In early January 2026, an AI system resolved a problem posed by the Hungarian mathematician Paul Erdős that had stood open for decades, the first time a listed Erdős problem has been settled largely by machine. The result has renewed a long-running argument among mathematicians and computer scientists about whether AI can generate new ideas or is mainly recombining human work at high speed.
What happened
According to a write-up posted to arXiv, Erdős Problem 728 was resolved by a combination of Aristotle, a formal-reasoning system built by the US startup Harmonic, and OpenAI’s GPT-5.2 Pro model. The proof was produced in Lean, a programming language for machine-checked mathematics, which means its correctness could be verified mechanically rather than by human reviewers alone. The result was announced on January 7 and the write-up was published shortly afterward.
The news spread quickly because Erdős problems are a well-known yardstick. Erdős, who died in 1996, left behind hundreds of conjectures and questions, many of them deceptively simple to state and stubbornly hard to settle. Thomas Bloom, a mathematician at the University of Manchester who maintains the online database of Erdős problems, has said in past commentary that work of this kind would be publishable if a graduate student had produced it.
A skeptical view from Terence Tao
Not everyone sees the episode as evidence of machine creativity. Terence Tao, the Fields Medal winner at UCLA, has described current AI systems as resembling a bright student who has memorized an enormous amount of material but does not always grasp it deeply, according to The Decoder’s account of his comments. In Tao’s view the result says more about the speed and breadth of the systems than about understanding; a model with access to vast prior literature can create the impression of insight even when its actual comprehension is limited.
That caution has a recent precedent. In October 2025, OpenAI executive Kevin Weil said on social media that GPT-5 had solved several open Erdős problems. Mathematicians soon pointed out that some of those “solutions” already existed in older research papers, including some written in German, and the claim was walked back. The episode nonetheless showed that AI could surface relevant results that human specialists had overlooked.
Direction rather than discovery
Researchers in other fields describe a similar pattern. Derya Unutmaz, an immunologist at the Jackson Laboratory, has said that modern AI systems now propose experiments and hypotheses that scientists had not considered. He characterizes this as help in setting the direction of research rather than direct discovery: narrowing fifty possible experiments to the five worth running.
The technical driver is the shift over the past 18 months toward reinforcement learning techniques that let models work on a problem for extended periods and try many approaches. This is what has produced apparent reasoning ability in mathematics, science and programming.
What remains unchanged is the need for human judgment. Specialists still frame the questions, guide the systems and scrutinize the output, and formal verification tools such as Lean are what make the machine-generated proofs trustworthy. The Erdős result shows AI has become a serious research tool. Whether it has become a source of original mathematical ideas is a question the field has not yet settled.
