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Data for Mathematical Copilots: Better Ways of Presenting Proofs for Machine Learning
The suite of datasets commonly used to train and evaluate the mathematical capabilities of AI-based mathematical copilots (primarily large language models) exhibit several shortcomings.
The unknotting number, hard unknot diagrams, and reinforcement learning
We have developed a reinforcement learning agent that often finds a minimal sequence of unknotting crossing changes for a knot diagram with up to 200 crossings, hence giving an upper bound on the unknotting number.
The signature and cusp geometry of hyperbolic knots
We introduce a new real-valued invariant called the natural slope of a hyperbolic knot in the 3-sphere, which is defined in terms of its cusp geometry.
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