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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.
This paper trains a small one-layer encoder-decoder transformer on the zeta map bijection for Dyck paths and uses mechanistic interpretability to extract a new explicit algorithm called the scaffolding map, demonstrating an AI-assisted approach to mathematical discovery.