Elements of purity:
A proof of a theorem can be said to be pure if it draws only on what is 'close' or 'intrinsic' to that theorem. In this Element we will investigate the apparent preference for pure proofs that has persisted in mathematics since antiquity, alongside a competing preference for impu...
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2024
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| Series: | Cambridge elements
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| Subjects: | |
| Online Access: | DE-12 DE-634 DE-92 DE-473 URL des Erstveröffentlichers |
| Summary: | A proof of a theorem can be said to be pure if it draws only on what is 'close' or 'intrinsic' to that theorem. In this Element we will investigate the apparent preference for pure proofs that has persisted in mathematics since antiquity, alongside a competing preference for impurity. In Section 1, we present two examples of purity, from geometry and number theory. In Section 2, we give a brief history of purity in mathematics. In Section 3, we discuss several different types of purity, based on different measures of distance between theorem and proof. In Section 4 we discuss reasons for preferring pure proofs, for the varieties of purity constraints presented in Section 3. In Section 5 we conclude by reflecting briefly on purity as a preference for the local and how issues of translation intersect with the considerations we have raised throughout this work |
| Item Description: | Title from publisher's bibliographic system (viewed on 05 Dec 2024) |
| Physical Description: | 1 Online-Ressource (77 Seiten) |
| ISBN: | 9781009052719 |
| DOI: | 10.1017/9781009052719 |
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| spelling | Arana, Andrew Peter Verfasser aut Elements of purity Andrew Arana Cambridge Cambridge University Press 2024 1 Online-Ressource (77 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge elements Title from publisher's bibliographic system (viewed on 05 Dec 2024) A proof of a theorem can be said to be pure if it draws only on what is 'close' or 'intrinsic' to that theorem. In this Element we will investigate the apparent preference for pure proofs that has persisted in mathematics since antiquity, alongside a competing preference for impurity. In Section 1, we present two examples of purity, from geometry and number theory. In Section 2, we give a brief history of purity in mathematics. In Section 3, we discuss several different types of purity, based on different measures of distance between theorem and proof. In Section 4 we discuss reasons for preferring pure proofs, for the varieties of purity constraints presented in Section 3. In Section 5 we conclude by reflecting briefly on purity as a preference for the local and how issues of translation intersect with the considerations we have raised throughout this work Mathematics / Philosophy Purity (Philosophy) Proof theory Logic, Symbolic and mathematical Erscheint auch als Druck-Ausgabe 9781009539708 Erscheint auch als Druck-Ausgabe 9781009055895 https://doi.org/10.1017/9781009052719?locatt=mode:legacy Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Arana, Andrew Peter Elements of purity Mathematics / Philosophy Purity (Philosophy) Proof theory Logic, Symbolic and mathematical |
| title | Elements of purity |
| title_auth | Elements of purity |
| title_exact_search | Elements of purity |
| title_full | Elements of purity Andrew Arana |
| title_fullStr | Elements of purity Andrew Arana |
| title_full_unstemmed | Elements of purity Andrew Arana |
| title_short | Elements of purity |
| title_sort | elements of purity |
| topic | Mathematics / Philosophy Purity (Philosophy) Proof theory Logic, Symbolic and mathematical |
| topic_facet | Mathematics / Philosophy Purity (Philosophy) Proof theory Logic, Symbolic and mathematical |
| url | https://doi.org/10.1017/9781009052719?locatt=mode:legacy |
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