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Who Can Understand the Proof? A Window on Formalized Mathematics
Stephen Wolfram discusses understanding proofs discovered using automated theorem proving. Based on Wolfram’s proof of the simplest axioms of logic of Boolean algebra.
Here’s a typical response where an LLM simply assumes that the · operator is associative (which it isn’t in Boolean algebra) then produces a proof that on first blush looks at least vaguely plausible, but is in fact completely wrong: And it’s notable that while we’ve had great success over the years in defining “human-accessible” high-level representations for what amount to the “inputs” and “outputs” of computations, that’s been much less true of the “ongoing processes” of computation—or, for example, of the innards of proofs. I was first seriously introduced to automated theorem proving in the late 1980s by Dana Scott, and have interacted with many people about it over the years, including Richard Assar, Bruno Buchberger, David Hillman, Norm Megill, Todd Rowland and Matthew Szudzik.
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