Post by @tao@mathstodon.xyz

2026-08-27 19:07 UTC

Let's say that in a given year, it was possible for a field to generate 100 solutions to various problems, and (by spending the extra month) generate 90 publication-quality writeups of these problems, leaving only 10 solutions that lack such writeups. Then, even if every solved result was announced with only a poorly written description of the result, the signal-to-noise ratio would remain quite high: nine times as many well written solutions as poorly written ones. Only a light amount of curation - such as via a peer-reviewed journal system - would be sufficient for filtering out the 10 results that lack a professional writeup, and obtain a very high quality curated stream of results that form a suitable base for further development of the field. But suppose that advances in AI reduce the problem solving time from six months to a single day, whereas the task of writing things up carefully to professional standards only decreases modestly, from one month to three weeks. So now, one has the choice between spending a day of effort to generate a poorly written solution, or invest a little over three weeks to generate a well written solution. In both cases, the net effort required has gone down, so production volume should go up significantly: for instance, the number of publication-quality writeups might increase from 90 to 500. But in the same time period, the total number of solutions that can be created (with or without a proper writeup) -- which are now far easier to generate still -- might go up from 100 to 5000. (2/4)

Replies (2)

@tao@mathstodon.xyz 2026-08-27 19:07

Each individual author is now capable of writing more and better papers in a shorter amount of time: but whereas previously 90% of the extant literature was well-written, the situation is now completely reversed: 90% of the literature will now be poorly written. At this point, traditional peer-review journals would become overwhelmed and unable to fully convert this stream of results into the type of high-quality curated content that they would have been able to do in the past. These numbers were artificial and exaggerated, but hopefully serve to illustrate the key tradeoff between volume and quality. It is sometimes claimed that such problems will solve themselves in time, because AI tools will get better in (say) exposition. This may be true to some extent, but the AI tools will concurrently get even better at generation than they are currently, and so the ratios will likely deteriorate further if current trends continue. (3/4)

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@tao@mathstodon.xyz 2026-08-27 19:07

Increased filtering (by various automated or semi-automated means) by journals and other curation sites may help somewhat, but I (somewhat reluctantly) am coming to the conclusion that in the new era of proof abundance, the high-quality and well-curated portion of the literature will become an increasingly small fraction of a much larger ocean of lower-quality (though often technically correct) results; but they may, by the same token, become the most valuable data sources for both the further internal development of mathematics, and its applications to other disciplines. (4/4)

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