Post #2920374

2026-05-10 18:11 UTC

Again, if one adopts the mindset that the solution to any issue with a proposed optimization is to simply perform more optimization, one could propose to just modify the rubric one is directing an AI tool to optimize to incorporate any such objection raised, iterating as needed. However, it is telling that we choose not to do this with (for instance) food preparation, with meals prepared by expert human chefs being valued at a premium above machine-prepared food, even when the latter is safe to eat, well-presented, easy to digest, convenient, and appealingly flavored. This is not to say that such processed foods do not have utility; but they are not seriously proposed as a complete replacement for the human art of cooking. I believe the situation with mathematics and AI-generated proofs will be analogous. (3/3)

Replies (4)

@fuglede@mastodon.social 2026-05-11 08:50

@tao@mathstodon.xyz I imagine you are familiar with tools like https://nowigetit.us/ that take as input a paper and output an interactive page for playing around with it. Probably works better for computation-heavy studies than pure proofs, but still. That one is a blender, optimized for exposition friendliness, and just like Dall-E outputs or other generated web sites, the output pages are rather bland. But solving that seems easier than the first two points; do “style transfer from a delicious exposition”.

Open ##2920375
@zussini@mathstodon.xyz 2026-05-11 23:50

@tao@mathstodon.xyz maybe we are heading to the era in which anybody can become a competitive mathematician, where prerequisites served as curricula usually do will not be as important as willingness to learn, tinker and struggle with it. Like with sports. There could be a massive mathlearning ahead of us. The digestion part can be easily seen in education with AI tools, it is now most important part.

Open ##2920376
@Bielefelder@mathstodon.xyz 2026-05-12 07:58

@tao@mathstodon.xyz One idea might be to include an AI-generated cartoon or comic picture into the final paper. I this gave this a try for Erdos #1196. Here is the poster draft: "The Glorious One plus Eight". https://althofer.de/the-glorious-one-plus-eight.jpg

Open ##2920377
@wikiemol@mathstodon.xyz 2026-05-12 11:38

@tao@mathstodon.xyz I think I have learned that the big rift between pro AI and anti AI sensibilities in mathematics (and programming actually) is mostly due to the rift between 'problem solvers' and 'theory builders' in Gower's words. To this end, the cooking analogy is a good one, but leaves out important things for the 'theory builder'. In the food case, chewing vs eating through a tube are functionally equivalent when it comes to essentially all strictly utilitarian considerations with regards to food. This may be true for the problem solver, but it is not the case for the theory builder. When we do the equivalent of putting mathematics through a blender, we actually change the 'theory being built'. I.e. in AI's case, the optimization you are describing is a *local* optimization, not a *global* optimization. And we are leaving *global* optimization entirely on the floor by using the AI only approach. In other words, it is not just enjoyment that we are missing, it is also longer term utilitarian benefits, like theory building, and paradigm shifting. 'Theory builders' will see little benefit from AI. A good theory builder will find relatively easy small proofs, that an AI probably could find, but not much time is saved in the process, because the bulk of the time for a theory builder is taken up by figuring out what we *should* prove, which an AI is entirely incapable of without some motivating problem, which a theory builder is not really interested in. Theory builders use problems as a testing board, not a motivator. On the other hand, 'problem solvers' will see immense benefit from AI. Both sides have trouble seeing the other's perspective.

Open ##2920378