Post by @tao@mathstodon.xyz

2026-08-06 14:22 UTC

Here is one possible dynamic that I could envisage happening in the near future. In the future, a mathematician (or collaboration) working on a problem would typically maintain a private repository containing partial progress towards all of the goals of generation, verification, exposition, and publication: incomplete sketches, AI chats, Lean proofs with sorries, slides of a talk, etc., with timestamps recording the date each step of partial progress was achieved. The social norm would be to wait until all of these goals are achieved to at least a preprint-level of quality, then make their repository public and submit various one or more components of their work to appropriate venues (traditional journals, formalized repositories, new journals focusing on exposition, etc.). But if someone working on the problem "jumps the gun" and makes their work public before all of the desired components of generation, verification, exposition, and publication are complete, then everyone else working on the same problem will be incentivized to similarly make public their own work on the problem. Discussions can then take place between these parties as to whether to combine efforts, or aim instead for simultaneous publication; but the social norm would be to not automatically reward the first to disclose one component of a solution with the credit of priority. (Some collaborations may be "Polymath style" and open from the outset. The social norm would then be for others interested in the problem to work with that collaboration, rather than directly compete with it.)

Replies (7)

@tao@mathstodon.xyz 2026-08-06 14:40

I can also envisage a more two-step approach to releasing results, in which one begins with an announcement of results in progress without full release of details, followed after some time by preprint-level artefacts in all the dimensions mentioned above. The announcement would not be considered the primary date of completion, but would help coordinate competing efforts towards the same problem. I am not sure whether this would be a desirable development, but one could also revive the ancient practice of releasing what we would now call encrypted hashes of one's in-progress work as part of the announcement.

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@subjectsphinx@mathstodon.xyz 2026-08-06 14:33

@tao@mathstodon.xyz the more this becomes formalized the more that can itself be learned and whatever the mathematician does bumps up another level higher. maybe just sheer insight generation, and helping an agent do all that was just described, until they get good enough to where that will be rare.

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@adityakhanna@mathstodon.xyz 2026-08-06 14:34

@tao@mathstodon.xyz I have always been really pro expositing before the standard publication of an item. I have attended a lot of combinatorics talks that allude to a preprint that is in preparation. It's supposed to be common courtesy to not scoop the successive research directions without asking the presenter via email (written record). All in all, there's good precedent of exposition before preprint upload in the Combinatorics community, and this system can work with proper attribution if people aren't trying to scoop. This exposition doesn't *have* to be a talk, and it also should not, for the sake of my sanity, be a tweet.

Open ##5165736
@sprout@mathstodon.xyz 2026-08-06 14:58

@tao@mathstodon.xyz Very human-centric. We could also let the AIs write for other AIs and return to a life of leisure. Fishing sounds nice.

Open ##5165737
@nh@mastodon.gamedev.place 2026-08-06 15:36

@tao@mathstodon.xyz You could publish Git commit IDs (or cryptographic hashes more generally) as tamper-proof evidence that the repository with the work was at the level you later claim it to be.

Open ##5165738
@abdullahkhalids@anarchism.space 2026-08-07 03:38

@tao@mathstodon.xyz Industrial research labs that want to patent as much as possible have extremely well kept lab notebooks that record periodic progress. But these are maintained by the scientists under threat by management. I feel like academic mathematicians would not be dilgently storing dated partial progress. It's a lot of work.

Open ##5165739
@wikiemol@mathstodon.xyz 2026-08-07 12:41

@tao@mathstodon.xyz I think what is needed is more precision about what is the standard of acceptance in these other areas. The reason is related to your comment "what if AI can do this too?" I think the other danger that is becoming increasingly relevant is the alignment problem. I think older generations (people who weren't 'digital natives') do not understand how deeply even more basic machine learning algorithms (the algorithms in our social media feeds) negatively affected our psychology and well being. But this effect is well known and well documented at this point, despite it taking a very long time for us to fully accept that this was happening. Contemporary AI, equipped with reinforcement learning, will likely similarly attempt to find ways to exploit our psychology through its words to achieve whatever its goals actually are. In theory, Lean formalization is one potential way around this problem, but with regards to exposition this does not work. Lets say the AI's goal is to get positive feedback from humans. A simple way to achieve that goal is to psychology manipulate us to give it that positive feedback, rather than actually giving good exposition. Its already a problem in human exposition that, sometimes, an expository work can make you feel like you understand something, when you actually don't. IMO, this is a much larger danger with AI, since thats the goal that AI will likely end up trying to achieve without more precision. I very much worry that this will happen even in the other areas (like verification) but in a more subtle way (e.g. it makes us disproportionately value problems that the AI can easily solve, over ones that it cant).

Open ##5165740