数学究竟是什么
What is mathematics, really?
Reuben Hersh · 初版 1997 年
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几乎所有哲学家都将数学视为孤立的、永恒的、非历史的、非人性的。在 What Is Mathematics, Really? 一书中，著名数学家 Reuben Hersh 提出了相反的主张。在对传统的数学哲学（尤其是柏拉图主义和形式主义）发起颠覆性质疑的同时，他表明数学必须被理解为一种人类活动、一种社会现象，是人类文化的一部分，历经历史演变，且只有置于社会语境中才能被理解。数学对象是由人类创造的，但并非凭空捏造，而是源自与既有数学对象的互动，以及科学的需求
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对这里讨论的话题感兴趣的人，我强烈推荐 Reuben Hersh 写的《What is Mathematics, Really?》[1]。[1] https://www.amazon.com/What-Mathematics-Really-Reuben-Hersh/...
For anyone interested in the topics discussed here, I highly recommend What is Mathematics, Really? [1] by Reuben Hersh [1] https://www.amazon.com/What-Mathematics-Really-Reuben-Hersh/...
几部破除常见数学迷思的优秀相关作品：(1) 《What Is Mathematics, Really?》，Hersh，1997 年。https://books.google.com/books/about/What_is_Mathematics_Rea... (2) 《Where Mathematics Comes From》，Lakoff 和 Nunez，2000 年。https://en.wikipedia.org/wiki/Where_Mathematics_Comes_From
Some very nice related works that dispel widespread math myths: (1) What Is Mathematics, Really? Hersh, 1997. https://books.google.com/books/about/What_is_Mathematics_Rea... (2) Where Mathematics Comes From. Lakoff and Nunez, 2000. https://en.wikipedia.org/wiki/Where_Mathematics_Comes_From
这里有一份包含 10 本优秀的通俗数学书的清单：https://www.theguardian.com/books/2012/jan/18/ian-stewart-to... 清单里的书，我读过《哥德尔、艾舍尔、巴赫》（GEB）和《What is Mathematics Really》，真心推荐。GEB 啃起来有点费劲，但它会以一种美妙的数学思维方式彻底打开你的脑洞。我最早是在高中读的，所以内容应该算相当通俗易懂了。
Here's a list of 10 good, popular mathematics books: https://www.theguardian.com/books/2012/jan/18/ian-stewart-to... Of the list, I've read Goedel, Escher, Bach", and What is Mathematics Really* and can recommend them wholeheartedly. GEB is a bit of a project, but it will bend your mind in a good, math-y way. I first read it in high school, so the material should be pretty accessible.
关于这个话题，Davis 以及 Davis/Hirsch 写的书堪称权威。《The Mathematical Experience》（1981）读起来非常棒。《What is mathematics really?》（1997）也很不错。
Davis and Davis/Hirsch wrote the book(s) on this. The mathematical experience (1981) is a great read. What is mathematics really? (1997) also fine.
我觉得 Davis 和 Hersh 也表达过这个观点。Ruben Hersh 的《what is mathematics really》给人的感觉就像是带你走进了香肠制造厂，揭开了背后的真相。
I think Davis and Hersh say this. Ruben Hersh "what is mathematics really" felt like it was opening the door to the sausage factory.
……数学史，包括像 Morris Kline 的《数学：确定性的丧失》（Mathematics: the loss of certainty）这类较近期的历史书。根据 Reuben Hersh 的其他著作（例如《The Mathematical Experience》和《What is mathematics really?》），数学可以被看作一种社会活动，其中研究什么以及什么被视作证明成立，与人类的存在和人类社会生活有着明确的关联。如果你认同这一点……
…histories of mathematics including more recent histories like Morris Kline's "Mathematics: the loss of certainty." According to other books by Reuben Hersh, such as "the Mathematical Experience" and "What is mathematics really?", mathematics can be seen as a social activity where what gets studied and what gets accepted as proven has a definite relationship to human existence and human social life. If you agree with this,…