In a development that has stunned the mathematical community, non-professional enthusiasts and powerful artificial intelligence chatbots are rapidly resolving long-standing open problems originally posed by the legendary Hungarian mathematician Paul Erdős.
As of mid-January 2026, more than a dozen such conjectures have moved from “unsolved” to “resolved” status on the authoritative Erdős Problems database, with many crediting AI tools for generating proofs or uncovering forgotten solutions.
The surge began gaining traction around Christmas 2025, following the release of advanced models like OpenAI’s GPT-5.2, which demonstrates markedly improved mathematical reasoning compared to earlier versions.
Since then, at least 15 problems have been marked solved on erdosproblems.com, with 11 explicitly noting AI involvement in discovery, proof construction, or verification.
One landmark case stands out: Erdős Problem #728, concerning properties of factorials and divisibility, was solved more or less autonomously by AI.
After iterative prompting and refinement, GPT-5.2 Pro generated a novel argument in the spirit of the original conjecture—one not replicated in existing literature, though related ideas appeared in prior work. The proof was formalized using Harmonic’s Aristotle tool, which translates natural-language reasoning into Lean, a computer-verifiable proof language.
Fields Medalist Terence Tao publicly highlighted this milestone on Mastodon in early January 2026, describing it as a qualitative leap where AI handled core reasoning with minimal human intervention beyond feedback.
Tao, who maintains a detailed GitHub wiki tracking AI contributions to Erdős problems, counts at least eight instances of “meaningful autonomous progress” by models, plus additional cases where AI efficiently located and built upon overlooked prior research.
In another prominent example, quantitative researcher Neel Somani prompted GPT-5.2 Pro to tackle Problem #397, involving equations with central binomial coefficients. The resulting proof, formalized in Lean via Aristotle, earned swift validation from Tao himself.
Amateur collaborators have also made headlines. Cambridge undergraduate Kevin Barreto and independent mathematician Liam Price targeted understudied, seemingly accessible problems.
Using chatbots to produce initial proofs and Aristotle for rigorous checking, they resolved at least one case (such as elements tied to Problem #205) without prior known solutions—though scrutiny later revealed some AI-generated “breakthroughs” rediscovered published results from years or decades earlier.
Thomas Bloom, the University of Manchester researcher who curates erdosproblems.com, describes Erdős’s questions as “very simple, but very hard.” The prolific mathematician scattered over 1,100 such conjectures across his six-decade career, often with cash prizes attached, turning them into enduring challenges in number theory, combinatorics, graph theory, and more.
Many remained obscure due to limited attention from professionals.Experts emphasize nuance amid the excitement. Tao likens current AI capabilities to “a really clever student who has memorized everything for the test but doesn’t have a deep understanding.”
Models excel at pattern recognition, exhaustive literature trawling, reformulating ambiguous statements, and applying standard techniques—particularly to the “long tail” of easier, neglected problems.
Kevin Buzzard of Imperial College London notes that these successes largely target “lowest-hanging fruit” that received little prior scrutiny.Still, the implications extend far beyond individual resolutions.
Tools like Aristotle and Lean dramatically reduce verification time, traditionally a major bottleneck. AI’s speed enables systematic sweeps of remaining unsolved problems (now roughly 660), potentially compressing discovery timelines from years to days or hours.Bloom sees a fundamental shift on the horizon: “This could change the way we do mathematics.”
Rather than replacing human insight, AI acts as a powerful co-pilot—accelerating routine work, surfacing forgotten results, and freeing researchers to pursue bolder, more creative directions.
As models continue advancing and mathematicians increasingly integrate them into workflows, the boundary between human and machine contributions in pure mathematics is blurring at unprecedented speed.
What began as Erdős’s playful yet profound challenges may now mark the opening of a transformative chapter in how humanity explores the abstract universe of numbers.
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