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@wikiemol@mathstodon.xyz

Post #2920370

2026-05-17 16:44 UTC

3. I think the frustration that 'Anti-AI' people, such as myself, have felt has been largely misunderstood (I think in many cases, even by 'Anti-AI' people themselves). The point is that the resolution of the 'crisis' mathematicians face in the future depends heavily on whether or not there are aspects of mathematical reasoning that are not computational. Whether there are or aren't is currently unclear. I can't speak for others, but the frustration that I feel is that there has not been any serious discussion of this among prominent figures. If I was a prominent figure, I would lead this discussion myself, but I am unfortunately not a prominent figure and so there is not much I can do. The bottom line for all of this is that aversion to AI may have been read as decrying AI as useless, but this is not the point: the point is that when I introspect about how I think about mathematics, it seems both subjectively and formally to be not a computational process at its core, and so all of the discussion around it based on the concept that AI will keep getting better feels entirely moot. AI may keep getting better, but if it only does so with an asymptote at the top that it can't get past, and the 'core' of pure mathematics lives above this asymptote, then there isn't really a problem except in the short term. And all AI does is force others to consider whether or not pure mathematics is computational. If pure mathematics is not computational, it doesn't really 'help' us do pure mathematics, because the 'pure' part is not computational. (12/n)

Replies (1)

  • @wikiemol@mathstodon.xyz 2026-05-17 16:46

    It's not that AI is 'useless', but that it is moot with regards to pure mathematics specifically. It just refocuses us on the kinds of things we were once focused on in the past, it does not fundamentally change our practice except insofar as it forces us to recon with classic questions we have devalued, questions that we have only really begun to fully devalue in the 21st century and late 20th century, that have more or less been left on the table, unanswered. If pure mathematics is not computational at its core, the only problem we face is a short term one, and is completely resolved if we can convince others that pure mathematics is not computational. Hopefully, I have provided some arguments that this view is at least possibly true, and subject to mathematical analysis (but perhaps not computationalist mathematical analysis) and examples of mathematical works from the past that exemplify this possibility. (13/13)

    Open ##2920371