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Number theorist Jared Lichtman says this AI proof is from "The Book", the highest compliment one can give. He also says: > I care deeply about this problem, an
by energy123 7mo ago
Number theorist Jared Lichtman says this AI proof is from "The Book", the highest compliment one can give. He also says:
> I care deeply about this problem, and I've been thinking about it for the past 7 years. I'd frequently talk to Maynard about it in our meetings, and consulted over the years with several experts (Granville, Pomerance, Sound, Fox...) and others at Oxford and Stanford. This problem was not a question of low-visibility per-se. Rather, it seems like a proof which becomes strikingly compact post-hoc, but the construction is quite special among many similar variations.
> The conjecture is 60 years old and many experts had consulted on the problem, making partial progress. I mentioned this to @thomasfbloom, and he replied: "perhaps the first Book Proof from AI?"
Terence Tao says:
> In any case, I would indeed say that this is a situation in which the AI-generated paper inadvertently highlighted a tighter connection between two areas of mathematics (in this case, the anatomy of integers and the theory of Markov processes) than had previously been made explicit in the literature (though there were hints and precursors scattered therein which one can see in retrospect). That would be a meaningful contribution to the anatomy of integers that goes well beyond the solution of this particular Erdos problem.
- seanhunter 7mo agoWell that’s interesting. Probably I’m wrong, but I still feel like something important is slipping away here.
- menaerus 7mo agoLike what exactly?
- krige 7mo agoNumber theorist Jared Lichtman is also involved with an AI startup so he might have a bit of an incentive to frame things this way.
- Zababa 7mo agoThank you, that feels like important context!
- energy123 7mo agoThis guy also says it's a book proof though: https://en.wikipedia.org/wiki/Thomas_Bloom https://en.wikipedia.org/wiki/Thomas_Bloom
- Zababa 6mo agoImportant context too, thanks! More context: - Thomas Bloom is the current owner of https://www.erdosproblems.com/ https://www.erdosproblems.com/ - He previously posted on X on the 2025/10/17 the following: > Hi, as the owner/maintainer of http://erdosproblems.com http://erdosproblems.com, this is a dramatic misrepresentation. GPT-5 found references, which solved these problems, that I personally was unaware of. The 'open' status only means I personally am unaware of a paper which solves it. [1] > GPT-5 has been a very useful tool in searching the literature, and this has been a valuable addition to the website. Its literature searching ability is already useful and impressive enough, no need to describe it as something it's not! [2] [1]: https://x.com/thomasfbloom/status/1979254235075059732 https://x.com/thomasfbloom/status/1979254235075059732 [2]: https://x.com/thomasfbloom/status/1979254675833549207 https://x.com/thomasfbloom/status/1979254675833549207 I don't have the mathematical chops or knowledge of mathematicians to evaluate any of that.
- martin293 6mo agoSource: https://www.math.inc/a-conversation-with-terry-tao https://www.math.inc/a-conversation-with-terry-tao However, I think this is still likely a very significant achievement/milestone.