Terence Tao, one of the most well known mathematicians, speaks up on AI in mathematics in his new paper:
โWhat if an AI tool generates a lengthy proof that is verified to be correct, but which nobody โ ๐ฏ๐ฐ๐ต ๐ฆ๐ท๐ฆ๐ฏ ๐ต๐ฉ๐ฆ ๐ฉ๐ถ๐ฎ๐ข๐ฏ๐ด ๐ธ๐ฉ๐ฐ ๐ฑ๐ณ๐ฐ๐ฎ๐ฑ๐ต๐ฆ๐ฅ ๐ต๐ฉ๐ฆ ๐ต๐ฐ๐ฐ๐ญ โ understands? This is no longer hypothetical. Sites devoted to collecting mathematical problems already contain dozens of AI-generated proof submissions. Many of these are likely to be correct; but in a substantial number of cases no human expert has yet volunteered to verify and vouch for them, and in several cases the human submitters have themselves declared that they are not qualified to do so.
We may soon be faced with the very real possibility of a verified proof of a major result that NO HUMAN understands well enough to explain.
For a proof to actually contribute to its field, then, it is NOT enough for it to be correct, and NOT enough for it to be readable. It also needs to be accepted and valued by the community: other mathematicians need to ๐ฑ๐ถ๐ด๐ฒ๐๐ ๐๐ต๐ฒ ๐ฟ๐ฒ๐๐๐น๐ ๐ฎ๐ป๐ฑ ๐ถ๐ป๐ฐ๐ผ๐ฟ๐ฝ๐ผ๐ฟ๐ฎ๐๐ฒ ๐ถ๐ ๐ถ๐ป๐๐ผ ๐๐ต๐ฒ๐ถ๐ฟ ๐ผ๐๐ป ๐๐ผ๐ฟ๐ธ.
Our current publication infrastructure relies on human editors and referees to provide this acceptance, voluntarily and largely without credit. This work is routinely regarded as less prestigious than the work of generating proofs in the first place; but it is an essential component of the profession, and it is precisely the mechanism by which the individual achievements of mathematicians are converted into collective progress and understanding.
Finally, even publication is not the last stage. Key results should ultimately become part of the definitive textbooks and reference material of their subject, in the form in which ๐๐ต๐ฒ๐ ๐ฎ๐ฟ๐ฒ ๐๐ฎ๐๐ด๐ต๐ ๐๐ผ ๐๐ต๐ฒ ๐ป๐ฒ๐
๐ ๐ด๐ฒ๐ป๐ฒ๐ฟ๐ฎ๐๐ถ๐ผ๐ป ๐ผ๐ณ ๐๐๐๐ฑ๐ฒ๐ป๐๐. This process of canonicalization is the slowest stage of all. It requires broad, deliberative consensus, and it is the stage least amenable to optimization by AI tools.โ
๐ Terence Tao concludes:
โWe will transition from an era of proof scarcity to an era of proof abundance. Most of our institutions โ journals, priority conventions, hiring and promotion criteria, prizes, the very notion of a research program โ were designed under the assumption of scarcity, and it should not surprise us if they behave poorly under abundance.
In some areas, particularly in education and in the training of young mathematicians, it will be crucial to emphasize ๐๐ต๐ฒ ๐ถ๐ฟ๐ฟ๐ฒ๐ฑ๐๐ฐ๐ถ๐ฏ๐น๐ ๐ต๐๐บ๐ฎ๐ป ๐ฎ๐๐ฝ๐ฒ๐ฐ๐ of our work, and to restrict the use of AI tools quite tightly; the goal of training a mathematician is NOT achieved by producing correct homework.
In other areas, we will need to take the initiative on AI usage, and define best practices for incorporating these tools into our workflows on our own terms rather than on terms set for us by vendors.โ
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[I highlighted & capitalized words in the text for clarity]
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