Group Knowledge and Mathematical Collaboration: A Philosophical Examination of the Classification of Finite Simple Groups

Joshua Habgood-Coote, Fenner Stanley Tanswell

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

In this paper we apply social epistemology to mathematical proofs and their role in mathematical knowledge. The most famous modern collaborative mathematical proof effort is the Classification of Finite Simple Groups. The history and sociology of this proof have been well-documented by Alma Steingart (2012), who highlights a number of surprising and unusual features of this collaborative endeavour that set it apart from smaller-scale pieces of mathematics. These features raise a number of interesting philosophical issues, but have received very little attention. In this paper, we will consider the philosophical tensions that Steingart uncovers, and use them to argue that the best account of the epistemic status of the Classification Theorem will be essentially and ineliminably social. This forms part of the broader argument that in order to understand mathematical proofs, we must appreciate their social aspects.

Original languageEnglish
Pages (from-to)1-27
Number of pages27
JournalEpisteme
Volume2021
DOIs
Publication statusPublished - 31 Aug 2021

Keywords

  • Social epistemology
  • mathematical practice
  • proof
  • group theory
  • classification of finite simple groups
  • collective knowledge
  • mathematical knowledge

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