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Social Studies of Science
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The Context of Proving

Eric Livingston

School of Social Science, University of New England, elivings{at}metz.une.edu.au

Discussions of mathematical problem-solving and heuristic reasoning have typically examined how proofs that are already known might be found. This approach has at least three problems: first, provers engaged in discovering proofs for themselves cannot have this perspective; second, if a proof is difficult, formulaic strategies quickly run out; third, beginning with a proof already in-hand separates reasoning about a proof from the actual circumstances in which such reasoning occurs. As an alternative approach to the study of mathematical reasoning, this paper presents a detailed descriptive account of the work of finding a specific proof, including the shifting of perspectives, the wrong paths, the mistakes and the outright errors. Even the appearance of a sketched diagram or of a course of mathematical writing can suggest unanticipated possibilities for finding a proof. This material is used to illustrate the paper’s central claim - that the ways that provers go about working on proofs provide the context for continuing that work and for discovering the reasoning that a particular proof is then seen to require.

Key Words: discovery • ethnomethodology • mathematics • proofs • reasoning

Social Studies of Science, Vol. 36, No. 1, 39-68 (2006)
DOI: 10.1177/0306312705053055
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