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Trying to teach X to someone forces you to tailor your words to that person’s psyche, which then causes you to see it from a new perspective. Holding the two perspectives together to ensure accuracy forces you to question that accuracy as a subroutine of the teaching effort. Answers of “no” can lead to new insights.
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.
I think that, at its most fundamental level, mathematics arises with the notion of
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difference
. In a universe of total sameness, there would be nothing to count, no surfaces or discernable dimensionality, and no waves or motions. Everything that mathematicians study depend on differences of various kinds.