With respect to OpenAI’s manuscripts, the case of Louis de Branges is highly relevant and instructive. 1) In 1964, de Branges claimed he had a proof for the invariant subspace problem. A large number of people spent a considerable amount of time to verify his claim. Eventually, an error popped up in the proof that was unresolvable. Two notable details from Paul Halmos, who was directly involved in this: a) The scale of the verification effort: Halmos recounts that a couple dozen mathematicians were examining the roughly 70-page manuscript, sometimes line by line. He personally worked on it for two months before asking to withdraw from the refereeing committee. b) Halmos's explicit criticism of the burden imposed on referees. He complained about authors exploiting editors and referees as assistants, validators, and proof checkers. 2) In 1984, de Branges claimed he had a proof of the Bieberbach conjecture. But by then, he had developed a reputation for announcing proofs that did not hold up. When he announced his proof, American mathematicians were not interested in reading it. His manuscript was approximately 385 pages long, and he could not initially find anyone willing to verify his proof. It was the mathematicians in the Soviet Union who worked through the argument with him, corrected his errors, and established its validity. 3) In early 2000s he claimed he had a proof of the Riemann hypothesis. Initially people read his manuscript and listened to him, but they found errors or didn’t find his approach convincing. He kept revising his work and coming up with new methods, but people kept finding errors. Eventually, everyone gave up reading his later claims and listening to him. It wasn’t worth investing the time in it. Now, de Branges was a serious mathematician, but with a reputation for too many incorrect proofs. The mathematical community just decided it wasn’t worth spending more time on his work. He was willing to explain his approach and present his proof, things that OpenAI hasn’t done. So OpenAI hasn’t really fulfilled the most basic requirements for getting their work validated by the mathematical community. They should ignore these manuscripts until OpenAI does its homework. There are people who claim OpenAI doesn’t care. But A) If OpenAI doesn’t care about the recognition and the validation from the mathematical community, why is it publishing papers? They’re not demonstrative of any ability until they’re validated. For doing basic college level math you don’t need to prove you can solve the Riemann Hypothesis. B) If the mathematical community doesn’t validate those results, could OpenAI credibly market a product based on frontier reasoning claims?⁠ Can they legitimately claim they have proved the Riemann Hypothesis? Who would be willing to pay for such a product that nobody has validated? Let’s assume for argument’s sake FDA approval is completely voluntary, and OpenAI claims it has come up with a new drug that cures cancer. If it doesn’t seek FDA approval or worse, fails in the process, how many physicians are going to prescribe it and how many patients are going to take that medicine?