Post by @antoinechambertloir@mathstodon.xyz

2026-09-10 08:11 UTC

#AI #Math The most recent case of the finite time solution of the forced Navier-Stokes equation has been discussed a lot in the recent days, on this network and in the mainstream press, but I will try to give a perspective on what happened recently. This is prompted by a friend informing me this morning of two annoying additional stories that taint the recent public success of AI generated proofs and will hopefully lead the mathematical community to address the question of predation and plagiarism. However, I won't address here the even more important questions posed by AI companies beyond merely quoting some of them: - its energetic cost; - its impact on minerals and other natural resources; - its direct and immediate consequences on the ecosystem (water heating, pollution, land waterproofing, etc.); - its impact on the work market, in particular those prompted by (actual or alleged) productivity gains; - its impact on learning, cognition, etc.; - its impact on the economic structure, tremendous announced gains/losses of companies that look like a Ponzi scheme; - its impact on the power structure, who owns what, who gives access to what; - its impact on the political structure, the surveillance capitalism, etc. These are fundamental issues that should be addressed more clearly in the mainstream medias, and that, in my view, suffice to object to the existence of AI. Anyway, what does it mean for academic math? 1/n

Replies (2)

@antoinechambertloir@mathstodon.xyz 2026-09-10 08:22

#AI #Math 2/n Before going on specific matters, I need to go back to what math is and to what it does. TL-DR;-) As far as it goes about automatization, math is probably the easiest of all sciences. In 1994, the mathematician William Thurston published a paper with the title “On proof and progress in mathematics” in which starts with stating the question What is it that mathematicians accomplish? His answer — you might find it circular — is that mathematicians push forward the human understanding of mathematics. This means that mathematicians have under the eyes a whole range of (abstract) objects for which they use sometimes colloquial names (group, ring, field, memberhip, sheaf, relation, knot, crystal…) and sometimes more specific names (perfectoid, hypersolvable, function, proof, set…) and they try to better understand the properties that these objects possess, and the relations between them. A whole field of mathematics is motivated by the fact that some of these objects model phenomena of the actual world in which we live, with the idea that the behaviour of the abstract mathematical objects might help us make actual decisions. But a large part of mathematics is just motivated by these abstract objects themselves, possibly with the hope that, some day, they could be useful to the real world, and sometimes in the expectation that they will never be useful to it. For example when being useful means helping killing people. https://www.ams.org/journals/bull/1994-30-02/S0273-0979-1994-00502-6/S0273-0979-1994-00502-6.pdf

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@failedLyndonLaRouchite@mas.to 2026-09-10 13:40

@antoinechambertloir@mathstodon.xyz cost for the 1st low Q sequence of the human genome: roughly 100 million US dollars current cost for a very hiQ sequence*: about US 50K *in the jargon, a phased T2T from HiFi Pacbio or 100x coverage ONT

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