OpenAI's reasoning model cracks an 80-year-old math puzzle, endorsed by three top mathematicians

📄Full Article· Automatically extracted by trafilaturaGemini 翻譯1840 words

OpenAI announced that its general-purpose reasoning model has produced an original mathematical proof, disproving a geometric conjecture proposed by Paul Erdős in 1946. Unlike the blunder 7 months ago, this time it has received public endorsements from three heavyweight mathematicians. (Previous coverage: OpenAI launches "ChatGPT Personal Finance" feature: connects to real bank accounts to help calculate expenses and plan mortgages) (Background: Vitalik's latest article explores "Formal Verification": combining AI will be the final form of software development, granting Ethereum ultimate security) A famous unsolved problem posed by Paul Erdős in 1946. Seven months ago, OpenAI apologized for a math post. This time, it returned with the endorsement of three mathematicians. OpenAI claimed earlier that its general-purpose reasoning model had accomplished something: producing an original mathematical proof that overturned a long-standing conjecture. According to the official OpenAI announcement, this is "the first time an AI has autonomously solved a major, previously unsolved open problem at the core of the field of mathematics." Today, we share a breakthrough on the planar unit distance problem, a famous open question first posed by Paul Erdős in 1946. For nearly 80 years, mathematicians believed the best possible solutions looked roughly like square grids. An OpenAI model has now disproved that… pic.twitter.com/j2g3Ze0zEG — OpenAI (@OpenAI) May 20, 2026 An 80-year-old geometric puzzle The so-called "unit distance problem" asks: Given n points in a plane, what is the maximum number of pairs of points at a distance of exactly 1? This problem was formally proposed by Erdős in 1946, with the core goal of determining the precise upper bound for the number of unit distance pairs. In 1984, Spencer, Szemerédi, and Trotter jointly proved the current best-known upper bound: O(n^(4/3)) — meaning that when there are n points in a plane, the number of point pairs with a distance of exactly 1 does not exceed the order of n to the power of 4/3. This result established the outline of the problem, but the precise lower bound remained unresolved. For nearly 80 years, mathematicians generally believed that the optimal arrangement was a "square grid," where points are arranged like a chessboard, maximizing the number of point pairs with a distance of 1. On an n×n square grid, one can easily construct unit distance pairs of the order n^(4/3), and the academic community had almost reached a consensus: this construction was near-optimal, and the answer was essentially that. OpenAI's reasoning model found a brand-new "family of constructions": a family of arrangements that can be extended infinitely, where each arrangement performs better than a square grid. The improvement is "polynomial," meaning it is not just a few extra point pairs; as the number of points n increases, the gap continues to widen according to a mathematically describable pattern. The mistake 7 months ago In October 2025, former OpenAI VP Kevin Weil posted on X, claiming that "GPT-5 found 10 solutions to previously unsolved Erdős problems" and made progress on 11 others. The message spread rapidly but was subsequently debunked one by one: GPT-5 did not produce any new solutions; it simply found answers in existing literature that had already been written by others. The key detail clarified afterward was that mathematician Thomas Bloom, who manages erdosproblems.com, pointed out that problems marked "open" on the website only meant that he was not sure if they had been solved, not that they were "unsolved." What GPT-5 found were exactly those problems that had already been solved but had not yet been updated on his website. Meta Chief AI Scientist Yann LeCun and Google DeepMind CEO Demis Hassabis mocked the post in public. At the time, OpenAI was heavily promoting GPT-5, making this failure particularly conspicuous. Weil eventually deleted the post, and Thomas Bloom directly called it out at the time, labeling the post a "dramatic distortion." This time, OpenAI simultaneously released a companion remarks PDF, jointly endorsed by three heavyweight mathematicians: Israeli mathematician Noga Alon, American mathematician Melanie Wood, and Thomas Bloom himself. Bloom wrote in the remarks: "AI is helping us explore more completely the mathematical edifice built over centuries. What other invisible miracles are waiting in the wings?"

Data Status✓ Full text extractedRead Original (動區 BlockTempo)

🔍Historical Similar Events· Keyword + Asset Matching6 items

2026-05-29

OpenAI launches secure MCP tunnel: Connecting ChatGPT to enterprise intranets

Similarity 120%關鍵字 openai同分類 zh

2026-05-29

Anthropic closes $65 billion Series H funding round at a $965 billion valuation, surpassing OpenAI

Similarity 120%關鍵字 openai同分類 zh

2026-05-27

OpenAI launches "AI Era Economic Future Initiative": investing $250 million to explore taxing capital, universal wealth funds..

Similarity 120%關鍵字 openai同分類 zh

2026-05-27