The mathematical realist concept of "the structure of mathematics"—at least as separate from the physical world—is problematic once you can no longer describe what that structure might be in a non-arbitrary way. But I see your point. I guess my response would be that the concept of "a proof"—which implies that you have demonstrated something beyond the possibility of contradiction—is not what really matters for your purposes. Ultimately, how an AI manipulates its representations of the world and how it internally represents the world are inextricably related problems. What matters is how well the AI can predict/retrodict/manipulate physical phenomena. Your AI can be a pragmatist about the concept of "truth."