--- format: "aidr-story-markdown/v1" id: "9c6bd61f8a15e0283cd44b223851d455a2983bc6fb068a2b0e78e7376f914158" canonical_url: "https://aidr.today/9c6bd61f?lang=en" title: "Anthropic AI Disproves 3SUM Conjecture With New Algorithm" lang: "en" requested_lang: "en" available_langs: ["en","vi"] translation_fallback: null fallback_fields: [] published_at: "2026-10-06T11:08:42.000Z" category: "Research" topics: ["anthropic","llm"] source_urls: ["https://huggingnews.com/ai/anthropic-ai-disproves-3sum-conjecture-with-new-algorithm-e1a12548","https://marketbrief.now/ai/anthropic-ai-disproves-3sum-conjecture-with-new-algorithm-e1a12548"] summary: "An algorithm discovered by an AI model refutes the APSP and Exact Triangle hypotheses and resolves the All-Pairs Shortest Paths problem in truly subcubic time, with a new paper and Lean formalization claiming these results disprove the Randomized Integer Word-RAM 3SUM Conjecture, and Anthropic employed an internal research model to certify the findings after the initial draft." --- # Anthropic AI Disproves 3SUM Conjecture With New Algorithm > [Open the canonical story]() **Published:** 2026-10-06T11:08:42.000Z **Category:** Research **Topics:** anthropic, llm ## Summary An algorithm discovered by an AI model refutes the APSP and Exact Triangle hypotheses and resolves the All\-Pairs Shortest Paths problem in truly subcubic time, with a new paper and Lean formalization claiming these results disprove the Randomized Integer Word\-RAM 3SUM Conjecture, and Anthropic employed an internal research model to certify the findings after the initial draft\. ## Sources - [Story source]() - [Story source]()