It took mathematicians 300 years to solve the mystery of why a general algebraic solution did not exist for polynomials of degree 5 and higher. The discovery of a bigger framework was required to push the boundary of our understanding. Do you think a unification of mathematics or physics requires yet another reformation of our current framework?
Sometimes it takes time of mathematics to catch physics, but sometimes it’s other way around. As we saw earlier, in the case of relativity, mathematics was there first and it physics needed to catch it.
I believe that over the years, both mathematics and physics will expand to be able to explain processes that we do not yet know, or prove theorems, give us answers … A hybrid may even emerge between the two! A new branch of STEM
I feel that fundamental physics will definitely need reformulation in terms of better notions of the origins of space and time. The foundations of mathematics as formulated in terms of set theory has been an ongoing project, and now category theory is also being put forward as a foundation. However, I’m not sure that the basic objects and tools of mathematical analysis will have to be reformulated. Addition will always be addition. Numbers will retain their properties of oddness and evenness, etc.
For physics I’d expect that the unification of quantum field theory and general relativity needs a novel input, and probably by someone without a reputation to lose. Another patent clerk perhaps …… the interesting question is how to test such a unified theory in some scenario though.
For mathematics I’d be more positive about unification because it lacks the constraints of real world measurement. The greatest burden here is to maintain logical consistency.