How to Read Mathematics 如何阅读数学[节选]——数学阅读时应该自省的几个问题

  
  
  
  

   
   
   
   
Why is this idea true?
   
   
   
   
为什么这个想法是对的？
   
   
   
   
Do I really believe it?
   
   
   
   
我是否确信它？
   
   
   
   
Could I convince someone else that it is true?
   
   
   
   
我能说服别人也信服它吗？
   
   
   
   
Why didn't the author use a different argument?
   
   
   
   
为什么作者没有用一个不同的论据？
   
   
   
   
Do I have a better argument or method of explaining the idea?
   
   
   
   
我有没有一个更好的论据或方法来说明这个思想？
   
   
   
   
Why didn't the author explain it the way that I understand it?
   
   
   
   
为什么作者不用我理解到的方式去阐述它？
   
   
   
   
Is my way wrong?
   
   
   
   
我的方法错了吗？
   
   
   
   
Do I really get the idea?
   
   
   
   
我确实理解这些方法了吗？
   
   
   
   
Am I missing some subtlety?
   
   
   
   
我是否搞错了某些细节？
   
   
   
   
Did this author miss a subtlety?
   
   
   
   
作者是否错失了某些细节？
   
   
   
   
If I can't understand the point, perhaps I can understand a similar
   
   
   
   
but simpler idea?
   
   
   
   
如果我不能理解这个观点，我是否能理解类似的更简单的思想？
   
   
   
   
Which simpler idea?
   
   
   
   
哪个思想更简单？
   
   
   
   
Is it really necessary to understand this idea?
   
   
   
   
对于理解这个思想，它确实是必要的吗？
   
   
   
   
Can I accept this point without understanding the details of why it
   
   
   
   
is true?
   
   
   
   
在不理解它成立的细节依据时，我能接受这个观点吗？
   
   
   
   
Will my understanding of the whole story suffer from not
   
   
   
   
understanding why the point is true?
   
   
   
   
在容忍一些我不理解的内容后，我能理解整个故事吗？
  
  
  
  

  完整版在这里，欢迎就翻译问题提出指正：

http://zerolabrary.appspot.com/static/mathread/html/index.html