A call for papers
The practice of proof in mathematical research faces some old challenges and new opportunities. The challenges include the length and difficulty of some proofs, the most notorious cases of which are too long for one person to read (let alone check) or too specialised for more than a handful of people to understand. Mathematics suffers with other disciplines the common difficulty of finding enough reviewers to serve its journals, and this raises questions about how reviewers reach their judgments about proofs and how reliable those judgments are. The new opportunities arise from technology, most obviously in the shape of proof assistants but also in digital communication and dissemination. The debate in the 1990s between Thurston and Jaffe & Quinn was in part about the threat that the newly-invented internet posed to the gatekeeping function of mathematics journals. Has the relationship between peer-reviewed publication and pre-publication circulation of results changed in the three decades since then?
In computer science and formal logic, proofs can be considered as mathematical objects in their own right. What new questions about proofs as mathematical objects arise from the emergence of proof assistants and homotopy type theory? For example, under what conditions can two proofs can be considered equivalent?
One might also ask whether there are different (epistemic) types of proofs, e.g. explanatory proofs, pure proofs, etc.? Did abstract structuralism impact the nature of proofs?
Papers that use historical analyses to illuminate the present are also welcome.
These questions are suggestions only. We seek articles that philosophically examine the proof practices and proof ideals of recent and contemporary mathematics.
Annals of Mathematics and Philosophy:
Deadline: 15 March 2025