So this is kindof my view of math. I feel like there are holes on both ends of it, where the 'middle' is sortof the notion of Turing Machines and Rational Numbers, which seem very well behaved, and seem like they can describe everything in our universe. Sortof. Except, it's not clear on the 'low' end what Turing Machines are built on. You can define one very precisely on paper with some cute mathematical symbols, but someone needs to know English and math before they can understand those symbols. The symbols are not 'self-evident', and so it's unclear where the floor is of what's sortof.. the most basic/foundational unit of math.
On the other end are Real numbers, and higher levels of infinity, and things like Godel's paradox. It seems like there are holes in the sky up there, and there are infinities so large that we cannot describe them (and not whatever infinity you're thinking of that is described as 'indescribable', since that one you can fathom, and there are ones you can't).
Also, not shown in this diagram, is the issue of consciousness, which does not seem to be explainable with math. So there are 3 holes in math.
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