Why Erdős's Legendary Problems Yield to Artificial Intelligence
OpenAI
OpenAI's internal AI model disproved Erdős's unit distance problem, a historic first. Later, a model named Astra solved more Erdős problems, marking a perceived phase shift in AI's mathematical abilities. The influence of Thomas Bloom's website, which compiled Erdős problems, is also examined.
OpenAI announced that an internal AI model found a counterexample to Paul Erdős's unit distance problem, a conjecture from 1946. The result was later improved by human mathematicians but was novel for using ideas from a distant area of mathematics. On August 1, OpenAI announced that another model, Astra, achieved 10 additional mathematical breakthroughs, solving three more Erdős problems. Noga Alon noted that these models are radically changing mathematical research. Thomas Bloom created the website erdosproblems.com in early 2023 to compile Erdős problems, and in August 2025 he added a comment section, fostering a community. An amateur mathematician, Wouter van Doorn, solved problem 1102 with help from the community, receiving feedback from Terence Tao. Later, Kevin Barreto and Liam Price, using GPT-5.2 and GPT-5.2 Pro, attempted to solve problems; they solved problem 333 but it turned out Erdős had solved it in 1977, and then solved problem 728 with no prior solution found.
- Abbreviations
- LLM = Large Language Model — Большая языковая модель
Source: Habr — хаб ИИ —
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