Proving Agency in Mathematical Practice: Practical, Social, and Mental Aspects

Mathematical reasoning is essential to the development of mathematical and scientific knowledge, and is a crucial skill in our science- and technology-based European societies.

Yet, despite the revolutionary advances in formal logic of the past century, the nature of reasoning and proofs in ordinary mathematical practice remains unclear.The ProvingAgency project aims to move forwards on this general question by shifting the focus from mathematical proofs themselves to the activity of proving that gives rise to them.

The approach to be developed proposes to structure the inquiry around the different dimensions of proving agency—the capacities of proving agents necessary to the realization of the activity of proving.

The ProvingAgency project will implement this approach concretely, within a restricted perimeter, in order to investigate three central aspects of proving agency: practical, social, and mental.Practical aspects are concerned with the practical knowledge required by mathematical agents to prove theorems.

One key element of such practical knowledge is the capacity to apply, adapt, and extend mathematical methods.

We will develop here an epistemological model of mathematical methods which will be informed by detailed and representative case studies.Social aspects are concerned with the issues that arise when several mathematical agents are proving a theorem together.

We will articulate here an account of the shared agency involved in the shared activity of proving together, which will be informed by a sociological study to be conducted on a group of mathematicians at the ETH mathematics department.Mental aspects are concerned with the mental dimension of the activity of proving.

We will aim here to provide a conception of proving as a mental activity that does justice to the fact that proving often requires to rely on mathematical artifacts, which we will do by building on recent developments in the emerging field of extended epistemology.