{"product_id":"elements-of-purity-9781009539708","title":"Elements of Purity","description":"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.\u003cul\u003e\n\u003cli\u003e\n\u003cstrong\u003ePublication date:\u003c\/strong\u003e 16 January 2025\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003ePage count:\u003c\/strong\u003e 84\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e Height 229 mm; Width 152 mm; Thickness 6 mm\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003ePublisher:\u003c\/strong\u003e Cambridge University Press\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eFormat:\u003c\/strong\u003e Hardback\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eISBN-13:\u003c\/strong\u003e 9781009539708\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"Andrew Arana","offers":[{"title":"Hardback","offer_id":50482170724602,"sku":"9781009539708","price":55.16,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0522\/4297\/2845\/files\/9781009539708.jpg?v=1790043997","url":"https:\/\/shulphink.com\/products\/elements-of-purity-9781009539708","provider":"Shulph Ink","version":"1.0","type":"link"}