{"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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Andrew Arana\u003cbr\u003e\u003cb\u003eBinding Type:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Cambridge University Press\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 01\/16\/2025\u003cbr\u003e\u003cb\u003eSeries:\u003c\/b\u003e Elements in the Philosophy of Mathematics\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 84\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.63lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.00h x 6.00w x 0.25d\u003cbr\u003e\u003cb\u003eISBN:\u003c\/b\u003e 9781009539708","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":43446862807177,"sku":"9781009539708","price":64.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0636\/9240\/6921\/files\/img_b391a4a8-15ee-4a93-acd6-2da9c135be1c.jpg?v=1741684096","url":"https:\/\/sonsanddaughtersbooks.com\/products\/elements-of-purity-9781009539708","provider":"Sons and Daughters Books","version":"1.0","type":"link"}