This is all really good advice. The four principles you lay out are something I’ve had a lot of trouble understanding and accepting.
And yeah, the principles are explicit partly because I needed to be told them as well. :-) In particular point 2 I got straight out of “How to read a book” and when I read it I was just like “ohhhhhh. You can do that?!”.
Thanks for sharing this. Have you used this technique for reading papers as well?
I received The Princeton Companion to Mathematics as a gift this past Christmas and began to read it cover to cover. After reading the initial introductory chapters which were mostly review from my university classes, and the history chapters, I stalled out when I got to the articles on specific topics that I had no experience with. Admittedly, this book was not designed to be read cover to cover in the first place so I feel less bad for stopping. I will have to try and approach it using the techniques in this post. There are just so many interesting topics it is hard to try and focus on really underdstanding one thing.
Sortof but not really. The techniques I use to read a paper loosely inspired this, but they’ve got a bit of a different focus and I’ve not explicitly reconciled the two yet. My paper reading technique doesn’t involve explicit lists but involves a lot more bike rides (really).
On the face of it I’d expect good paper reading techniques to be at least somewhat different from good textbook reading techniques though: The prioritization matters less because papers are so much shorter, and papers are written for a different audience so can often be much harder reading.
Admittedly, this book was not designed to be read cover to cover in the first place so I feel less bad for stopping.
Honestly, the mathematics textbook that is designed to be read cover to cover is rare as hens teeth, and most of them are more like monographs than textbooks (I’ve a few I’d put i this category and they’re all in the region of 100 pages).