If a grand unified theory ("Theory of Everything") is proposed that can only be demonstrated mathematically, I think it would be very unsatisfactory.  Scientific method requires that for a hypothesis to become a theory, it must be based on observation/evidence and must be predictive and testable, with a condition set for its failure.  Although there can be mathematical proofs for, say, associativity, science does not work by "proof" in this way and I do not believe that any mathematical solution, no matter how elegant, will be deemed sufficient.  Note that even that most elegant of equations, E=MC2, had to make predictions before it was accepted.