Science is about the testable. Math (and logic) is about the provable. Philosophy is about the more fundamental questions.
But a lot of theoretical physics straddles between your definition of science and maths. Not just String Theory but most of the Standard Model and General Relativity. Einstein wasn't trying to create a testable theory when he wanted to see what SR would say about gravity. He was simply trying to find a mathematically consistent framework that would deal with accelerating bodies and not violate SR. He didn't say, "Well I will work on this because it's testable". He just worked on the framework and its conclusions, after the fact, could be tested - lucky for Einstein. Of course, if it wasn't testable we might never know who Einstein was - so we're lucky both ways, I guess.