Back

Erdos 281 solved with ChatGPT 5.2 Pro

223 points11 hourstwitter.com
xeeeeeeeeeeenu9 hours ago

> 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...

nl9 hours ago

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!

TZubiri8 hours ago

Maybe it was in the training set.

magneticnorth8 hours ago

I think that was Tao's point, that the new proof was not just read out of the training set.

+3
rzmmm7 hours ago
cubefox7 hours ago

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.

jojobas2 hours ago

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

MattGaiser6 hours ago

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.

cubefox6 hours ago

The difference is that Claude Code actually solves practical problems, but pure (as opposed to applied) mathematics doesn't. Moreover, a lot of pure mathematics seems to be not just useless, but also without intrinsic epistemic value, unlike science. See https://news.ycombinator.com/item?id=46510353

jstanley6 hours ago

Applications for pure mathematics can't necessarily be known until the underlying mathematics is solved.

Just because we can't imagine applications today doesn't mean there won't be applications in the future which depend on discoveries that are made today.

teiferer5 hours ago

It's hard to know beforehand. Like with most foundational research.

My favorite example is number theory. Before cyptography came along it was pure math, an esoteric branch for just number nerds. defund Turns out, super applicable later on.

+1
baq5 hours ago
amazingman6 hours ago

It's unclear to me what point you are making.

glemion435 hours ago

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.

danielbln4 hours ago

The goal posts are strapped to skateboards these days, and the WD40 is applied to the wheels generously.

+1
sampullman2 hours ago
BoredPositron3 hours ago

You can just wait and verify instead of the publishing, redacting cycles of the last year. It's embarrassing.

threethirtytwo9 hours ago

[flagged]

magnio8 hours ago

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

furyofantares8 hours ago

The problem is more that it's an LLM-generated comment that's about 20x as long as it needed to be to get the point across.

+1
cubefox7 hours ago
+2
threethirtytwo8 hours ago
catlifeonmars7 hours ago

That’s just the internet. Detecting sarcasm requires a lot of context external to the content of any text. In person some of that is mitigated by intonation, facial expressions, etc. Typically it also requires that the the reader is a native speaker of the language or at least extremely proficient.

catoc7 hours ago

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

mkarliner6 hours ago

regardless of if this text was written by an LLM or a human, it is still slop,with a human behind it just trying to wind people up . If there is a valid point to be made , it should be made, briefly.

catoc5 hours ago

If the point was triggering a reply, the length and sarcasm certainly worked.

I agree brevity is always preferred. Making a good point while keeping it brief is much harder than rambling on.

But length is just a measure, quality determines if I keep reading. If a comment is too long, I won’t finish reading it. If I kept reading, it wasn’t too long.

rixed7 hours ago

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

eru7 hours ago

> 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)"

johnfn8 hours ago

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.

AstroBen8 hours ago

Their comments are full of "it's not x, it's y" over and over. Short pithy sentences. I'm quite confident it's AI written, maybe with a more detailed prompt than the average

I guess this is the end of the human internet

prussia7 hours ago

To give them the benefit of the doubt, people who talk to AI too much probably start mimicking its style.

+2
4k93n27 hours ago
threethirtytwo8 hours ago

Your intuition on AI is out of date by about 6 months. Those telltale signs no longer exist.

It wasn't AI generated. But if it was, there is currently no way for anyone to tell the difference.

catlifeonmars7 hours ago

I’m confused by this. I still see this kind of phrasing in LLM generated content, even as recent as last week (using Gemini, if that matters). Are you saying that LLMs do not generate text like this, or that it’s now possible to get text that doesn’t contain the telltale “its not X, it’s Y”?

+1
comp_throw78 hours ago
+3
velox_neb8 hours ago
CamperBob28 hours ago

(edit: removed duplicate comment from above, not sure how that happened)

undeveloper8 hours ago

the poster is in fact being very sarcastic. arguing in favor of emergent reasoning does in fact make sense

threethirtytwo8 hours ago

It's a formal sarcasm piece.

CamperBob28 hours ago

It's bizarre. The same account was previously arguing in favor of emergent reasoning abilities in another thread ( https://news.ycombinator.com/item?id=46453084 ) -- I voted it up, in fact! Turing test failed, I guess.

(edit: fixed link)

+1
threethirtytwo8 hours ago
habinero8 hours ago

We need a name for the much more trivial version of the Turing test that replaces "human" with "weird dude with rambling ideas he clearly thinks are very deep"

I'm pretty sure it's like "can it run DOOM" and someone could make an LLM that passes this that runs on an pregnancy test

nurettin8 hours ago

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?

threethirtytwo8 hours ago

[flagged]

undeveloper8 hours ago

come out of the irony layer for a second -- what do you believe about LLMs?

jorvi6 hours ago

I mean.. LLMs have hit a pretty hard wall a while ago, with the only solution being throwing monstrous compute at eking out the remaining few percent improvement (real world, not benchmarks). That's not to mention hallucinations / false paths being a foundational problem.

LLMs will continue to get slightly better in the next few years, but mainly a lot more efficient. Which will also mean better and better local models. And grounding might get better, but that just means less wrong answers, not better right answers.

So no need for doomerism. The people saying LLMs are a few years away from eating the world are either in on the con or unaware.

77773322158 hours ago

If all of it is going away and you should deny reality, what does everything else you wrote even mean?

habinero8 hours ago

Yes, it is simply impossible that anyone could look at things and do your own evaluations and come to a different, much more skeptical conclusion.

The only possible explanation is people say things they don't believe out of FUD. Literally the only one.

doctoboggan9 hours ago

Can anyone give a little more color on the nature of Erdos problems? Are these problems that many mathematicians have spend years tackling with no result? Or do some of the problems evade scrutiny and go un-attempted for most of the time?

EDIT: After reading a link someone else posted to Terrance Tao's wiki page, he has a paragraph that somewhat answers this question:

> Erdős problems vary widely in difficulty (by several orders of magnitude), with a core of very interesting, but extremely difficult problems at one end of the spectrum, and a "long tail" of under-explored problems at the other, many of which are "low hanging fruit" that are very suitable for being attacked by current AI tools. Unfortunately, it is hard to tell in advance which category a given problem falls into, short of an expert literature review. (However, if an Erdős problem is only stated once in the literature, and there is scant record of any followup work on the problem, this suggests that the problem may be of the second category.)

from here: https://github.com/teorth/erdosproblems/wiki/AI-contribution...

QuesnayJr6 hours ago

Erdos was an incredibly prolific mathematician, and one of his quirks is that he liked to collect open problems and state new open problems as a challenge to the field. Many of the problems he attached bounties to, from $5 to $10,000.

The problems are a pretty good metric for AI, because the easiest ones at least meet the bar of "a top mathematician didn't know how to solve this off the top of his head" and the hardest ones are major open problems. As AI progresses, we will see it slowly climb the difficulty ladder.

pessimist10 hours ago

From Terry Tao's comments in the thread:

"Very nice! ... actually the thing that impresses me more than the proof method is the avoidance of errors, such as making mistakes with interchanges of limits or quantifiers (which is the main pitfall to avoid here). Previous generations of LLMs would almost certainly have fumbled these delicate issues.

...

I am going ahead and placing this result on the wiki as a Section 1 result (perhaps the most unambiguous instance of such, to date)"

The pace of change in math is going to be something to watch closely. Many minor theorems will fall. Next major milestone: Can LLMs generate useful abstractions?

radioactivist9 hours ago

Seems like the someone dug something up from the literature on this problem (see top comment on the erdosproblems.com thread)

"On following the references, it seems that the result in fact follows (after applying Rogers' theorem) from a 1936 paper of Davenport and Erdos (!), which proves the second result you mention. ... In the meantime, I am moving this problem to Section 2 on the wiki (though the new proof is still rather different from the literature proof)."

dust427 hours ago

Personally, I'd prefer if the AI models would start with a proof of their own statements. Time and again, SOTA frontier models told me: "Now you have 100% correct code ready for production in enterprise quality." Then I run it and it crashes. Or maybe the AI is just being tongue-in-cheek?

Point in case: I just wanted to give z.ai a try and buy some credits. I used Firefox with uBlock and the payment didn't go through. I tried again with Chrome and no adblock, but now there is an error: "Payment Failed: p.confirmCardPayment is not a function." The irony is, that this is certainly vibe-coded with z.ai which tries to sell me how good they are but then not being able to conclude the sale.

And we will get lots more of this in the future. LLMs are a fantastic new technology, but even more fantastically over-hyped.

becquerel6 hours ago

You get AIs to prove their code is correct in precisely the same ways you get humans to prove their code is correct. You make them demonstrate it through tests or evidence (screenshots, logs of successful runs).

sequin9 hours ago

FWIW, I just gave Deepseek the same prompt and it solved it too (much faster than the 41m of ChatGPT). I then gave both proofs to Opus and it confirmed their equivalence.

The answer is yes. Assume, for the sake of contradiction, that there exists an \(\epsilon > 0\) such that for every \(k\), there exists a choice of congruence classes \(a_1^{(k)}, \dots, a_k^{(k)}\) for which the set of integers not covered by the first \(k\) congruences has density at least \(\epsilon\).

For each \(k\), let \(F_k\) be the set of all infinite sequences of residues \((a_i)_{i=1}^\infty\) such that the uncovered set from the first \(k\) congruences has density at least \(\epsilon\). Each \(F_k\) is nonempty (by assumption) and closed in the product topology (since it depends only on the first \(k\) coordinates). Moreover, \(F_{k+1} \subseteq F_k\) because adding a congruence can only reduce the uncovered set. By the compactness of the product of finite sets, \(\bigcap_{k \ge 1} F_k\) is nonempty.

Choose an infinite sequence \((a_i) \in \bigcap_{k \ge 1} F_k\). For this sequence, let \(U_k\) be the set of integers not covered by the first \(k\) congruences, and let \(d_k\) be the density of \(U_k\). Then \(d_k \ge \epsilon\) for all \(k\). Since \(U_{k+1} \subseteq U_k\), the sets \(U_k\) are decreasing and periodic, and their intersection \(U = \bigcap_{k \ge 1} U_k\) has density \(d = \lim_{k \to \infty} d_k \ge \epsilon\). However, by hypothesis, for any choice of residues, the uncovered set has density \(0\), a contradiction.

Therefore, for every \(\epsilon > 0\), there exists a \(k\) such that for every choice of congruence classes \(a_i\), the density of integers not covered by the first \(k\) congruences is less than \(\epsilon\).

\boxed{\text{Yes}}

CGamesPlay8 hours ago

> I then gave both proofs to Opus and it confirmed their equivalence.

You could have just rubber-stamped it yourself, for all the mathematical rigor it holds. The devil is in the details, and the smallest problem unravels the whole proof.

yosefk7 hours ago

How dare you question the rigor of the venerable LLM peer review process! These are some of the most esteemed LLMs we are talking about here.

Davidzheng6 hours ago

"Since \(U_{k+1} \subseteq U_k\), the sets \(U_k\) are decreasing and periodic, and their intersection \(U = \bigcap_{k \ge 1} U_k\) has density \(d = \lim_{k \to \infty} d_k \ge \epsilon\)."

Is this enough? Let $U_k$ be the set of integers such that their remainder mod 6^n is greater or equal to 2^n for all 1<n<k. Density of each $U_k$ is more than 1/2 I think but not the intersection (empty) right?

Paracompact4 hours ago

Indeed. Your sets are decreasing periodic of density always greater than the product from k=1 to infinity of (1-(1/3)^k), which is about 0.56, yet their intersection is null.

This would all be a fairly trivial exercise in diagonalization if such a lemma as implied by Deepseek existed.

(Edit: The bounding I suggested may not be precise at each level, but it is asymptotically the limit of the sequence of densities, so up to some epsilon it demonstrates the desired counterexample.)

Klover8 hours ago

Here's kimi-k2-thinking with the reasoning block included: https://www.kimi.com/share/19bcfe2e-d9a2-81fe-8000-00002163c...

nsoonhui8 hours ago

I am not familiar with the field, but any chance that the deepseek is just memorizing the existing solution? Or different.

https://news.ycombinator.com/item?id=46664976

utopiah8 hours ago

Sure but if so wouldn't ChatGPT 5.2 Pro also "just memorizing the existing solution?"?

nsoonhui8 hours ago

No it's not, you can refer to my link and subsequent discussion.

+1
utopiah8 hours ago
logicchains6 hours ago

Opus isn't a good choice for anything math-related; it's worse at math than the latest ChatGPT and Gemini Pro.

amluto9 hours ago

I find it interesting that, as someone utterly unfamiliar with ergodic theory, Dini’s theorem, etc, I find Deepseek’s proof somewhat comprehensible, whereas I do not find GPT-5.2’s proof comprehensible at all. I suspect that I’d need to delve into the terminology in the GPT proof if I tried to verify Deepseek’s, so maybe GPT’s is being more straightforward about the underlying theory it relies on?

carbocation10 hours ago

The erdosproblems thread itself contains comments from Terence Tao: https://www.erdosproblems.com/forum/thread/281

Eufrat5 hours ago

There was a post about Erdős 728 being solved with Harmonic’s Aristotle a little over a week ago [1] and that seemed like a good example of using state-of-the-art AI tech to help increase velocity in this space.

I’m not sure what this proves. I dumped a question into ChatGPT 5.2 and it produced a correct response after almost an hour [2]?

Okay? Is it repeatable? Why did it come up with this solution? How did it come up with the connections in its reasoning? I get that it looks correct and Tao’s approval definitely lends credibility that it is a valid solution, but what exactly is it that we’ve established here? That the corpus that ChatGPT 5.2 was trained on is better tuned for pure math?

I’m just confused what one is supposed to take away from this.

[1] https://news.ycombinator.com/item?id=46560445

[2] https://chatgpt.com/share/696ac45b-70d8-8003-9ca4-320151e081...

redbluered10 hours ago

Has anyone verified this?

I've "solved" many math problems with LLMs, with LLMs giving full confidence in subtly or significantly incorrect solutions.

I'm very curious here. The Open AI memory orders and claims about capacity limits restricting access to better models are interesting too.

bpodgursky10 hours ago

Terence Tao gave it the thumbs up. I don't think you're going to do better than that.

bparsons9 hours ago

It's already been walked back.

energy1239 hours ago

Not in the sense of being a "subtly or significantly incorrect solution".

ashleyn9 hours ago

I guess the first question I have is if these problems solved by LLMs are just low-hanging fruit that human researchers either didn't get around to or show much interest in - or if there's some actual beef here to the idea that LLMs can independently conduct original research and solve hard problems.

utopiah8 hours ago

That's the first warning from the wiki : <<Erdős problems vary widely in difficulty (by several orders of magnitude), with a core of very interesting, but extremely difficult problems at one end of the spectrum, and a "long tail" of under-explored problems at the other, many of which are "low hanging fruit" that are very suitable for being attacked by current AI tools.>> https://github.com/teorth/erdosproblems/wiki/AI-contribution...

dyauspitr9 hours ago

There is still value on letting these LLMs loose on the periphery and knocking out all the low hanging fruit humanity hasn’t had the time to get around to. Also, I don’t know this, but if it is a problem on Erdos I presume people have tried to solve it atleast a little bit before it makes it to the list.

utopiah8 hours ago

Is there though? If they are "solved" (as in the tickbox mark them as such, through a validation process, e.g. another model confirming, formal proof passing, etc) but there is no human actually learning from them, what's the benefit? Completing a list?

I believe the ones that are NOT studied are precisely because they are seen as uninteresting. Even if they were to be solved in an interesting way, if nobody sees the proof because they are just too many and they are again not considered valuable then I don't see what is gained.

ogogmad2 hours ago

You don't see value in having a cheap way to detect when a problem is easy or hard? That would seem unimaginative.

zkmon2 hours ago

I wonder if they tried Gemini. I think Gemini could have done better, as seen from my experiences with GPT and Gemini models on some simple geometry problems.

energy1237 hours ago

A surprising % of these LLM proofs are coming from amateurs.

One wonders if some professional mathematicians are instead choosing to publish LLM proofs without attribution for career purposes.

kristopolous7 hours ago

It's probably from the perennial observation

"This LLM is kinda dumb in the thing I'm an expert in"

fatherwavelet4 hours ago

This is just not true at this point but believe whatever you want to believe.

fatata1234 hours ago

[dead]

Davidzheng6 hours ago

I'm actually not sure what the right attribution method would be. I'd lean towards single line on acknowledgements? Because you can use it for example @ every lemma during brainstorming but it's unclear the right convention is to thank it at every lemma...

Anecdotally, I, as a math postdoc, think that GPT 5.2 is much stronger qualitatively than anything else I've used. Its rate of hallucinations is low enough that I don't feel like the default assumption of any solution is that it is trying to hide a mistake somewhere. Compared with Gemini 3 whose failure mode when it can't solve something is always to pretend it has a solution by "lying"/ omitting steps/making up theorems etc... GPT 5.2 usually fails gracefully and when it makes a mistake it more often than not can admit it when pointed out.

a_tartaruga9 hours ago

Out of curiosity why has the LLM math solving community been focused on the Erdos problems over other open problems? Are they of a certain nature where we would expect LLMs to be especially good at solving them?

krackers9 hours ago

I guess they are at a difficulty where it's not too hard (unlike millennium prize problems), is fairly tightly scoped (unlike open ended research), and has some gravitas (so it's not some obscure theorem that's only unproven because of it's lack of noteworthiness).

Davidzheng6 hours ago

I actually don't think the reason is that they are easier than other open math problems. I think it's more that they are "elementary" in the sense that the problems usually don't require a huge amount of domain knowledge to state.

xigoi5 hours ago

The Collatz conjecture can be stated using basic arithmetic, yet LLMs have not been able to solve it.

Davidzheng5 hours ago

I agree it's easier than Collatz. I just mean I am not sure it's much easier than many currently open questions which are less famous but need more machinery.

_fizz_buzz_2 hours ago

That is also one of the hardest problems.

becquerel6 hours ago

People like checking items off of lists.

charmpic4 hours ago

I'm looking forward to chatgpt 5.3pro. I also use chatgpt 5.2pro for various program consultations. It's been very helpful.

vercaemert3 hours ago

I was hoping there'd be more discussion about the model itself. I find the last couple of generations of Pro models fascinating.

Personally, I've been applying them to hard OCR problems. Many varied languages concurrently, wildly varying page structure, and poor scan quality; my dataset has all of these things. The models take 30 minutes a page, but the accuracy is basically 100% (it'll still striggle with perfectly-placed bits of mold). The next best model (Google's flagship) rests closer to 80%.

I'll be VERY intrigued to see what the next 2, 5, 10 years does to the price of this level of model.

energy1232 hours ago

We're eventually going to get it at cerebras inference latency. It's going to be wild.

niemandhier7 hours ago

Is there explainability research for this type of model application? E.g. a sparse auto encoder or something similar but more modern.

I would love to know which concepts are active in the deeper layers of the model while generating the solution.

Is there a concept of “epsilon” or “delta”?

What are their projections on each other?

supermatt3 hours ago

What does "solved with" mean? The author claims "I've solved", so did the author solve it or GPT?

klohto3 hours ago

When you use a calculator, did you really solve it or was it the calculator?

supermatt3 hours ago

With a calculator I supply the arithmetic. It just executes it with no reasoning so im the solver. I can do the same with an LLM and still be the solver as long as it just follows my direction. Or I can give it a problem and let it reason and generate the arithmetic itself, in which case the LLM is effectively the solver. Thats why saying "I've solved X using only GPT" is ambiguous.

But thanks for the downvote in addition to your useless comment.

dernett9 hours ago

This is crazy. It's clear that these models don't have human intelligence, but it's undeniable at this point that they have _some_ form of intelligence.

brendyn9 hours ago

If LLMs weren't created by us but where something discovered in another species' behaviour it would be 100% labelled intelligence

te00062 hours ago

Yes, same for the case where the technology would have been found embodied in machinery aboard a crashed UFO.

qudat9 hours ago

My take is that a huge part of human intelligence is pattern matching. We just didn’t understand how much multidimensional geometry influenced our matches

keeda9 hours ago

Yes, it could be that intelligence is essentially a sophisticated form of recursive, brute force pattern matching.

I'm beginning to think the Bitter Lesson applies to organic intelligence as well, because basic pattern matching can be implemented relatively simply using very basic mathematical operations like multiply and accumulate, and so it can scale with massive parallelization of relatively simple building blocks.

bob10297 hours ago

Intelligence is almost certainly a fundamentally recursive process.

The ability to think about your own thinking over and over as deeply as needed is where all the magic happens. Counterfactual reasoning occurs every time you pop a mental stack frame. By augmenting our stack with external tools (paper, computers, etc.), we can extend this process as far as it needs to go.

LLMs start to look a lot more capable when you put them into recursive loops with feedback from the environment. A trillion tokens worth of "what if..." can be expended without touching a single token in the caller's context. This can happen at every level as many times as needed if we're using proper recursive machinery. The theoretical scaling around this is extremely favorable.

sdwr9 hours ago

I don't think it's accurate to describe LLMs as pattern matching. Prediction is the mechanism they use to ingest and output information, and they end up with a (relatively) deep model of the world under the hood.

visarga8 hours ago

The "pattern matching" perspective is true if you zoom in close enough, just like "protein reactions in water" is true for brains. But if you zoom out you see both humans and LLMs interact with external environments which provide opportunity for novel exploration. The true source of originality is not inside but in the environment. Making it be all about the model inside is a mistake, what matters more than the model is the data loop and solution space being explored.

D-Machine9 hours ago

"Pattern matching" is not sufficiently specified here for us to say if LLMs do pattern matching or not. E.g. we can say that an LLM predicts the next token because that token (or rather, its embedding) is the best "match" to the previous tokens, which form a path ("pattern") in embedding space. In this sense LLMs are most definitely pattern matching. Under other formulations of the term, they may not be (e.g. when pattern matching refers to abstraction or abstracting to actual logical patterns, rather than strictly semantic patterns).

keeda9 hours ago

Yes, the world model building is achieved via pattern matching and happens during ingestion and training, but that is also part of the intelligence.

DrewADesign9 hours ago

Which is even more true for humans.

csomar7 hours ago

Intelligence is hallucination that happens to produce useful results in the real world.

eru7 hours ago

Well, Alpha Go and Stockfish can beat you at their games. Why shouldn't these models beat us at math proofs?

_fizz_buzz_5 hours ago

Chess and Go have very restrictive rules. It seems a lot more obvious to me why a computer can beat a human at it. They have a huge advantage just by being able to calculate very deep lines in a very short time. I actually find it impressive for how long humans were able to beat computers at go. Math proofs seem a lot more open ended to me.

thfuran6 hours ago

Alpha go and stockfish were specifically designed and trained to win at those games.

Davidzheng6 hours ago

And we can train models specifically at math proofs? I think only difference is that math is bigger....

threethirtytwo8 hours ago

I don't think they will ever have human intelligence. It will always be an alien intelligence.

But I think the trend line unmistakably points to a future where it can be MORE intelligent than a human in exactly the colloquial way we define "more intelligent"

The fact that one of the greatest mathematicians alive has a page and is seriously bench marking this shows how likely he believes this can happen.

xyzsparetimexyz1 hour ago

Yes it is intelligent, but so what? Its not conscious, sentient or sapient. It's a pattern matching chinese room.

altmanaltman9 hours ago

Depends on what you mean by intelligence, human intelligence and human

ekianjo9 hours ago

It's pattern matching. Which is actually what we measure in IQ tests, just saying.

jadenpeterson9 hours ago

There's some nuance. IQ tests measure pattern matching and, in an underlying way, other facets of intelligence - memory, for example. How well can an LLM 'remember' a thing? Sometimes Claude will perform compaction when its context window reaches 200k "tokens" then it seems a little colder to me, but maybe that's just my imagination. I'm kind of a "power user".

rurban9 hours ago

I call it matching. Pattern matching had a different meaning.

ekianjo8 hours ago

what are you referring to? LLMs are neural networks at their core and the most simple versions of neural networks are all about reproducing patterns observed during training

rurban7 hours ago

You need to understand the difference between general matching and pattern matching. Maybe should have read more older AI books. A LLM is a general fuzzy matcher. A pattern matcher is an exact matcher using an abstract language, the "pattern". A general matcher uses a distance function instead, no pattern needed.

Ie you want to find a subimage in a big image, possibly rotated, scaled, tilted, distorted, with noise. You cannot do that with a pattern matcher, but you can do that with a matcher, such as a fuzzy matcher, a LLM.

You want to find a go position on a go board. A LLM is perfect for that, because you don't need to come up with a special language to describe go positions (older chess programs did that), you just train the model if that position is good or bad, and this can be fully automated via existing literature and later by playing against itself. You train the matcher not via patterns but a function (win or loose).

TZubiri8 hours ago

As someone who doesn't understand this shit, and how it's always the experts who fiddle the LLMs to get good outputs, it feels natural to attribute the intelligence to the operator (or the training set), rather than the LLM itself.

wewxjfq6 hours ago

The LLMs that take 10 attempts to un-zero-width a <div>, telling me that every single change totally fixed the problem, are cracking the hardest math problems again.

mikert899 hours ago

I have 15 years of software engineering experience across some top companies. I truly believe that ai will far surpass human beings at coding, and more broadly logic work. We are very close

anonzzzies9 hours ago

HN will be the last place to admit it; people here seem to be holding out with the vague 'I tried it and it came up with crap'. While many of us are shipping software without touching (much) code anymore. I have written code for over 40 years and this is nothing like no-code or whatever 'replacing programmers' before, this is clearly different judging from the people who cannot code with a gun to their heads but still are shipping apps: it does not really matter if anyone believes me or not. I am making more money than ever with fewer people than ever delivering more than ever.

We are very close.

(by the way; I like writing code and I still do for fun)

utopiah8 hours ago

Both can be correct : you might be making a lot of money using the latest tools while others who work on very different problems have tried the same tools and it's just not good enough for them.

The ability to make money proves you found a good market, it doesn't prove that the new tools are useful to others.

fc417fc8028 hours ago

> holding out with the vague 'I tried it and it came up with crap'

Isn't that a perfectly reasonable metric? The topic has been dominated by hype for at least the past 5 if not 10 years. So when you encounter the latest in a long line of "the future is here the sky is falling" claims, where every past claim to date has been wrong, it's natural to try for yourself, observe a poor result, and report back "nope, just more BS as usual".

If the hyped future does ever arrive then anyone trying for themselves will get a workable result. It will be trivially easy to demonstrate that naysayers are full of shit. That does not currently appear to be the case.

danielbln8 hours ago

What topic are you referring to? ChatGPT release was just over 3 years ago. 5 years ago we had basic non-instruct GPT-3.

+1
fc417fc8028 hours ago
visarga8 hours ago

But the trend line is less ambiguous, models got better year over year, much much better.

+1
fc417fc8028 hours ago
sekai5 hours ago

> I have 15 years of software engineering experience across some top companies. I truly believe that ai will far surpass human beings at coding, and more broadly logic work. We are very close

Coding was never the hard part of software development.

pelorat4 hours ago

Getting the architecture mostly right, so it's easy to maintain and modify in the future is IMO hard part, but I find that this is where AI shines. I have 20 years of SWE experience (professional) and (10 hobby) and most of my AI use is for architecture and scaffolding first, code second.

daxfohl9 hours ago

They already do. What they suck at is common sense. Unfortunately good software requires both.

anonzzzies9 hours ago

Most people also suck at common sense, including most programmers, hence most programmers do not write good software to begin with.

523-asf19 hours ago

Even a 20 year old Markov chain could produce this banality.

marktl9 hours ago

Or is it fortunate (for a short period at least).

523-asf19 hours ago

Gotta make sure that the investors read this message in an Erdos thread.

AtlasBarfed8 hours ago

Is this comment written by AI?

user39393829 hours ago

They can only code to specification which is where even teams of humans get lost. Without much smarter architecture for AI (LLMs as is are a joke) that needle isn’t going to move.

danielbln3 hours ago

Real HN comment right here. "LLMs are a joke" - maybe don't drink the anti-hype kool aid, you'll blind yourself to the capability space that's out there, even if it's not AGI or whatever.

renewiltord7 hours ago

It’s funny. in some kind of twisted variant of Cunningham’s Law we have:

> the best way to find a previous proof of a seemingly open problem on the internet is not to ask for it; it's to post a new proof

IAmGraydon9 hours ago

This is showing as unresolved here, so I'm assuming something was retracted.

https://mehmetmars7.github.io/Erdosproblems-llm-hunter/probl...

nl8 hours ago

I think that just hasn't been updated.

logicallee7 hours ago

how did they do it? Was a human using the chat interface? Did they just type out the problem and immediately on the first reply received a complete solution (one-shot) or what was the human's role? What was ChatGPT's thinking time?

logicallee7 hours ago

very interesting. ChatGPT reasoned for 41 minutes about it! Also, this was one-shot - i.e. ChatGPT produced its complete proof with a single prompt and no more replies by the human, (rather than a chat where the human further guided it.)

magicalist8 hours ago

Funny seeing silicon valley bros commenting "you're on fire!" to Neel when it appears he copied and pasted the problem verbatim into chatGPT and it did literally all the other work here

https://chatgpt.com/share/696ac45b-70d8-8003-9ca4-320151e081...

jrflowers9 hours ago

Narrator: The solution had already appeared several times in the training data

ares62310 hours ago

This must be what it feels like to be a CEO and someone tells me they solved coding.

beders7 hours ago

Has anyone confirmed the solution is not in the training data? Otherwise it is just a bit information retrieval LLM style. No intelligence necessary.