Livingson2006
| Livingson2006 | |
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| BibType | ARTICLE |
| Key | Livingson2006 |
| Author(s) | Eric Livingston |
| Title | The context of proving |
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| Tag(s) | EMCA, Mathematics, Proof |
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| Year | 2006 |
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| Journal | Social Studies of Science |
| Volume | 36 |
| Number | 1 |
| Pages | 39–68 |
| URL | Link |
| DOI | 10.1177/0306312705053055 |
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Abstract
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.
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