My answer to a question on Quora: Have you ever gotten answers by intuition in math but don’t know how to explain it?

In mathematics, an answer without explanation (proof) is not an answer. What you call “answer” or “result” (while this result is still not proven) is called a “conjecture”.

• Yes, mathematicians systematically produce conjectures in the process of work.
• Yes, they frequently do that using their intuition.
• These conjectures could be proved (sometimes much later) , or get refuted and die.

Refutation is no less important than proof. Without refutation, mathematics is a car without brakes.

In my life, I produced hundreds of conjectures. Most of them died, some instantly. Some are still open – that is, not proven and not refuted.