Ten advances in mathematics and theoretical computer science
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Replace philosophers for mathematicians and Douglas Adams was spot on again.Whilst current models can't 'intuit' and come up with conjectures, they can certainly disprove some of them very quickly through the kind of grind that humans can't do. I suppose there really are some mathematicians out there today, whose last few years of study, have just…
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one of the early premises of how ai takeoff would go was that a system that could solve open problems in advanced mathematics would also discover novel advances in math and computer science that directly unlock drastically better software performance. we are seeing frontier level math breakthroughs (ie performance that would put it in the top 100…
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Any computable problem will eventually fall to computers.LLMs have made math proofs more computable, in the sense that a computer can both generate potential solutions and check the validity of its solutions on its own, with a reasonable chance of converging on something correct. I assume this was already doable to some extent, but it seems like…
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Not being an expert in any of the fields OpenAI has "advanced" I don't want to prematurely downplay the significance of this contribution. However, I am worried that the language they are using in this blog post is exaggerating for the sake of marketing.It is true there hasn't been a reliable computational approach to solving these problems…
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The GitHub repo with the Lean formalizations just came out a couple of hours ago: https://github.com/openai/ten-proofsIt also links to a paper written by an LLM where the model "reconstructs how the proof came together" based on the unpublished reasoning traces: https://cdn.openai.com/pdf/reasoning-walkthroughs.pdfI wish they'd publish the prompts…
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People argue whether we are at y-5, y, or y+5, meanwhile we seem to be on a y=2^x exponential that keeps delivering more and more impressive results.The most interesting question to me is what will be consumed by the exponential like math seems to be undergoing, and what won’t. Writing has been quite stubborn, but I’ve noticed Fable to be quite a…
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Henry Yuen's (whose work problem 6 builds on) comments on this are worth reading IMO:
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Pretty cool. The impact of AI is getting undeniable, there aren’t many positions left to move the goalposts to at this stage, next they’ll have to be outside the stadium entirely.The sooner people can be broken out of their denial about all this the better, and we can start actually taking it seriously.