Erdős Problems Fall to AI — and the Debate Over the Death of Mathematics

In January 2026 Erdős problem #728, one of the open problems left by the Hungarian mathematician Paul Erdős, was solved using OpenAI's GPT-5.2 Pro and Aristotle, a Lean-based prover from the startup Harmonic. The formal proof was completed on 6 January, and the next day Terence Tao of UCLA wrote that the problem "was solved more or less autonomously by AI", in the spirit of the problem, with the result, to the best of his knowledge, not replicated in existing literature. It started a wave of Erdős problems falling to AI, and by the second half of the year a debate over whether AI would end mathematics as a human practice.

The Erdős problems and erdosproblems.com

Erdős posed an enormous number of problems in papers and letters, often attaching prize money he paid out of his own pocket. According to Quanta Magazine, after his death in 1996 a nonprofit foundation in Iowa promised to honour his bounties.

The person who gathered them in one place was Thomas Bloom of the University of Manchester. In early 2023 he launched erdosproblems.com, intended for his own use, and had ChatGPT write the site's code. When he added comments in August 2025, a community grew around it that included many people who were not professional mathematicians. As of August 2026 the site listed 565 solved and 652 open problems. Because the problems vary widely in difficulty and importance and sit in one public list, they became a convenient yardstick for AI.

Prelude: claims that did not hold up

The first stir was a misfire. In October 2025 the OpenAI executive Kevin Weil posted on X that GPT-5 had found solutions to 10 previously unsolved Erdős problems. According to The Decoder, Bloom explained that "open" on his site only meant he personally did not know of a solution, and that GPT-5 had in fact found existing papers. The post was deleted, and Google DeepMind's Demis Hassabis called the episode "embarrassing".

In December a proof of Problem #333 posted by the student Kevin Barreto turned out to be in a 1977 paper by Erdős himself. Tao offered a theory: AI tools were becoming capable enough "to pick off the lowest hanging fruit amongst the problems listed as open", meaning problems amenable to simple proofs with standard techniques, but those were precisely the problems most likely to have been solved somewhere in the literature already.

Problem #728: what was new

Problem #728 is a question about divisibility of factorials, an offshoot of a 1975 study of the prime factorisation of binomial coefficients by Erdős, Graham, Ruzsa and Strauss. As Tao explained, the problem was vaguely worded; after the AlphaProof team noticed trivial solutions, participants on the site added a constraint to capture its intended spirit. According to the account Nat Sothanaphan posted on arXiv, Barreto announced on 4 January a proof from Aristotle based on an argument by GPT-5.2 Pro; on 5 January he asked GPT-5.2 Pro to upgrade the argument to the version the forum had settled on; and on 6 January Aristotle produced a Lean proof. Tao wrote that he found something else even more interesting than the solution: the emerging AI-powered capability to rapidly write and rewrite expositions of it.

A caveat followed. In an edit dated 5 March, Tao noted that the AI's methods turned out to be very similar to a 2014 paper by Carl Pomerance, who had since released a short note showing that his methods also solve #728. Even so, Tao wrote, the AI-generated solution was the first to address the problem explicitly.

The size of the wave: a success rate of 1–2%

Problems #729 (10 January) and #401 (11 January) were also solved with AI, and both were later found to yield to modifications of the #728 argument. On 11 February Tao described a hectic two months of human, AI and hybrid solutions in which nearly 50 more problems were marked solved. Yet he also estimated that the true success rate of these tools on Erdős problems was "only on the level of a percentage point or two", because successes go viral while failures go unreported. The solutions were overwhelmingly concentrated near the easy end of the difficulty spectrum.

In May, Tao, Jared Duker Lichtman, Barreto, Liam Price and others published a paper resolving Problem #1196, a result that began with community experiments using AI. Quanta reports that Bloom was surprised that most new results came from hobbyists and undergraduates using public LLMs rather than from corporate labs. That changed in May, when DeepMind and OpenAI each announced major results.

The debate over the death of mathematics

The more results arrived, the louder the questions about mathematics itself became.

The worried. Noga Alon of Princeton told Quanta he had stopped working on Erdős problems: "Once AI started to solve them, there is no point anymore." Bloom described a growing number of 100- to 200-page papers produced by people without mathematical training who had AI write and check the proof, adding: "But no human has read it, and no human is going to read it. It's a huge challenge now." Tao wrote in April: "We are transitioning in mathematics from an era of proof scarcity to an era of proof abundance." He warned that AI proofs nobody had verified or digested could kill off interest in a problem by marking it solved. In July the community began classifying such problems as "open (Lean)": formally proved, but not yet understood by humans.

On 2 June the Leiden Declaration, written by a working group of 16 researchers, was published and endorsed by the International Mathematical Union. According to Leiden University it does not seek to ban AI from mathematics but calls for norms such as disclosing AI use and treating AI as a tool rather than an author. IMU Vice President Ulrike Tillmann wrote: "Mathematics is, and should always remain, a profoundly human endeavour." On 11 September a group of Fields medallists including Tao issued a statement titled "A Severe Misalignment of AI in Mathematics", declaring that "The goals of the AI companies and the goals of the mathematical community are severely misaligned."

The optimists and the middle ground. In a March paper, Tao and Tanya Klowden asserted that "artificial intelligence is a natural evolution of human tools" and argued that its development and use must remain fundamentally human-centred. They suggested AI is relatively safe for reviewing human work but unsafe for building structures beyond what humans or verification tools can check. The amateur Wouter van Doorn conceded that LLMs are better at mathematics than he is, but said: "If you want to play piano, you aren't going to hire a piano-playing machine that does it better than you." Alon himself expects that "many and maybe most good mathematicians will use AI".

What changed, and for whom

The first winners were amateurs outside universities; Quanta portrays Bloom's site as a place where tenure and titles did not matter. Experienced researchers, meanwhile, lost something, as long-standing problems lost their appeal. People moved too: according to Quanta, in July 2026, on the day he received the Fields Medal, Jacob Tsimerman announced he was leaving academia for OpenAI.

AI companies had to adjust as well. In October OpenAI said it had consulted the independent Advisory Group on Mathematics and Artificial Intelligence at the Institute for Advanced Study on how to release new mathematical results, and pledged $5 million to a new Simons Foundation initiative to help mathematicians examine and build on AI-produced results. Half a century after the four color theorem (1976), the question of computers and proof had returned at a new scale. The thread is on the AI and mathematics timeline, and the wider social story on the AI and society timeline.