You might be interested in the recent following great peace from Quanta magazine touching exactly on that subject.
Just a side remark - there is a difference between "how to prove" and "what to prove" when it comes to theorems - to some extent one of the beauties in math - is that there is a certain amount of inspiration or at least subjective aesthetic taste on what makes for an "interesting" theorem. In chess or go - you have a clear objective of winning a game with a fixed set of laws - but in math the objective itself - that is which theorems are worth while proving - is a huge part of the mathematical creative process.