AI Solves Decades‑Old Erdős Problems: A Turning Point in Mathematical Reasoning
Published on: May 28, 2026
In late May 2026, two leading AI research labs—OpenAI and Google DeepMind—announced that their systems had independently cracked long‑standing mathematical problems posed by prolific mathematician Paul Erdős, signaling a watershed moment for AI in pure mathematical discovery.
On May 20, OpenAI declared that a general‑purpose reasoning model had autonomously disproved the so‑called unit‑distance conjecture in combinatorial geometry, an open problem unresolved since Erdős posed it in 1946. The model produced a multi‑step proof using algebraic number theory, passed independent expert review, and surprised mathematicians with its depth and originality.
Just days later, DeepMind revealed that its AI system called AlphaProof Nexus had autonomously solved nine out of 353 open Erdős problems and proved 44 conjectures from the Online Encyclopedia of Integer Sequences. Crucially, each proof was verified using the Lean formal proof assistant, ensuring logical correctness, at an estimated cost of only a few hundred dollars per problem.
Anthropic also joined the fray on May 26, announcing that its model Claude Mythos had independently produced an elegant and more concise proof of the unit‑distance conjecture—arriving at the same conclusion as OpenAI but via a distinct path using agent‑based collaboration. Early reviewers noted that Mythos’s proof stood out for its brevity and originality.
These near‑simultaneous breakthroughs have ignited conversation in the AI and mathematics communities about whether frontier models are transitioning from statistical pattern generators toward genuine logical reasoners capable of research‑level contributions. DeepMind’s emphasis on formal verification adds robust credibility to their findings, while Anthropic’s proof style highlights the creative potential of multi‑agent AI systems.
While these achievements are remarkable, some experts urge caution. The broader unit‑distance problem remains only partially resolved, and doubts persist about claims of AI “autonomy” given limited transparency into model pipelines. Nevertheless, the ability of AI to generate verifiable, peer‑reviewable proofs at scale represents a major conceptual shift in human‑machine collaboration in scientific discovery.
As of May 28, 2026, AI systems have proven capable of tackling open research problems that have eluded mathematicians for decades. Whether this marks the beginning of a new era in mathematical innovation or a powerful tool to augment human insight remains an open and exciting question.
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