Post #2920368

2026-05-17 16:42 UTC

Tl;dr: The main points are as follows: 1. I think the following are not replicable by a computer because of the alignment problem: - Question generation - Definitions - Philosophical curiosity 2. I think the formalist paradigm has made mathematicians as a whole think that this 'crisis' we face due to AI is somehow not subject to mathematical inquiry. But we have faced many mathematical crisis in the past, and the reaction has always been to use mathematics to resolve the crisis. It is only now, because of the computational paradigm, that we feel as though we must resort to something outside of our formal reasoning capabilities (like analogies, or attempting to predict the future of our cultural development). But this isn't true. For example, even though analyzing when definitions and questions are 'correct' is likely something that lies outside of our computationalist or foundationalist paradigm, this doesn't mean that it is not subject to mathematical reasoning. It could just mean that computationalism is wrong. So, the solution to the problem is to investigate this question as best we can, and iron out these limitations. We need something that is more along the lines of a paradigm shift, not a shift in workflow. (11/n)

Replies (1)

@wikiemol@mathstodon.xyz 2026-05-17 16:44

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)

Open ##2920370