I often read about how famous theoretical physicists have made ground-breaking contributions to physics, but I always end up wondering how they are able to "discover" something that they have never seen or experienced. I believe that it has to do with the application of mathematical theories to a physical context, but I fail to imagine how that could be done. Do they just "fiddle around" with different types of math until they find one that works? And if so, how do they go about discovering the exact equations using that math and also proving that the resulting theory and equations are right? Please go in as much detail as possible.