Post by @atif@mathstodon.xyz

2026-08-10 01:21 UTC

@maxpool@mathstodon.xyz when i first saw this (posted as a serious comment) i was like: should it really be obvious to me that *this* much math (say up to 2022) was needed for the machines to be able to take it to the “endgame”, whatever that endgame may be? did anyone before 2022 speculate that we already developed enough advanced math that a “super intelligent” entity would be able to outpace the humans in all aspects in development of mathematics, using the mathematics that was developed up to 2022 as a starting point? does that mean that most of the existing stuff is good enough—to be eternalised in a sense, or good enough of a seed, so to speak—and most of it doesn’t need to be rebuilt? if yes, what an accomplishment mathematics of today is! if not, we are still in business the whole argument seemed rather silly after i convinced myself that the thing i ask in the first paragraph really isn’t obvious.. but i could be wrong it’s a fun meme though 🙂 @tao@mathstodon.xyz

Replies (2)

@jdw@mathstodon.xyz 2026-08-10 10:14

@atif@mathstodon.xyz @maxpool@mathstodon.xyz @tao@mathstodon.xyz As many of my friends can confirm, I was predicting that AI would outperform humans in mathematics already ~10 years ago (and I had a number of heated debates about this back then). This was roughly the time when I learned about proof assistants and when programs like AlphaZero and AlphaGo achieved new peek performances in games like chess and Go. I must admit though that I expected the method for solving math would be old fashioned reinforcement learning, the game state being a Lean context window, allowed moves being applicable Lean tactics and a winning move being a completed proof. The analogy between making progress on a math problem by stating and proving a helpful intermediate result and improving the own position in chess or Go seemed very obvious to me. I just couldn't answer the question who would pay for the development of such a system. I did not predict that natural language processing would be solved first and that the math AI would be the same program that would spam social media networks with political propaganda and render graphics designers, copywriters, composers and software developers jobless together with mathematicians.

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@maxpool@mathstodon.xyz 2026-08-10 11:15

@atif@mathstodon.xyz @tao@mathstodon.xyz I don't see evidence that machines outpace humans in all aspects of the development of mathematics. Using the skills vs. intelligence distinction from https://arxiv.org/abs/1911.01547 used as the basis for the ARC Prize https://arcprize.org/, it's clear that machines master many skills and techniques that human mathematicians already know, and then can tirelessly search for solutions using these existing skills. But could they develop a completely new and novel technique or a new field in mathematics in order to solve a very hard problem? Not yet, I think. What would be an ARC Prize-style problem for mathematics?

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