Using Large Language Models as a Co-Author in Undergraduate Quantum Group Research

Abstract: This article describes the use of Claude CLI and its Opus 4.6 model, as a tool for writing an entirely AI-generated mathematics research paper. The resulting paper is comparable in scope and quality to papers previously produced by advanced undergraduate students in eight-week summer REU programs advised by the author. The main result is a new explicit formula for a central element of $U_q(so_12)$, which can be used for an interacting particle system with Markov duality. Using SageMath and a sparse PBW-basis pairing matrix that admits symbolic inversion, Claude reduced the central-element computation by several orders of magnitude: a calculation that took 60 hours in a 2023 Python implementation completed in under a minute on a laptop. The article reflects on the implications for undergraduate research mentorship: if generative AI can now produce research of REU caliber, advisors must select problems that better demonstrate the qualities valued by graduate admissions committees. Limitations including poor runtime estimates and literal handling of differing mathematical conventions are documented.