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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.