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I have been pondering the following for some time: What does it take to say ''I have read that math book''? I realize that I want to $\textit{read}$ some math books, but I'm not quite sure when I can say (to myself) that I have. Is it when I can derive all the results from first principles, not looking in the book? Is it when I have solved all the problems within the book? Tried to expand on some of the material in the book? After a couple of read-throughs? When is it? I would like to hear your thoughts on this. Thanks guys.

Numbersandsoon
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    there is no right answer here. There are levels. Some books I've "read" a half dozen times and I know I still have much to understand. In my view, there are higher levels of understanding I have yet to attain. I know, once I study certain proofs and read certain books then a curtain will be lifted and math will never look the same to me again. Time to read, what a luxury... – James S. Cook Jan 20 '14 at 15:59
  • I don't understand this kind of question... You try to learn math on your own? You don't have any school/teacher? I liked the university, where we were getting hard homeworks and I had to study some parts on my own, but it was driven by the teacher. Our solution were discussed and we were advised specifically where to start learning. I think, this was the best way. Not just reading a book without anything else. – V-X Jan 20 '14 at 16:51
  • Thanks to everyone for your answers! Very useful! – Numbersandsoon Jan 21 '14 at 11:38

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This one may vary wildly from person to person. That said, I've always considered a math book read when 1) the contents are known to me, for reference purposes, and 2) most or all of the results are proven in a way that I comprehend and can redo if necessary (though, not necessarily without reading a bit again)

Chris Bonnell
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