Mathematics has long been situated at the intersection of two very different kinds of knowledge making: it’s a part of common, basic, rational knowledge of everyday people and simultaneously a part of esoteric, elite, and rare knowledge held by only a select few. Books and articles aiming to popularize or explain mathematics have long succeeded by exploiting this intersection. Popularizations can provide a shortcut to “thinking like a genius”: Archimedes, Gauss, or Newton may have come up with it; but if you buy this book you, too, can understand it. They also have the advantage of “explaining everything”: Think number theory is esoteric? It’s also the key to Bitcoin! Wonder why you should learn about catenary curves? Look at the Golden Gate Bridge! Perhaps as a result, no other scientific or technical field compares even remotely in the sheer quantity of popular expository books that have been written over time. Despite the number of them, nearly every mathematics popularization is based on one of four types. (Not that different from mathematics itself, in that the switching of a single postulate might lead to an entirely new realm of discovery.) The first type features short accounts of individual puzzles and their solutions. Martin Gardner’s “Mathematical Games” column in Scientific American, which ran from the 1950s to the 1980s, is the best-known modern example, though similar versions in Ladies’ Diary and elsewhere date back centuries. The second type is an anthology of curiosities, such as Douglas Hofstadter’sGödel, Escher, Bach or Theoni Pappas’s The Joy of Mathematics, which presents vignettes of mathematical problems and concepts that often have surprising interconnections and relevance for everyday experiences. The third type features

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谁想成为数学家？

数学长期以来一直处于两种截然不同的知识创造的交叉点：它是普通人普通、基本、理性知识的一部分，同时也是只有少数人掌握的深奥、精英和稀有知识的一部分。旨在普及或解释数学的书籍和文章长期以来一直通过利用这一交叉点而取得成功。大众化可以提供一条“像天才一样思考”的捷径：阿基米德、高斯或牛顿可能已经想出了它；但如果你买了这本书，你也能理解它。他们还有“解释一切”的优势：认为数论深奥？这也是比特币的关键！想知道为什么您应该了解悬链线曲线？看金门大桥！或许因此，任何其他科学或技术领域都无法与随时间推移而编写的流行说明书籍的数量相提并论。尽管数量众多，但几乎所有数学普及都基于四种类型之一。（与数学本身并没有什么不同，因为单个假设的转换可能会导致一个全新的发现领域。）第一种类型以对单个谜题及其解决方案的简短描述为特色。Martin Gardner 在《科学美国人》中的“数学游戏”专栏从 1950 年代到 1980 年代是最著名的现代例子，尽管《女士日记》和其他地方的类似版本可以追溯到几个世纪之前。第二种是好奇心选集，如道格拉斯·霍夫施塔特的哥德尔、埃舍尔、巴赫或西奥尼·帕帕斯的《数学的乐趣》，它呈现了数学问题和概念的小插曲，这些小插曲通常与日常经验有着惊人的相互联系和相关性。第三类特点