Human mathematicians are being outcounterexampled
xenaproject.wordpress.com
July 20, 2026
11 min read
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Summary
ChatGPT disproved Erdős’ Unit Distance conjecture in discrete geometry on May 20, 2026. Human mathematicians have acknowledged this achievement and its implications for the field of formalization and AI tools.
Key Takeaways
- ChatGPT disproved Erdős’ Unit Distance conjecture in discrete geometry using a theorem from number theory by Golod and Shafarevich.
- Logical Intelligence autoformalized the ChatGPT-generated proof in Lean, demonstrating real-time formalization of complex mathematical concepts.
- OpenAI's new model, Sol, generated 1.2 million lines of Lean code in three weeks, achieving significant advancements in formalizing global class field theory.
- The development of large AI-generated mathematics is becoming inevitable, raising concerns about the trustworthiness of AI-generated code.
Community Sentiment
Positives
- ChatGPT could have saved Yitang Zhang years of struggle by quickly identifying flaws, allowing mathematicians to focus on fruitful problems instead of dead ends.
- The ability to find counterexamples means mathematicians can avoid wasting time on false proofs, which ultimately leads to more productive research.
- Counterexamples refine theorem statements, improving the overall quality of mathematical discourse and fostering new insights.
Concerns
- Counterexamples may lead to answers, but they don't provide the deep understanding that elegant proofs offer, leaving a gap in mathematical comprehension.
- There's a pervasive sense of frustration with the politics in academia, which overshadow the merit of genuine mathematical discovery.
