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...
Gespeichert in:
| Beteilige Person: | |
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| Format: | E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2024
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| Schriftenreihe: | Cambridge elements. Elements in the philosophy of mathematics
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| Links: | https://doi.org/10.1017/9781009052719 |
| Zusammenfassung: | 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. |
| Umfang: | 1 Online-Ressource (77 Seiten) |
| ISBN: | 9781009052719 |
| ISSN: | 2399-2883 |
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| spelling | Arana, Andrew Peter Elements of purity Andrew Arana Cambridge Cambridge University Press 2024 1 Online-Ressource (77 Seiten) txt c cr Cambridge elements. Elements in the philosophy of mathematics 2399-2883 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. Erscheint auch als Druck-Ausgabe 9781009055895 Erscheint auch als Druck-Ausgabe 9781009539708 |
| spellingShingle | Arana, Andrew Peter Elements of purity |
| 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 |
| work_keys_str_mv | AT aranaandrewpeter elementsofpurity |