math.HO — History and Overview
The Grothendieckian Programme: An Overview — Seven Open Works on Mathematics and Machine Reasoning
The Grothendieckian Programme is a series of seven works on machine reasoning about mathematics (34 volumes, 26,021 pages), released openly on Zenodo in October 2026 with an overview volume. Two of the works specify a reasoning architecture — a core that holds mathematical worlds as typed, versioned and verifiable objects, and a kernel that reasons inside such worlds by sites, sheaves and descent. Five apply one method, recursive mathematical discovery, to the Riemann Hypothesis, the conjecture of Birch and Swinnerton-Dyer, the Hodge conjecture, the abc conjecture and the Langlands programme, and record what it proves, what it reduces to stated hypotheses and what it leaves open. This paper describes the architecture, the five research subjects, the method, the published corpus and the open process by which the works are to be reviewed and continued. None of the works claims a proof of any of these conjectures; they are first drafts and have not been peer-reviewed.