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AI systems, including ChatGPT and OpenAI's Sol, have disproved and fully formalized the Erdős Unit Distance conjecture, marking a milestone in AI-assisted mathematics. The article discusses the process and implications for the future of mathematical proof verification.
Thomas Bloom provides an expository blog post on recent counterexamples to the Erdős unit distance conjecture and sum-product conjecture over the reals, including an OpenAI-assisted disproof of the unit distance conjecture and a collaborative disproof of the sum-product conjecture, sketching the constructions and intuition behind them.
A roundup of the top AI papers of the week (May 18-24) covering a survey on code-as-harness for agents, OpenAI's autonomous resolution of the unit distance conjecture, and a memory model for continual learning without forgetting.
An internal OpenAI model has disproved Erdős's unit distance conjecture, solving a famous open problem in mathematics and demonstrating AI's potential to contribute to high-level research.
The OpenAI reasoning model successfully constructed a counterexample, disproving the 80-year-old Erdős unit distance conjecture, demonstrating the capability of general-purpose models to solve open math problems.