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Post #2581817

2026-05-14 00:01 UTC

My talk on "New Mathematical Workflows" at Stanford last week is now online: https://www.youtube.com/watch?v=Uc2zt198U_U One key recommendation in the talk is to now de-prioritize the historical emphasis on competing to be the first to provide a proof for a given unsolved mathematical problem. When we were in the proof scarcity era, the "local" goal of obtaining any proof at all for a problem was fairly well aligned with the more "global" goal of collectively advancing our understanding of mathematics as a community. However, now that the ability to optimize this local goal has increased rapidly to the point of "proof abundance", we have now reached the point where Goodhardt's law https://en.wikipedia.org/wiki/Goodhart%27s_law has kicked in, and further unrestricted overoptimization of this goal will no longer create genuine mathematical progress, and may in fact inhibit it in various ways. However, there is scope for more controlled, and still meaningful, optimization in this direction along carefully chosen workflows (such as mathematics competitions) that are specifically designed to accommodate heavy AI use.

Replies (3)

  • @quantisan@hachyderm.io 2026-05-15 03:54

    @tao@mathstodon.xyz Thanks for sharing! I'm still digesting. But the point about a very literate genie reminded me of this comedy skit... https://youtu.be/lM0teS7PFMo?si=U48jIk6Yc_9-L65M

    Open ##2920357

  • @wikiemol@mathstodon.xyz 2026-05-17 16:26

    @tao@mathstodon.xyz I want to emphasize first that I do think this is a wonderful and informative talk. In particular, I am extremely happy to see the point about optimization being sometimes detrimental to progress being discussed openly. That said, while I agree with the problems you have articulated, I continue to disagree with the proposed solutions. I will attempt to be a bit more productive than my previous comments on your posts, and try and articulate the solution to the problem that I see as best as I can, but I am not sure how to articulate it concisely, so please forgive the length. There is a tl;dr at the end extracting the main points. What I have to say is based on an assumption: that the part of the human mind that is relevant to the 'utilitarian' aspects of mathematics is either completely reproducible by a computer, or it isn't. If the former is true, then any attempt at trying to change our workflow in terms of 'infrastructure' will at best be a temporary fix. The bottom line is that there will be no incentive for anyone to enforce this infrastructure without a drastic cultural change. Over a long enough time scale any workflow change along the lines of creating 'walkable' cities will get stamped out. This may seem pessimistic, except if the utilitarian aspects of the human mind are not reproducible by a computer. I am not sure which is true, but without any serious investigation of whether this is true or not, we cannot make meaningful progress on the 'crisis' mathematics faces in the future, because without this investigation, our proposals may be based entirely on faulty assumptions. (1/n)

    Open ##2920358

  • @xeroxed@mastodon.social 2026-06-23 13:06

    @tao@mathstodon.xyz sir the video is now private

    Open ##4296007