The mathematical community has witnessed a major breakthrough. OpenAI recently announced that its latest internal reasoning model successfully generated an original mathematical proof, formally refuting the unit distance conjecture proposed by the renowned mathematician Paul Erdős in 1946. This achievement marks the first time that artificial intelligence has independently solved an open problem in the core field of mathematics using its long-chain reasoning capabilities.

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Escaping the Retrieval Quagmire, Expert Independent Verification

Notably, just seven months ago, OpenAI was criticized by the academic community for "retrieving existing answers from literature" and being pseudo-original when claiming to solve multiple Erdős problems. This time, OpenAI learned from its mistakes and proactively invited several internationally renowned mathematicians, including Thomas Bloom, for independent verification, and the rigor of the proof has received clear support from various scholars.

Previously, AI's achievements in the field of mathematics were mostly limited to re-verifying theorems already known to humans. However, this reasoning model has completely broken through the traditional understanding held by mathematicians for nearly 80 years. Previously, mathematicians generally believed that the optimal solution to this conjecture would roughly follow a grid-like arrangement, but OpenAI's model took a different approach, independently discovering a new construction method that performs better.

Overcoming Hallucination Issues, Impacting Frontier Science

From a technical perspective, solving such open mathematical problems places strict demands on AI's logical chain. Mathematical proofs involve several complex derivation steps, and any mistake at one step can lead to failure overall, which also means that this reasoning model has largely overcome the common "hallucination" issue found in traditional large language models.

Although some scholars point out that the proof still needs more time for peer review, its potential spillover effects have already attracted widespread attention. The unit distance conjecture is closely related to combinatorial geometry and graph theory. The application of this achievement is expected to directly affect research on protein folding in biology, crystal structure analysis in materials science, and the design and optimization of drug molecules in the future.