Neel Somani, a quant-turned-startup-founder, fed Erdős Problem #281 into GPT-5.2 Pro on January 17th and got back a working proof using ergodic theory. Terence Tao verified it within a day and called it "perhaps the most unambiguous instance" of AI solving an open math problem. That assessment stood for about a day before someone dug up an old reference.
The solution is real, to be clear. GPT-5.2 produced a proof that works, using Haar measure on profinite integers and the Birkhoff ergodic theorem. Not the kind of tools Erdős typically reached for. Tao noted the approach was "rather different" from anything in the literature he could find.
Then came the literature
A forum user named KoishiChan started digging through old references. What they found: a 1966 book by Halberstam and Roth contains Rogers' theorem, which combined with a 1936 paper by Davenport and Erdős pretty much solves the problem. Davenport and Erdős. As in, Paul Erdős himself.
Tao's reaction in the forum thread: "Now I am really puzzled, because Erdős would certainly have known both of these facts in 1980."
How do you pose an open problem that you already solved 44 years earlier? Tao speculates maybe someone mentioned the solution at a cocktail party and it never got written up. Or maybe Erdős just didn't connect the dots between his own results. The man did publish more papers than anyone in math history, so losing track of a few wouldn't be shocking.
The pattern keeps repeating
This makes the fourth Erdős problem GPT-5.2 has gotten credit for in January. Problems #728, #729, and #397 fell in the first week of the month. But there's a recurring issue: what counts as "solved by AI" versus "AI found existing literature" versus "AI produced novel proof" keeps getting muddier.
The Tao wiki on GitHub tracks all this. Problem #281 just got moved from Section 1 (novel methods) to Section 2 (prior literature found). The wiki now shows the answer existed in Davenport-Erdős 1936 plus Rogers' theorem from Halberstam-Roth 1966.
Eight problems have seen meaningful autonomous AI progress according to Tao's count. Six more where AI located and built on previous research. But a new database tracking all attempts shows actual success rates around 1-2%, clustered heavily around the easier problems.
Why Tao isn't celebrating
Tao has been consistent about tempering expectations. These are, in his words, the "lowest hanging fruit." Problems where nobody really tried. His Mastodon posts lay it out: the more AI involvement in a solution, the simpler that solution tends to be. Selection effect. AI scales well for systematic sweeps of obscure problems, which means it's good at picking off exactly the ones humans never bothered with.
GPT-5.2 scores 77% on competition-level math. It scores 25% on open-ended research problems. That 52-point gap is the whole story.
The erdosproblems.com database has 1,135 problems total. About 680 remain open. Some are genuinely hard, problems that have resisted serious expert effort for decades. Others are what Tao calls problems that Erdős "clearly did not put much effort/thought into." The AI is solving the second kind.
The real question
Forum moderator Thomas Bloom put it well: sometimes Erdős stated problems without trying hard to solve them himself. Maybe he mentioned something interesting at a conference and it got catalogued as an "open problem" without anyone actually working on it. Fifty years of being "unsolved" doesn't mean fifty years of failed attempts.
What happens when the easy ones run out? The site maintainers are already seeing an influx of low-quality AI-generated proof attempts. One user apologized for attracting "AI slop" after their legitimate success made everyone think they could just paste problems into ChatGPT.
The Aristotle tool from Harmonic can formalize proofs in Lean automatically. That pipeline actually works. But the hard math, the stuff that would actually represent a breakthrough? Tao estimates 1-2% of open Erdős problems are currently accessible to AI methods with minimal human help. The rest aren't going anywhere soon.
