Why Erdős Problems Are Falling to AI
quantamagazine.org
August 5, 2026
16 min read
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Summary
OpenAI's internal AI model discovered a counterexample to the "unit distance" problem, a conjecture proposed by Paul Erdős in 1946. This marks a significant achievement in the application of AI to solve longstanding mathematical questions.
Key Takeaways
- OpenAI's internal AI model provided a counterexample to the "unit distance" problem, a conjecture posed by Paul Erdős in 1946.
- On August 1, OpenAI's unreleased model Astra made 10 additional mathematical advances, including solutions to three more Erdős problems.
- Mathematicians are recognizing a phase transition in AI's mathematical capabilities, significantly changing the way mathematical research is conducted.
- Thomas Bloom created a website, erdosproblems.com, to track Erdős problems, utilizing ChatGPT to write the Python code for the site.
Community Sentiment
Positives
- The AI's ability to tackle long-standing math problems shows a groundbreaking shift in intellectual capabilities, hinting at future advancements in various scientific fields.
- Commenters are buzzing about the potential for AI to generate new mathematical conjectures, which could redefine how we approach proofs and discoveries.
Concerns
- There's a palpable skepticism about whether AI breakthroughs actually lead to meaningful utility, with some arguing that if no one understands the results, do they matter at all?
- Concerns are raised that relying on AI for complex math might lead us to relinquish our intellectual faculties to a supercomputer, which could be dangerous.
