科学与数学people.vcu.edu
如何阅读数学
How to Read Mathematics
2017 — 2022，它一次次回到首页
黑点是上首页（≥ 50 分）的那次投稿，空心点是没冲上去的投稿，点越大分数越高。
导读
这篇文章讲解如何阅读数学文本：数学写作高度浓缩，读者需要放慢速度、逐行推敲，用纸笔演算例子，而不是像读普通文章那样扫读。作者强调数学阅读是主动过程，'数学不是旁观者的运动'。
为什么经久不衰：它把读数学比作读乐谱而非读代码，提醒技术人放下'快速浏览'的习惯，这种阅读方法论的建议多年后依然适用。
HN 评论精选
用具体例子和直觉检验数学推导，比逐行跟公式更能发现错误
费曼理解复杂问题的方法简单而优雅：'我脑子里必须始终带着一个具体例子并看着它运行。有人一开始觉得我慢、不懂问题，因为我问很多愚蠢的问题。但后来对方在一堆方程中间说错时，我会立刻喊停——方程说结果应该如此，而我知道实际方向反了，那肯定有错。对方以为我在跟着数学步骤走，其实我是在用具体的物理例子和经验直觉来检验。'
wimagguc查看英文原文
Feynman’s method to understand complex problems is so simple and elegant! Surely you’re joking, mr Feynman: ”I can’t understand anything in general unless I’m carrying along in my mind a specific example and watching it go. Some people think in the beginning that I’m kind of slow and I don’t understand the problem, because I ask a lot of these “dumb” questions: “Is a cathode plus or minus? Is an an-ion this way, or that way?” But later, when the guy’s in the middle of a bunch of equations, he’ll say something and I’ll say, “Wait a minute! There’s an error! That can’t be right!” The guy looks at his equations, and sure enough, after a while, he finds the mistake and wonders, “How the hell did this guy, who hardly understood at the beginning, find that mistake in the mess of all these equations?” He thinks I’m following the steps mathematically, but that’s not what I’m doing. I have the specific, physical example of what he’s trying to analyze, and I know from instinct and experience the properties of the thing. So when the equation says it should behave so-and-so, and I know that’s the wrong way around, I jump up and say, “Wait! There’s a mistake!”
数学是写给人看的自然语言，不能像读代码那样机械地读
我想让计算机行业的人明白：数学通常不是一种形式化的计算机语言。符号和术语的含义因作者而异，人们写作带有不同的'口音'，偶尔有些模糊和不正式——但比其他类型的写作少得多。数学是写给人看的，不是写给计算机的。不要像读代码那样读数学，它更像读乐谱：选对节奏、强调哪些音符、如何诠释，都需要人来完成。
jordigh查看英文原文
One thing that I really would like to impress upon computer people is that mathematics is not (usually) a formal computer language. Symbols and technical terms change meaning depending on the author, people write with different "accents". There's a little ambiguity and informality at times, but a whole lot less than other kinds of writing. Mathematics is (usually) written for humans, not computers. Don't attempt to read mathematics as you read code. To keep making bad analogies, it's a bit more like reading music. Picking the right tempo, the notes to accentuate, the interpretation -- this all requires a human. Computer still make crude approximations.
主动精读公式并配合记忆训练，才能克服'扫一眼就过'的坏习惯
'数学不是旁观者的运动'这句话帮我熬过了大学并乐在其中——我是软件工程师，不是数学家。但十年后我仍会'扫一眼'论文和教材里的公式，得强迫自己真正看懂它们。对重要的公式（泰勒、傅里叶级数、傅里叶变换等），我会做成 Anki 卡片逐字记住。光理解不够，能在脑中随时'调出'公式来审视和运用是无价的。
anyfoo查看英文原文
"Mathematics is not a spectator sport". No quote was more useful to get me through Uni, and enjoying it in the process. I'm a software engineer, not a mathematician. That being said, a decade later I still catch myself often "glancing" over equations in papers and textbooks, and have to force myself to really look at them and check that I indeed "got them". I don't know what it is, maybe I just need more training/habit around it. There's a tendency for me to half-consciously say to myself "yeahyeah I'll get it from reading the text" or "I'll get to it later", which usually does not work. For more important equations (Taylor, sinc function, all the variations of Fourier Series, Fourier Transform, DFT, DTFT) I actually write them down as flash cards in Anki and learn them verbatim. Yes, I have to understand them otherwise it's useless, but being able to just "make the equations appear" in my head to look at and work with them is invaluable. Even after understanding, I won't derive the Taylor Series myself (and even if I did, I would not always want to repeat that), so the old adage that understanding is better than rote memorization is useless here.
先自己尝试证明再对照原文，是高手的读论文方法
一位经验丰富的数学家曾告诉我：'我读论文的方法是先读摘要，然后尝试自己陈述结果并证明它。卡住的时候再去看论文，看我哪里错了。'效果因人而异。
OccamsRazr查看英文原文
As an experienced mathematician once told me: "The way I read papers is by first reading the abstract. Then I try to state the results and prove them myself. When I get stuck I go to the paper to see what I got wrong." Mileage may vary.
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