Professional mathematicians are amazed at the progress made by amateurs in solving ancient problems with the assistance of AI tools — a development they believe could lead to a new way of doing mathematics.
Amateur mathematicians are using Artificial Intelligence chatbots to solve old problems — an unexpected development, which took professionals by surprise.
Although the issues at hand are not the most advanced of the mathematical canon, the success of AI models in addressing them shows that their mathematical performance exceeded a significant thresholdresearchers say, could fundamentally change the way we do math.
The problems being addressed originate from the legendary Hungarian mathematician Paul Erdőswho during his six-decade career became famous for putting deceptively simple but extraordinarily difficult questions.
“The questions tended to be very simple but very difficult“, explains the mathematician to the magazine Thomas Bloomfrom the University of Manchester, in the United Kingdom, which maintains one that catalogs these problems and monitors progress in resolving them.
At the time of Erdős’ death in 1996, more than 1000 of your problems remained unresolved, covering various mathematical fields, from Combinatorial Analysis to Number Theory.
Currently, these problems serve as important markers of progress in the respective disciplines, making any advance significant for the mathematical community.
A accessibility of Erdős problemsoften simple to state despite its difficulty, made them natural candidates for experimentation with AI tools like ChatGPT.
Bloom reports that around October of last year, mathematicians began to successfully use AI models to locate relevant references in the mathematical literature that helped with their solutions, which marked a dramatic improvement over previous attempts when AI chatbots simply invented non-existent articles.
“Before, when I tried ChatGPT, simply invented articlescompletely hallucinating, and that’s why I had given up using it“, recalls Bloom.
“But clearly there has been some kind of change around October. In fact, I found genuine articles, because I had read them alland often in a non-trivial way.”
Shortly after, AI tools began to introduce partial improvements to the results, some of which had been found in previous articles, while others seemed new.
This progress inspired Kevin Barretoan undergraduate mathematics student at the University of Cambridge, and Liam Pricean amateur mathematician, searching simple and little studied Erdős problems that could be solved with the help of AI.
They selected the problem number 728a Number Theory conjecture, and submitted it to ChatGPT-5.2 Pro.
“I looked at the statement and thought, ‘This could perhaps be resolved by ChatGPT, so let’s try, and in fact, presents a very elegant argument and which many people would agree was quite sophisticated”, explains Barreto.
To verify their work, Barreto and Price employed another AI tool called Aristotledeveloped by AI company Harmonic.
O Aristotle converts conventional mathematical proofs in Lean, a mathematical programming language that allows instantaneous computer verification of correctness. This verification step is crucialnotes Bloom, as it conserves the limited time researchers have to verify results.
In mid-January, six of Erdős’ problems had been resolved with AI tools, and small improvements or partial solutions in seven other problems
However, professional mathematicians later discovered that five of these had already been resolved in mathematical literature. Just the problem number 205 is a genuinely new solution from Barreto and Price, which has sparked a debate about whether these tools are genuinely demonstrating new ideas or simply unearth forgotten solutions.
Bloom argues that the distinction matters less than it might seemnoting that AI models often translate problems into new forms and discover articles that do not explicitly mention Erdős.
“Many of these articles I would not have foundand perhaps no one would have found them for much longer without this type of AI tool use”, he observes.
Questions remain about how far this approach can extend. The problems solved so far are not among the most demanding in mathematics — perhaps equivalent to first-year PhD work — but that remains impressive, argues Bloom.
Terence Taofrom the University of California, Los Angeles, who validated some of the AI-assisted solutions, considers that we may be on the threshold of a entirely new mathematical methodology.
“This is a kind of math that just isn’t done“, says Tao. “We don’t do mathematics on a large scale because we don’t have the intellectual resources, but AI is showing that we can.”
