Recipes and Instructions in Mathematical Proofs

Thimothy GowersChaire CombinatoireCollège de FranceAnnée 2022-2023Séminaire : Recipes and Instructions in Mathematical ProofsIntervenant(s)Fenner Tanswell, Vrije Universiteit BrusselWhat is a mathematical proof? What role do proofs play in mathematical knowledge? The standard model is that a proof is a logically structured sequence of assertions, beginning from accepted premises and proceeding by established inference rules to a conclusion. In this talk, I will offer an alternative model, the recipe model of proof, which sees proofs as providing instructions for a process of mathematical reasoning. To support this model, I'll show some results from a corpus linguistics study of maths preprint articles from the arXiv looking at the prevalence of instructions in the written language of proofs. I'll then argue that this model provides a different perspective on both the logical structure of real proofs, and the kinds of knowledge proofs generate and communicate.