Artificial intelligence has become a genuine talking point in pure mathematics, and the long list of problems posed by the prolific 20th-century mathematician Paul Erdős has become one of the most visible testing grounds. The story of how large language models have been applied to these problems is one of real progress mixed with early overclaiming, and the distinction between the two matters.
What the Erdős problems are
Paul Erdős left behind a vast collection of conjectures, ranging from small curiosities to central open questions in number theory and combinatorics. Many are catalogued on the community site erdosproblems.com, maintained by mathematician Thomas Bloom, which tracks more than a thousand of them. A crucial detail is what “open” means on such a list: it typically indicates that the curator is not aware of a published solution, not a guarantee that no solution exists anywhere in the literature. That nuance became central to how AI results were interpreted.
The 2025 episode: solved, or found?
In late 2025, widely shared claims suggested that a GPT-5-class model had “solved” a batch of Erdős problems. On closer inspection, several of those cases involved the model locating existing solutions buried in older or obscure papers that the wider community had overlooked, rather than producing original proofs. That is a genuinely useful capability, but it is retrieval, not novel mathematics, and the initial framing was walked back after mathematicians pointed out the difference. The episode became a cautionary example of how easily AI results in specialised fields can be overstated when a headline outruns the detail.
Where AI has genuinely helped
More carefully documented results followed. Mathematicians have used GPT-5-class tools as research aids to make progress on specific Erdős problems, with the AI suggesting approaches that a human expert then checks, corrects and completes. In at least one case, an AI-generated proof of a long-standing Erdős conjecture was formalised in the proof-checking language Lean and machine-verified before being confirmed by a leading mathematician, which is a far stronger standard of evidence than an unverified text output. Used this way, the models function as fast but fallible collaborators: they can propose paths, recall relevant results and handle routine steps, while the mathematician supplies judgement and rigour.
How mathematicians view the tools
The prevailing view among researchers who have used the latest models is measured rather than either dismissive or breathless. Many describe current systems as useful research aids whose suggestions are often flawed and require expert eyes to sort out, but which are meaningfully more capable than earlier models. At the same time, there is broad agreement that AI is not yet solving the field’s major open problems on its own, nor replacing mathematicians. The Erdős collection is attractive as an informal benchmark precisely because it is large and varied, but performing well on it is not the same as advancing the frontier of mathematics.
What to watch
Three distinctions are worth keeping in mind when reading claims about AI and mathematics. First, retrieving an existing proof from the literature is different from generating a new one, and the two are easily conflated in headlines. Second, an AI-produced argument is only as trustworthy as its verification: formal checking in a system such as Lean, followed by expert review, is what turns a plausible-looking output into a result. Third, peer review still matters, and the number of AI-assisted proofs that have passed full journal review remains small, even if that is beginning to change. AI is now a real part of the mathematician’s toolkit, but the most reliable results are those that survive independent human and machine scrutiny rather than those announced on social media. For broader context on how fast AI capabilities and investment are advancing, see coverage of the scale of AI funding. Detailed reporting is available from Scientific American.
