My preference would still be for the final writeup for this result to be primarily human-generated in the most essential portions of the paper, though I can see a case for delegating routine proofs to some combination of AI-generated text and Lean code. But to me, the more interesting capability revealed by these events is the ability to rapidly write and rewrite new versions of a text as needed, even if one was not the original author of the argument.

This is sharp contrast to existing practice where the effort required to produce even one readable manuscript is quite time-consuming, and subsequent revisions (in response to referee reports, for instance) are largely confined to local changes (e.g., modifying the proof of a single lemma), with large-scale reworking of the paper often avoided due both to the work required and the large possibility of introducing new errors. However, the combination of reasonably competent AI text generation and modification capabilities, paired with the ability of formal proof assistants to verify the informal arguments thus generated, allows for a much more dynamic and high-multiplicity conception of what a writeup of an argument is, with the ability for individual participants to rapidly create tailored expositions of the argument at whatever level of rigor and precision is desired.

Presumably one would still want to have a singular "official" paper artefact that is held to the highest standards of writing; but this primary paper could now be accompanied by a large number of secondary alternate versions of the paper that may be somewhat looser and AI-generated in nature, but could hold additional value beyond the primary document. (5/5)

Addendum: as portions of my text above have been quoted out of context, I would like to also draw attention to the various caveats listed at github.com/teorth/erdosproblem regarding the extent to which one can draw broader conclusions about AI mathematics capabilities from the progress in solving Erdos problems.

0

If you have a fediverse account, you can quote this note from your own instance. Search https://mathstodon.xyz/users/tao/statuses/115871649394962391 on your instance and quote it. (Note that quoting is not supported in Mastodon.)