erdosproblems

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...

> 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...

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

Also the very fact that https://github.com/teorth/erdosproblems/wiki/AI-contribution... exist totally change the landscape. Because it's public it's safe to assume it's part of the input dataset so from now on, how does one evaluate the pace of progress, in particular for non open source models?

You're thinking of a previous report from a month ago, #897 or #481, or the one from two weeks ago, #728. There's a new one from a week ago, #205, which is genuinely novel, although it is still a relatively "shallow" result. Terence Tao maintains a list [1] of AI attempts (successful and otherwise). #205 is currently the only success in section 1, the "full solution for which subsequent literature review did not find new relevant prior partial or full solutions" section - but it is in that section. As to speed, as far as I know the recent results are all due to GPT 5.2, which is barely a month old, or Aristotle, which is a system built on top of some frontier LLMs and which has only been accessible to the public for a month or two. I have seen multiple mathematicians report that GPT-5.2 is a major improvement in proof-writing, e.g. [2] [1

I don't think I quoted you out of context. In any case, Terence Tao and co. are doing wonderful work in this area. I'd encourage everyone to bookmark the following link: https://github.com/teorth/erdosproblems/wiki/AI-contribution... It's a rapidly evolving story and I expect H1 2026 to bring much clarity on this topic. Especially with upcoming model releases and more professional mathematicians taking an interest.

This is a great achievement for AI! I quickly read through the thread but found that Tao's page on Github to be easier to comprehend, https://github.com/teorth/erdosproblems/wiki/AI-contribution... It classifies the advancements based on the level of AI input. In particular, the entry in Table 1 related to the original post has both a green and yellow light, reflecting the skepticism from others.

For context, Terence Tao started a wiki page titled “AI contributions to Erdős problems”: https://github.com/teorth/erdosproblems/wiki/AI-contribution... (as mentioned in an earlier post https://mathstodon.xyz/@tao/115818402639190439) — even relative to when he started this page less than two weeks ago (Dec 31), the current result (for problem [728]) represents a milestone: it is the first green in Section 1 of that wiki page.