However, I don't think it is reasonable to assume that AI tools can only be valuable if they can be rigorously mathematically characterized. The "holy grail" of intelligence -- that is, actual human intelligence -- certainly can't or at least hasn't been mathematically characterized, and I don't think anyone will ever offer any "proof" (mathematical or otherwise) that the biological brain is inherently wired to arrive at or at least tend to converge to correct solutions to intelligence problems. And of course no one will argue that human intelligence isn't valuable!