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This paper presents an AI agent built on GPT-5.5 Pro that autonomously generated correct proofs disproving the Erdős–Szemerédi sum-product conjecture over ℝ in 7 out of 8 trials, using a three-stage prompting pipeline.
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.