, whatever humans can imagine, they can usually create.
