I was a theoretical physicist for 13 years, and struggled a lot with this question [how to read hard stuff]. I found it very useful to develop several different styles for reading mathematics and physics. Mostly I did this in the context of reading papers, not books, but the comments below are easily adapted to books.
One unusual but very useful style was to set a goal like reading 15 papers in 3 hours. I use the term "reading" here in an unusual way. Of course, I don't mean understanding everything in the papers. Instead, I'd do something like this: for each paper, I had 12 minutes to read it. The goal was to produce a 3-point written LaTeX summary of the most important material I could extract: usually questions, open problems, results, new techniques, or connections I hadn't seen previously. When time was up, it was onto the next paper. A week later, I'd make a revision pass over the material, typically it would take an hour or so.
I found this a great way of rapidly getting an overview of a field, understanding what was important, what was not, what the interesting questions were, and so on. In particular, it really helped identify the most important papers, for a deeper read.
For deeper reads of important papers or sections of books I would take days, weeks or months. Giving lectures about the material and writing LaTeX lecture notes helped a lot.
Other ideas I found useful:
- Often, when struggling with a book or paper, it's not you that's the problem, it's the author. Finding another source can quickly clear stuff up.
- The more you make this a social activity, the better off you'll be. I organize lecture courses, write notes, blog the notes, and so on. E.g. http://michaelnielsen.org/blog/?p=252 (on Yang-Mills theories) and http://michaelnielsen.org/blog/?page_id=503 (links to some of my notes on distributed computing).
- On being stuck: if you feel like you're learning things, keep doing whatever you're doing, but if you feel stuck, try another approach. Early on, I'd sometimes get stuck on a book
by
sennoma
2009-06-20 20:28
learn
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michaelnielsen
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advice