Sure. But even there you start with an understanding of how you want to solve the problem and then spend all your time writing the proof in a way that the compu

Sure. But even there you start with an understanding of how you want to solve the problem and then spend all your time writing the proof in a way that the computer can prove that you have indeed solved it correctly. At all times you generally start with an idea of a solution - you might prototype stuff to test out different solutions and how you like them but with things that are less pure R&D you need to prototype less.