The Proof Engine Programme: Reliable AI-Assisted Mathematics and Accountable Research

Abstract

AI-assisted mathematics creates an opportunity to organize research around two interacting, potentially overlapping roles. Reliable mathematical production turns questions into warranted, readable results. Structural research extracts general mechanisms, connects results, develops new questions and creates tools. We argue that this division can help an expanding supply of mathematical arguments become shared mathematical knowledge. Human intelligence remains central to research design, structural judgment and responsible evaluation, while AI can contribute to both roles. In the Proof Engine programme, the author's primary expertise is engineering reliable production. He also contributes to structural development within his mathematical understanding, while looking to specialist mathematicians for deeper synthesis. Open problems supply inspiration and concrete tests; each investigation is directed toward a reusable mathematical contribution. Human authorship identifies this intellectual contribution and responsibility for the particular solution, its evidence and its correction. The programme tests this arrangement by connecting original questions, readable papers and inspectable formal evidence. Its completed formalization standard is kernel-only closure: the proof-assistant kernel checks the principal conclusions and their mathematical dependencies under declared foundations, while a separate review checks agreement with the intended mathematics. The immediate engineering challenge is to make these checks feasible; further work concerns reuse, structural understanding and research direction. We specify release commitments and prospective tests through which this account can be assessed.