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No doubt there’ll at least be some “natural-science-like” characterizations of what’s going on. The same is true of axioms for areas of abstract algebra like group theory—as well as basic Euclidean geometry (at least for integers). Will there still be “human-level descriptions” that involve numbers? But there is a subtlety here.
How Math Relates to Humans. And if we’re going to make a “general theory of mathematics” a first step is to do something like we’d typically do in naturalscience, and try to “drill down” to find a uniform underlying model—or at least representation—for all of them. So how about logic, or, more specifically Boolean algebra ?
And in fact, to my knowledge, my Boolean algebra axiom is actually the only truly unexpected result thats ever been found for the first time using automated theorem proving. But what about something more like a theory in naturalscience? But, OK, so we know its true. And thats interesting.
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