[xeeeeeeeeeeenu]

> no prior solutions found.

This is no longer true, a prior solution has just been found[1], so the LLM proof has been moved to the Section 2 of Terence Tao's wiki[2].

[1] - https://www.erdosproblems.com/forum/thread/281#post-3325

[2] - https://github.com/teorth/erdosproblems/wiki/AI-contribution...

[nl]

Interesting that in Terrance Tao's words: "though the new proof is still rather different from the literature proof)"

And even odder that the proof was by Erdos himself and yet he listed it as an open problem!

[pfdietz]

The theorem is implied by an older result of Erdos, but is not a result of Erdos. Apparently this is because the connection is something called "Roger's Theorem" that was quite obscure.

https://terrytao.wordpress.com/2026/01/19/rogers-theorem-on-...

"This theorem is somewhat obscure: its only appearance in print is in pages 242-244 of this 1966 text of Halberstam and Roth, where the authors write in a footnote that the result is “unpublished; communicated to the authors by Professor Rogers”. I have only been able to find it cited in three places in the literature: in this 1996 paper of Lewis, in this 2007 paper of Filaseta, Ford, Konyagin, Pomerance, and Yu (where they credit Tenenbaum for bringing the reference to their attention), and is also briefly mentioned in this 2008 paper of Ford. As far as I can tell, the result is not available online, which could explain why it is rarely cited (and also not known to AI tools). This became relevant recently with regards to Erdös problem 281, posed by Erdös and Graham in 1980, which was solved recently by Neel Somani through an AI query by an elegant ergodic theory argument. However, shortly after this solution was located, it was discovered by KoishiChan that Rogers’ theorem reduced this problem immediately to a very old result of Davenport and Erdös from 1936. Apparently, Rogers’ theorem was so obscure that even Erdös was unaware of it when posing the problem!"

[TZubiri]

Maybe it was in the training set.

[davidhs]

It looks like these models work pretty well as natural language search engines and at connecting together dots of disparate things humans haven't done.

[pfdietz]

They're finding them very effective at literature search, and at autoformalization of human-written proofs.

Pretty soon, this is going to mean the entire historical math literature will be formalized (or, in some cases, found to be in error). Consider the implications of that for training theorem provers.

[p-e-w]

Every time this topic comes up people compare the LLM to a search engine of some kind.

But as far as we know, the proof it wrote is original. Tao himself noted that it’s very different from the other proof (which was only found now).

That’s so far removed from a “search engine” that the term is essentially nonsense in this context.

[cubefox]

This illustrates how unimportant this problem is. A prior solution did exist, but apparently nobody knew because people didn't really care about it. If progress can be had by simply searching for old solutions in the literature, then that's good evidence the supposed progress is imaginary. And this is not the first time this has happened with an Erdős problem.

A lot of pure mathematics seems to consist in solving neat logic puzzles without any intrinsic importance. Recreational puzzles for very intelligent people. Or LLMs.

[glemion43]

It shows that a 'llm' can now work on issues like this today and tomorrow it can do even more.

Don't be so ignorant. A few years ago NO ONE could have come up with something so generic as an LLM which will help you to solve this kind of problems and also create text adventures and java code.

[jojobas]

It's hard to predict which maths result from 100 years ago surfaces in say quantum mechanics or cryptography.

[antonvs]

> "intrinsic importance"

"Intrinsic" in contexts like this is a word for people who are projecting what they consider important onto the world. You can't define it in any meaningful way that's not entirely subjective.

[MattGaiser]

There is still enormous value in cleaning up the long tail of somewhat important stuff. One of the great benefits of Claude Code to me is that smaller issues no longer rot in backlogs, but can be at least attempted immediately.

[threethirtytwo]

This is a relief, honestly. A prior solution exists now, which means the model didn’t solve anything at all. It just regurgitated it from the internet, which we can retroactively assume contained the solution in spirit, if not in any searchable or known form. Mystery resolved.

This aligns nicely with the rest of the canon. LLMs are just stochastic parrots. Fancy autocomplete. A glorified Google search with worse footnotes. Any time they appear to do something novel, the correct explanation is that someone, somewhere, already did it, and the model merely vibes in that general direction. The fact that no human knew about it at the time is a coincidence best ignored.

The same logic applies to code. “Vibe coding” isn’t real programming. Real programming involves intuition, battle scars, and a sixth sense for bugs that can’t be articulated but somehow always validates whatever I already believe. When an LLM produces correct code, that’s not engineering, it’s cosplay. It didn’t understand the problem, because understanding is defined as something only humans possess, especially after the fact.

Naturally, only senior developers truly code. Juniors shuffle syntax. Seniors channel wisdom. Architecture decisions emerge from lived experience, not from reading millions of examples and compressing patterns into a model. If an LLM produces the same decisions, it’s obviously cargo-culting seniority without having earned the right to say “this feels wrong” in a code review.

Any success is easy to dismiss. Data leakage. Prompt hacking. Cherry-picking. Hidden humans in the loop. And if none of those apply, then it “won’t work on a real codebase,” where “real” is defined as the one place the model hasn’t touched yet. This definition will be updated as needed.

Hallucinations still settle everything. One wrong answer means the whole system is fundamentally broken. Human mistakes, meanwhile, are just learning moments, context switches, or coffee shortages. This is not a double standard. It’s experience.

Jobs are obviously safe too. Software engineering is mostly communication, domain expertise, and navigating ambiguity. If the model starts doing those things, that still doesn’t count, because it doesn’t sit in meetings, complain about product managers, or feel existential dread during sprint planning.

So yes, the Erdos situation is resolved. Nothing new happened. No reasoning occurred. Progress remains hype. The trendline is imaginary. And any discomfort you feel is probably just social media, not the ground shifting under your feet.

[eru]

> This is a relief, honestly. A prior solution exists now, which means the model didn’t solve anything at all. It just regurgitated it from the internet, which we can retroactively assume contained the solution in spirit, if not in any searchable or known form. Mystery resolved.

Vs

> Interesting that in Terrance Tao's words: "though the new proof is still rather different from the literature proof)"

[catoc]

I firmly believe @threethirtytwo’s reply was not produced by an LLM

[johnfn]

I suspect this is AI generated, but it’s quite high quality, and doesn’t have any of the telltale signs that most AI generated content does. How did you generate this? It’s great.

[magnio]

Pity that HN's ability to detect sarcasm is as robust as that of a sentiment analysis model using keyword-matching.

[nurettin]

Why not plan for a future where a lot of non-trivial tasks are automated instead of living on the edge with all this anxiety?

[rixed]

Are you expecting people who can't detect self-dellusions to be able to detect sarcasm, or are you just being cruel?