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

Project description

A closer look at the capacities needed by those who ‘prove’ the truths of the universe

Proofs are central to mathematics and physics, helping us to explain the way the universe works. These rigorous logical arguments unequivocally demonstrate the truth of a given proposition or theorem. With the support of the Marie Skłodowska-Curie Actions programme, the ProvingAgency project will take an unconventional look at proofs – focusing on the capacities needed by the ‘provers’ to prove their proposed truths. The practical aspects relate to the practical knowledge required. The social aspects come into play when groups work together to prove theorems. Finally, the mental aspects are concerned with the mental dimension of the activity of proving, including the reliance on mathematical artefacts produced by humans.


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.

Funding Scheme



Net EU contribution
€ 308 746,56
Rue michel ange 3
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Ile-de-France Ile-de-France Paris
Activity type
Research Organisations
EU contribution
No data

Partners (1)