After OpenAI's Navier-Stokes announcement, Harvard mathematicians are divided over whether AI proofs require human understanding
After OpenAI's Navier-Stokes announcement, Harvard mathematicians are divided over whether a correct AI proof requires human understanding. Rohan Paul points out that a proof both shows a proposition to be true and teaches mathematicians reusable methods, whereas AI proofs often achieve only the former. Mathematicians value the certainty and technique of a proof; an AI proof that no one understands provides certainty but not technique.
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Using the disagreement among Harvard mathematicians, this presents the trade-off for AI proofs between certainty and reusable methods.
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Harvard mathematicians are split over whether correct AI proofs need human understanding, after OpenAI’s Navier-Stokes claim.
A proof does 2 things: it shows a statement is true, and it teaches other mathematicians a method they can reuse, and AI proofs often deliver only the first.
Mathematicians value proofs for 2 reasons, certainty and technique, and an AI proof that nobody understands gives them certainty while withholding the technique.