Post #2581819
2026-05-10 18:10 UTC
Replies (5)
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@tao@mathstodon.xyz 2026-05-10 18:11
I can return to the culinary analogy I have been using recently to illustrate this point. We chew food that is hard to swallow, in order to make it easier to digest. And we have cooking techniques to make tough foods more tender, to reduce the amount of chewing needed. However, if one decided to automate and optimize digestion by minimizing the chewing needed, the logical solution would be to put all of our meals into a blender and serve them through feeding tubes. This technically solves the problem of indigestion, but is not a popular option (save for people too ill to chew food properly). There are other valuable benefits of eating, such as the sensory enjoyment of the experience or the ability to create a social event around a meal, which go beyond the mere ingestion of nutrients, and which would be negatively impacted by such an overemphasis on maximizing digestibility. This is not to say that blenders and similar devices are useless; but their use cases are situational. In a similar vein, using AI tools to make mathematical papers "as easy to read" as possible are not necessarily desirable; they can be useful in identifying particular pockets of "artificial difficulty" in a draft paper that would benefit from a rewrite (similar to how an overly tough piece of meat could be tenderized before serving), but using them to smooth out "natural difficulties" in a text that actually are of benefit for the reader to "chew over" can end up being counterproductive to the actual goal of advancing the collective understanding of the result by the community. (2/3)
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@naras@mathstodon.xyz 2026-05-10 18:44
@tao@mathstodon.xyz If I recall correctly, you even used "proof indigestion" in your talk which made me laugh. I think there are analogs in programming too and one can replace "proof" with "code". I constantly catch Claude doing unnecessary things and stop it before I lose the ability to grok the output. For example, can we replace generated implementation of algorithm A by AI with a better algorithm B. If so, we are on firmer ground.
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@dimpase@mathstodon.xyz 2026-05-10 20:06
@tao@mathstodon.xyz there is an ethical/philosophical component to the third component in particular. The food analogy it too crude here. For a proof is only really digestible if there is a maths community consensus on it. There are maths examples of similar situations in the pre-LLMs era: 4-colouring problem, CFSC --classification of the finite simple groups, etc. These demonstrate indigestible proofs, with constant (although seemingly running out of steam) more or less (less in the CFSC case) successful attempts to improve their digestibility. These also demonstrate the social side of indigestibility - CFSC declared "complete" by the main driving forces of the program, in part for reasons of finances, well ahead of real completeness resulted in the crumbling of the program. A similar, but much larger in scale, affecting all the branches of the maths, crumbling would occur if top mathematicians started to declare maths "solved" - in exchange for being showered by grants from LLM/AI dealers. And this seems to be happening already.
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@masonporter@mastodon.social 2026-05-10 20:07
@tao@mathstodon.xyz I essentially agree with the cooking/chef analogy, but there is also an important consideration for that (which, if I understand correctly, also occurs in the setting of chefs). While certain people (say, like us and, we hope, like all of our students) will need and want to digest proofs, there is a much larger set of people who don't care. That includes many of the people who might employ our students. Wealthy people value fancy chefs. A much larger set of people don't care.
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@domotorp@mathstodon.xyz 2026-05-11 19:17
@tao@mathstodon.xyz I think a better metaphor would be flight navigators. As much as I would love to picture myself as a heroic hunter or a masterchef, research math is different, because few people see it daily, while everybody eats and enjoys food, not to mention that there is no tech involved. Flight navigators were experts in determining position, needed on all flights. After GPS, nobody needed them anymore, so they had to look for other jobs. Research math is a similar skill: it is essential, but affects the lives of most people indirectly, so most of us might end up like flight navigators.