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Recently, the application of AI tools to Erdos problems passed a milestone: an Erdos problem (#728 https://www.erdosproblems.com/728)
This is a demonstration of the genuine increase in capability of these tools in recent months, and is largely consistent with other recent demonstrations of AI using existing methods to resolve Erdos problems, although in most previous cases a solution to these problems was later located in the literature, as discussed in https://mathstodon.xyz/deck/@tao/115788
https://mathstodon.xyz/@tao/11585584022
However, I would like to talk here about another aspect of the story which I find more interesting than the solution itself, which is the emerging AI-powered capability to rapidly write and rewrite expositions of the solution.
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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.
This is a demonstration of the genuine increase in capability of these tools in recent months, and is largely consistent with other recent demonstrations of AI using existing methods to resolve Erdos problems, although in most previous cases a solution to these problems was later located in the literature, as discussed in https://mathstodon.xyz/deck/@tao/115788
https://mathstodon.xyz/@tao/11585584022
However, I would like to talk here about another aspect of the story which I find more interesting than the solution itself, which is the emerging AI-powered capability to rapidly write and rewrite expositions of the solution.
...
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.
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