Erdos 281 solved with ChatGPT 5.2 Pro • Hacker News Board

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#151

Post by catoc » Sun, Jan 18, 2026, 9:07 AM UTC

mkarliner wrote: post #142

catoc wrote: post #111

Earlier quoted context omitted.

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

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.

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.

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#152

Post by _fizz_buzz_ » Sun, Jan 18, 2026, 9:10 AM UTC

eru wrote: post #93

dernett wrote: post #9

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.

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

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.

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#153

Post by sekai » Sun, Jan 18, 2026, 9:16 AM UTC

mikert89 wrote: post #7

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

> 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.

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#154

Post by hexaga » Sun, Jan 18, 2026, 9:26 AM UTC

efskap wrote: post #145

TZubiri wrote: post #118

Earlier quoted context omitted.

forgive the skepticism, but this translates directly to "we asked the model pretty please not to do it in the system prompt"

Would it really be infeasible to take a sample and do a search over an indexed training set? Maybe a bloom filter can be adapted

It's not the searching that's infeasible. Efficient algorithms for massive scale full text search are available.

The infeasibility is searching for the (unknown) set of translations that the LLM would put that data through. Even if you posit only basic symbolic LUT mappings in the weights (it's not), there's no good way to enumerate them anyway. The model might as well be a learned hash function that maintains semantic identity while utterly eradicating literal symbolic equivalence.

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#155

Post by baq » Sun, Jan 18, 2026, 9:28 AM UTC

cubefox wrote: post #144

MattGaiser wrote: post #131

Earlier quoted context omitted.

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.

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

You’re confusing immediately useful with eventually useful. Pure maths has found very practical applications over the millennia - unless you don’t consider it pure anymore, at which point you’re just moving goalposts.

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#156

Post by glemion43 » Sun, Jan 18, 2026, 9:32 AM UTC

rzmmm wrote: post #102

magneticnorth wrote: post #52

Earlier quoted context omitted.

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

The model has multiple layers of mechanisms to prevent carbon copy output of the training data.

Do you have a source for this?

Carbon copy would mean over fitting

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#157

Post by glemion43 » Sun, Jan 18, 2026, 9:33 AM UTC

ffsm8 wrote: post #139

TZubiri wrote: post #118

Earlier quoted context omitted.

forgive the skepticism, but this translates directly to "we asked the model pretty please not to do it in the system prompt"

It's mind boggling if you think about the fact they're essential "just" statistical models It really contextualizes the old wisdom of Pythagoras that everything can be represented as numbers / math is the ultimate truth

They are not just statistical models

They create concepts in latent space which is basically compression which forces this

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#158

Post by glemion43 » Sun, Jan 18, 2026, 9:35 AM UTC

cubefox wrote: post #117

xeeeeeeeeeeenu wrote: post #18

> 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...

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 nea…

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.

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#159

Post by cubefox » Sun, Jan 18, 2026, 9:46 AM UTC

baq wrote: post #155

cubefox wrote: post #144

Earlier quoted context omitted.

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

You’re confusing immediately useful with eventually useful. Pure maths has found very practical applications over the millennia - unless you don’t consider it pure anymore, at which point you’re just moving goalposts.

No, I'm not confusing that. Read the linked comment if you're interested.

Re: Erdos 281 solved with ChatGPT 5.2 Pro

#160

Post by xigoi » Sun, Jan 18, 2026, 9:52 AM UTC

Davidzheng wrote: post #135

krackers wrote: post #15

Earlier quoted context omitted.

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).

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.

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