What is the "answer" to a theorem? If by "answer" you mean the conclusion of the theorem, then mathematicians guess these all the time; such guesses are generally referred to as conjecture.
A conjecture is someone, usually a well known expert in the field, saying, "I think this is true but have not been able to prove it." It's not considered a theorem until someone proves it. A famous example is the Goldbach conjecture. No proof has been found but people have been searching for a proof for a long time but so far no one has proven it.
