My answer to a question on Quora: **Why are mathematicians so obsessed with proofs? Many theorems are just intuitive.**

Your belief that “many theorems are just intuitive” indicates that you are at very early stages of learning mathematics. 99.99% of mathematics is beyond “immediate intuition”. If you do not agree – then please give an example of an “intuitive” theorem about, say, Hilbert spaces, or etale cohomology.

Mathematical intuition is something that has to be trained and controlled — and proofs is the only known tool for achieving that.