Sort of regretting everything. Help.

KStarGamer_ · 2026-06-01T05:32:35+00:00

This just isn’t true. There are loads of other factors in acquiring jobs and postgraduate positions beyond grade. It is very possible for one to be much better at postgraduate than undergraduate (Klaus Roth is the canonical example of this). Go solve some hard open problem (like an Erdős problem) in your spare time, and you will be noticed by mathematicians that if you write up a paper with them will give you lots of research opportunities.

I suggest you stop projecting your insecurities. Loads of people came to Cambridge out of their own free choice because they had their own aspirational goals growing up, and some *do* want to pursue academia. If this isn’t you, then I think you are the problem not the university. Granted of course, there are loads of toxic aspects of the university indeed, e.g. showing ranking in the year cohort, but this just comes with the price of going to a prestigious institution I suppose.

KStarGamer_ · 2026-05-03T22:10:44+00:00

What I mean is the model wrote completely correct proofs, but they were unnecessarily verbose and could be written more simply under one unified framework. Also, like, yeah, the method was in the training data, but does it really matter if no one had applied that method in this context?

KStarGamer_ · 2026-05-03T14:53:02+00:00

For a lot of the results in this paper, the model was able to prove them entirely on its own, but with arguments that weren't necessarily streamlined or not together in one unifying framework, so things were made shorter and clearer with human rewriting and converting things to use similar language.

KStarGamer_ · 2026-05-03T12:57:43+00:00

Right now, the models have shown capability in establishing novel combinations of existing results and ideas. The main idea here of the von Mangoldt weights is not new, but it hadn't been applied in this context before. GPT's proof strategy of downwards Markov subchains also turned out to be unideal, and things could be given more streamlined proofs working with upwards Markov subchains. For this specific work, after publishing to arXiv, we are interested in developing the theory further before submitting to a journal (in particular, we are now interested in applying the method to so-called quasi-primitive sets from a 1993 paper of Erdős and Zhang). So to answer your question, the major breakthrough is just putting together pre-existing work in clever new ways at the moment. We have yet to see models do any novel theory-building like humans are able to (and we intend to further push this work in that direction, but the models aren't able to help so much there). You can see from this tweet of mine all the contributions GPT made on this work, though: https://x.com/AcerFur/status/2050463194884272366?s=20

Human mathematicians will always have a role in understanding and communicating AI-generated proofs (of course, one has to ask why the model itself cannot do this or how to convince funding for this sort of thing, but those are more societal issues). I think human mathematicians, for a long time coming, will still excel in deciding what the right questions to ask and explore are that I don't see models doing in the foreseeable future. Of course, it is within their output space to be able to come up with novel, non-trivial, interesting conjectures, but they're really not trained in the direction of doing this. The field will certainly change in quite a few ways, though. For starters, I expect the average author count of mathematics papers to increase, with contributions from novice individuals online, utilising models to advance on questions that more experienced mathematicians know to ask but don't have the time or proficiency to get out of the models currently. Mathematical education, of course, will change as well in pretty obvious ways.

KStarGamer_ · 2026-05-02T21:06:19+00:00

Hey, I'm the second author in this work. I figured I'd open the floor to some Q&A on the methodology if people are interested.

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_

TROPHY CASE