Mathematicians' best trick, even for the furthest reaching number theories, is to assume something, and then show that this leads to a contradiction (or not, in which case simulate it to big numbers).
What you're thinking of is a bit beyond, more into the metaphysical. The standard idea is to devise an experiment which confirms theory; and then look for independent confirmation under various locations, equipment, etc. What seems to happen though with theory is that it becomes virtually confirmed when various fields of math and theoretical physics converge on the notion (, even before actually demonstrated in black and white).
Like when Schrodinger's Wave Equation stuff was worked in terms of set theory, and then, later, as explicit functional calculus. Another example, had there been no Higgs particle, as contentious and flawed as that might be still in theory, the entire Standard Model of particle physics would have fallen. Very unlikely from what has been already verified.
Sure, the metaphysical "final theory" has to let go somehow, because every thing dies, and is reborn. Right?
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