Post #2920365

2026-05-17 16:37 UTC

Here 'famous' does not necessarily mean millennium prize level famous, but also includes famous enough for a small group of people who don't know each-other to come to learn about the same ideas and questions independently. The trouble is, this kind of motivation is not very useful in an age of AI, because this method renders all aspects of mathematical practice essentially decidable. Instead, the burden we will face in the future is that our work will have to "light someone's soul on fire" in the same way the blue eyed islander puzzle does, or otherwise hope that someone else's soul has already been lit, and that they stumble upon your work on their own due to shared curiosity. This ability for humans to 'light up each-others souls' is the essence of the alignment problem. Pure mathematics papers will no longer be able to start with an introduction with a structure consisting only of "in so and so et al, xyz was proved, then Smith et al expanded on xyz by proving lmnop. In the present paper, we expand further by generalizing lmnop to all fantasy creatures, not just unicorns, we do so by..." This is because this leaves the burden of justifying the present work as a philosophically edifying to the reader, and as you discuss in this talk, this is no longer pragmatically possible. Pure mathematics has never been pursued for only philosophical reasons, but it seems to me that modern mathematicians have essentially banished philosophical discussion entirely, and the totality of this banishment seems to have only fully taken over in the 21st century as a result of the development of computers making the formalist paradigm seem entirely natural. (8/n)

Replies (1)

@wikiemol@mathstodon.xyz 2026-05-17 16:38

But this has always seemed contradictory to the notion of "pure" mathematics, since it is motivated primarily by "the love of wisdom" for lack of a better term. One may object that this invites all kinds of 'crankery'. I.e. that the previous structure was primarily geared towards knowing immediately the difference between 'crankery' and 'non crankery', and that this became necessary because of the internet. But for a pragmatic rebuttal, this problem is potentially solved by lean formalized proofs becoming cheaper. One can now look at a result being proved and see that it was truly proved in the paper. Since that is no longer the bottle neck, the way in which the result should be interpreted by humans, and the way in which it enhances our understanding of interesting philosophical questions, is the most valuable part of the paper. The peer review process becomes more about looking at the lean formalized result being proved, and reading the philosophical interpretation/discussion, and deciding if that interpretation is actually correct, or if there are serious rebuttals to it. For example, the formalized theorem may be 'the wrong theorem', or perhaps some of the philosophical discussion is not actually philosophical, and can be settled entirely formally. These are both situations that would warrant rejection of the paper. This means that this philosophical discussion still requires the mathematician to know and utilize classic formal reasoning, but it is just that it must be used in an entirely different way. (9/n)

Open ##2920366