Article URL: https://borretti.me/article/mathematics-without-mathematicians Comments URL: https://news.ycombinator.com/item?id=49142083 Points: 25 # Comments: 29

Yesterday, OpenAI announced the solution to ten open problems in mathematics, all discovered by a yet-unreleased model. There’s only one, the coding theory one, where I know enough to say “huh, that’s important”, but according to the mathematicians I trust this is important. Inevitably, people will spin some sophistry to cope, to convince themselves nothing will change. And that’s fine. People need to cope. But we can’t put our heads in the sand forever while the world is transformed around us. So, here is a list of ways people will cope about AI taking over mathematics, and how each cope is likely to be refuted by reality. My intent is not to horribly depress everyone but rather to help them metabolize the implications of this technology. The arguments here are somewhat portable: replace “mathematics” with “botany” or whatever as needed. The AIs will exceed humans in taste and intuition. At some point, the human pointing the way will get worse results than the human saying “here’s a proof checker, have fun” and paying for the tokens. The AIs will be better teachers than the humans. In any case, there won’t be a human audience for expository work of frontier math. This is a nice cope. The AIs are explorers out in the frontiers, the humans gratefully receive their Lean proofs, and then discourse over them, choose which results are relevant, shape those results into a little brick for the great cathedral of algebra. Analogous to the above: the AIs will build the cathedral on their own. They will be better architects than us. This works until the AIs have blasted so deep into the deductive closure of mathlib that the distance from elementary mathematics to the frontier exceeds what any human can hope to learn in their lifetime, no matter how narrow their focus. We won’t! This misunderstands who the audience will be. AIs will do frontier math, downstream, AIs will use the new math to do frontier science, finally, AIs will use the new science to do frontier engineering. No human needs to understand any of it, firms that put humans in the loop to understand the results will be outcompeted by those which don’t.