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.