Claude Mythos Solves OpenAI’s Landmark Erdos Problem with a Simple Proof
A new AI system, Claude Mythos, has reportedly solved a classic Erdos problem that OpenAI had previously highlighted as a major mathematical challenge. The solution arrived in the form of a surprisingly short and elegant proof.
The breakthrough demonstrates that large language models can now handle abstract reasoning tasks once thought to require human intuition. Researchers are calling the proof “cute” for its simplicity.
OpenAI had featured the problem as a benchmark for AI mathematical reasoning. Claude Mythos, developed by Anthropic, completed the proof without human intervention.
The Problem: A Decades-Old Open Question
The Erdos problem, named after legendary mathematician Paul Erdos, had stumped experts for years. It involves a deceptively simple combinatorial pattern that resisted formal proof.
OpenAI had listed it among their “landmark” problems to test AI’s ability to reason beyond pattern matching. Many attempts by both humans and machines had failed.
The problem’s apparent simplicity masked deep logical traps. Previous AI solutions either relied on brute force or failed to close the final step.
The Solution: A “Cute” Proof
Claude Mythos produced a proof that fits on a single page. It uses only elementary number theory and a clever symmetry argument.
“The proof is almost embarrassingly straightforward once you see it,” said one source familiar with the work. “That’s why it’s so impressive.”
The system did not require special training or iterative search. It generated the proof in a single forward pass, then validated it logically.
“The proof is almost embarrassingly straightforward once you see it. That’s why it’s so impressive.”
Implications for AI Research
The result challenges assumptions about machine creativity. Claude Mythos did not recombine existing proofs — it invented a new approach.
OpenAI has not yet publicly commented on the submission. However, internal sources suggest the proof has passed initial verification.
If confirmed, this marks the first time an AI has solved a problem from Erdos’s personal collection without direct human guidance.
What This Means for Math and AI
Mathematicians may need to reconsider which problems are “safe” from AI. The boundary between routine calculation and genuine insight is blurring.
Claude Mythos is part of a broader push toward general-purpose AI systems. Its success on a formal reasoning task signals progress in areas like theorem proving, logic, and abstract thought.
Background on the Erdos Problem
Paul Erdos posed hundreds of problems over his career, many carrying cash prizes. The solved problem belongs to a subset focused on number theory and combinatorial structures.
OpenAI had used the problem as a benchmark in their 2024 paper on mathematical reasoning in LLMs. At the time, no model could solve it.
The proof itself is expected to be published in a peer-reviewed journal. Anthropic has not yet released the full details.
Potential Limitations
Some experts caution that a single success does not mean general mastery. Claude Mythos may have benefited from the problem’s specific structure.
Reproducibility remains a concern. The system’s output depends on random seeds and prompt phrasing.
Further tests on other Erdos problems are underway. Early results suggest mixed performance on more complex versions.
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