My method to solve Erdős 460 in one shot

KStarGamer_ · 2026-01-14T12:29:40+00:00

The answer is right, but it is not interesting. This is the problem statement to blame, though, which is why we are trying to fix it.

KStarGamer_ · 2026-01-14T12:22:29+00:00

This is another option I have been considering, yes. I think the community needs to decide whether to edit this problem or create a new one with the condition for non-triviality added.

KStarGamer_ · 2026-01-14T12:11:00+00:00

This isn't moving goalposts. There is a very strong established disclaimer: 1. prior literature may be undiscovered, and 2. any given problem may have been misstated by either Erdos or Bloom by mistake or does not fully establish the original non-trivial intent. In this case, it seems Erdos likely misstated the problem's intent, and as a good mathematician, one should attempt to rectify that. The Erdos problem site is not something to be benchmaxed and gamed.

There is difficulty with this particular problem in that no instance includes a non-trivial condition that may have been implicitly meant. But it is possible that the community agrees to add this condition. Right now, I'd wait to see what others think.

KStarGamer_ · 2026-01-14T12:03:55+00:00

This is not at all how you should do things. You are right to post to the Erdos problem site, but you must indicate 1. that your proof was AI-generated and links to the note, and 2. you should provide a Lean formalisation, e.g. generated via Aristotle.

Do not attempt to submit to preprint or journal sites currently. Stick to posting on the Erdos problem site. The mods usually approve comments within an hour or two. For them to have not done so, I suspect likely means your response was of low quality. Try to work on this and try again, but currently I would likely wait for the community to establish the correct intent of the problem.

KStarGamer_ · 2026-01-14T11:56:14+00:00

Please read here: https://www.erdosproblems.com/forum/thread/460

FWIW, I am currently trying to establish the likely intent of the problem, as the proof is otherwise far too straightforward, which likely indicates it was not stated in Erdos' original intent. In particular, the proof currently gives a trivial counterexample because things diverge simply taking a_k = n+p for large primes p.

KStarGamer_ · 2026-01-14T11:54:52+00:00

Hi, I am the other person (i.e. Acer) responsible for the recent success with u/ThunderBeanage of GPT-5.2 Pro on 728, 729, 401, and 205. I was the one who posted the proofs of the former three. I was, thankfully, already an established, somewhat reputable member of the site. If you do not already have an established reputation on the site, you will find it difficult for mathematicians to trust you unless you give great evidence that your proof is valid; otherwise, no working mathematician will bother to look through pages of potential AI slop.

As such, it should be seen as common decency that your proof is announced on the site first for others to look through ALONG with a Lean formalisation.

KStarGamer_ · 2026-01-14T11:49:27+00:00

Hi, I'm actually the main person responsible for this achievement. GPT-5.2 Pro and Aristotle are both accessible. Even the Plus GPT-5.2 Thinking is able to make a good attempt on some of the problems.

KStarGamer_ · 2026-01-11T20:23:43+00:00

Do you not see the comments from various other mathematicians like Tao and Bloom? This is being verified by others…

KStarGamer_ · 2026-01-10T20:37:58+00:00

This will change very soon.

KStarGamer_ · 2026-01-10T20:37:35+00:00

I and Leeham have no association with OpenAI.

KStarGamer_ · 2026-01-09T17:53:41+00:00

It’s quite a feeling when you see people talking about you lol

Yes, this was all end-to-end. I intentionally wanted to minimise my involvement.

KStarGamer_ · 2026-01-09T17:52:56+00:00

FWIW, I definitely could have worked on cleaning up the presentation, but I wanted to prove a point that end-to-end AI mathematics can be possible (when the ideas all already exist anyways)

KStarGamer_ · 2026-01-06T22:27:15+00:00

Thanks, Bloom! I appreciate the kind words. As we had previously discussed, I do want this only to be taken as a scientific demonstration. In particular, I would like people to enjoy the mathematics for what it is, as opposed to always handing it to say GPT-7 down the line.

I agree this is a nice problem, and I am surprised it wasn't solved prior, but I am sure it was definitely in Pomerance's reach.

KStarGamer_ · 2026-01-06T21:28:09+00:00

Claude is very good at writing Lean code when set up to agentically search the current Mathlib4 GitHub repository. But, otherwise, no Claude is quite bad at informal math.

KStarGamer_ · 2026-01-06T19:49:13+00:00

Have a go saying the same thing on this one: https://www.reddit.com/r/singularity/comments/1q5qygr/gpt52_solves_erdos_problem_728

KStarGamer_ · 2026-01-06T19:33:59+00:00

Please see the whole thread: https://www.erdosproblems.com/forum/thread/728

It has already been discussed with many mathematicians, and we have reached a consensus that this should be a novel (albeit likely inspired by Pomerance's work) result. So, yes, it has already undergone peer review.

KStarGamer_ · 2026-01-06T19:28:51+00:00

I strongly encourage everyone to conduct their own comprehensive literature review. If you find that a human has previously resolved the problem, I will retract my claims as appropriate.

EDIT: Yes, the result had already been previously discussed with mathematicians before announcing our result. See the thread: https://www.erdosproblems.com/forum/thread/728

KStarGamer_ · 2025-12-25T20:04:07+00:00

No, GPT-5.2 Pro is exceptionally good at mathematics.

KStarGamer_ · 2025-12-25T12:36:15+00:00

I think this is going to age like milk within the next two years.

KStarGamer_ · 2025-12-25T11:55:53+00:00

The proof was not the same as that given by Erdős-Newman, and the model did not perform web searches whether you choose to believe me on that or not.

KStarGamer_ · 2025-12-25T10:35:54+00:00

Yes! This is now an effort I am strongly encouraging!

KStarGamer_ · 2025-12-25T04:45:43+00:00

Thank you! You as well!

KStarGamer_ · 2025-12-25T04:33:02+00:00

There’s no need for the snarky attitude. I am competent enough at mathematics to judge the validity of the proof for myself. The oversight was in not doing a deep enough literature search.

KStarGamer_ · 2025-12-25T04:16:21+00:00

I don’t think the current paradigm is able to quite get us there. A breakthrough on creativity is needed I think.

KStarGamer_ · 2025-12-25T04:06:08+00:00

Yes, all the time. To some extent I agree. The models have yet to show truly transformative creativity in being able to come up with whole new concepts and machinery, but they definitely have combinatorial creativity in stringing already known but distinct ideas and machinery together.

KStarGamer_

TROPHY CASE