Post #2920367

2026-05-17 16:39 UTC

This burden of 'lighting up the soul' is the same burden that most of the humanities have had throughout most of history, including pure mathematics. It was only the development of the formalist paradigm that lifted this burden, but only for a time, and now we are seeing this burden placed back on our shoulders. I think primary examples of papers that 'light up the soul' can be found in recreational mathematics in the mid 20th century. For example, Penrose's work on the Penrose tilings and also in analyzing MC Escher illustrations using cohomology are both examples of work which 'lights up the soul', at least for me. (10/n)

Replies (1)

@wikiemol@mathstodon.xyz 2026-05-17 16:42

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)

Open ##2920368