I never felt I properly understood a proof unless I understood it both intuitively and formally. The formalism is to make sure your intuitions are water-tight.

I never felt I properly understood a proof unless I understood it both intuitively and formally. The formalism is to make sure your intuitions are water-tight. But there are proofs you can accept are formally correct without intuitively understanding them - I would accept the truth of such proof but not feel like I understood them.