An LLM-assisted corpus study finds that roughly 3% to 12% of 5,000 arXiv math papers contain clear or borderline appeals to mathematical explanation, with frequency varying by subfield.
A geometric proof of the existence of Whitney stratifications
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abstract
A stratification of a singular set, e.g. an algebraic or analytic variety, is, roughly, a partition of it into manifolds so that these manifolds fit together "regularly". A classical theorem of Whitney says that any complex analytic set has a stratification. This result was extended by Lojasiewicz to real (semi)analytic sets. In this paper we present a short geometric proof of existence of stratifications based on Thom's transversality theorem and Milnor's curve selection lemma and not relying on difficult results of Lojasiewicz.
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Using Large Language Models to Study Mathematical Practice
An LLM-assisted corpus study finds that roughly 3% to 12% of 5,000 arXiv math papers contain clear or borderline appeals to mathematical explanation, with frequency varying by subfield.