语言与文风2022news.ycombinator.com
Ask HN：有哪些数学书仅因写法出色而值得推荐？
Ask HN: Math books you recommend just for the way they are written?
导读
这是 Hacker News 上一则求荐帖：有哪些数学书光是「写法」就值得一读。楼主以 Jaynes 的《概率论：科学逻辑》为例，称赞它先让读者理解，再谈严谨，不像大多数教材那样一上来就罗列公理。对写作者来说，这串讨论实际上是在谈「解释性写作」：怎样把难懂的东西讲得让人读得下去。
可以直接用的写作要点
- 01
把读者理解放在形式严谨之前：先讲清楚「为什么」，再补「严格定义」。
- 02
用图像、类比和可视化直觉替代枯燥的公理罗列，让抽象概念有落脚点。
- 03
让长内容可以分段读：每一块自成一体，读者随时能停下来再回来。
- 04
写作风格本身可以成为被推荐的理由；把「读起来愉快」当作和内容同等重要的标准。
HN 评论精选
好书靠视觉直觉和从零搭建的叙事，而不是干巴巴的严谨。
Arnold 的书风格独特，值得体会；Needham 的《可视化复分析》在视觉直觉上堪称盛宴；Penrose 的《通向实在之路》是杰作，几乎从零搭建起通往前沿物理所需的全部数学，多数人只能长期分段读，但过程极为愉快：有教科书的实质内容，却没有干巴巴的严谨；Stepanov 的《从数学到泛型编程》也值得期待。
ssivark查看英文原文
A few that come to mind immediately: 1. Books by VI Arnold. To get a sense of his style, see https://www.uni-muenster.de/Physik.TP/~munsteg/arnold.html 2. Visual Complex Analysis by Tristan Needham is an absolute treat in visual intution. 3. The road to reality by Roger Penrose. This is an absolute masterpiece building up to cutting edge physics and all the necessary math from scratch. Reading the whole thing is probably a long-term project for most readers, but it can easily be read in chunks, and is an absolutely pleasurable experience (with most of the conceptual substance of a textbook, but without the dry rigor) and a fascinating taste of what/how Penrose sees. 4. From Mathematics to Generic Programming by Alex Stepanov. I've read only small bits from Stepanov, but I'm really looking forward to reading the whole book.
可视化路线能把抽象数学讲得可感可知。
推荐 Harold Edwards 的《高等微积分：微分形式方法》，以及 Tristan Needham 的《可视化复分析》和《可视化微分几何与形式》——这几本都以可视化和直观见长。
sixbrx查看英文原文
Harold Edwards: Advanced Calculus: A Differential Forms Approach (https://www.maa.org/press/maa-reviews/advanced-calculus-a-differential-forms-approach#:~:text=Edwards%E2%80%99%20approach%20is%20to%20take%20calculus%20proper%20and,as%20a%20linear%20functional%20acting%20on%20differential%20forms.) Tristan Needham: Visual Complex Analysis (https://www.maa.org/press/maa-reviews/visual-complex-analysis) Tristan Needham: Visual Differential Geometry and Forms (https://press.princeton.edu/books/paperback/9780691203706/visual-differential-geometry-and-forms)
「长篇慢讲」的写法适合自学，配套书单也很有用。
强烈推荐我正在读的 Jay Cummings 的《Proofs: A Long Form Math Textbook》，它用「长篇」的方式慢慢讲证明；另外 Mark Saroufim 和 Susan Rigetti 各有一份数学书单，我长期在跟着读。
__rito__查看英文原文
I highly recommend the one that I am currently reading: Proofs: A Long Form Math Textbook by Jay Cummings [0]. There are two lists [1][2], one by Mark Saroufim, another one by Susan Rigetti that I have been following for quite some time now and intend to follow for the next months and years. [0]: https://longformmath.com [1]: https://marksaroufim.medium.com/technical-books-i-%EF%B8%8F-4af8f3ddd205 [2]: https://susanrigetti.com/math
数学书也可以写得俏皮、有漫游感。
立刻想到两本：一本是《Winning Ways for Your Mathematical Plays》，另一本是《A Singular Mathematical Promenade》，后者在网上可免费读到。
cevi查看英文原文
A few immediately come to mind: 1. Winning Ways for Your Mathematical Plays 2. A Singular Mathematical Promenade, available for free online: https://perso.ens-lyon.fr/ghys/promenade/ There are many other math books I really like - over the years I've collected a long list of reading recommendations: https://notzeb.com/rec.html (most of them won't fit as answers to this question)
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