Using Large Language Models to Study Mathematical Practice

The philosophy of mathematical practice (PMP) looks to evidence from working mathematics to help settle philosophical questions. One prominent program under the PMP banner is the study of explanation in mathematics, which aims to understand what sorts of proofs mathematicians consider explanatory and what role the pursuit of explanation plays in mathematical practice. PMP researchers have recently turned to corpus analysis methods as a promising alternative to small-scale case studies. Such methods stand to benefit, it would seem, from the sophisticated text-comprehension capabilities of today's frontier large language models (LLMs). This paper reports the results from such a corpus study making use of Google's Gemini 2.5 Pro. Based on a sample of 5000 mathematics preprints, the experiments yielded a dataset of hundreds of useful annotated examples. Its aim was to gain insight on questions like the following: How often do mathematicians make claims about explanation in the relevant sense? Do mathematicians’ explanatory practices vary in any noticeable way by subject matter? Which philosophical theories of explanation are most consistent with a large body of non-cherry-picked examples? How might philosophers make further use of AI tools to gain insights from large datasets of this kind? As the first PMP study making extensive use of LLM methods, it also seeks to begin a conversation about these methods as research tools in practice-oriented philosophy and to evaluate the strengths and weaknesses of current models for such work.