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I was a theoretical physicist for 13 years, and struggled a lot with this question. 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 or a paper for a week. It was only later that I realized that I mostly got stuck when either (a) it was an insubstantive point; or (b) the book was badly written; or (c) I was reading something written at the wrong level for me. In any case, remaining stuck was rarely the right thing to do.

- Have a go at proving theorems / solving problems yourself, before reading the solution. You'll learn a lot more.

- Most material isn't worth spending a lot of time on. It's better to spend an hour each seriously reviewing 10 quantum texts, and finding one that's good, and will repay hundreds of hours of study, than it is to spend 10 hours ploughing through the first quantum text that looks okay when you browse through it in the library. Understanding mathematics deeply takes a lot of time. That means effort spent in identifying high quality material is often repaid far more than with (say) a novel or lighter non-fiction.

Agree with Michael's points. My strategy: Buy problem books instead of text books!

- I KNOW I won't be able to finish them. That means it's OK not to, so I don't feel bad - but also that I shouldn't buy too many.

- The material within is bite-sized. Early problems teach you what you need for later ones, and you can always stop and come back later.

- Constant feedback is rewarding. Also, some say you only understand what you create for yourself.

- If I'm not advancing at all in a problem book, then I find open books on the internet, or (better!) I buy the Dover Publications paperback of the book by a master/inventor of the field, usually for $7 or so.

Here's my list of distributed papers, I think you're missing quite a few good ones:


But, more importantly, I'm curious about the 15/3-routine. How often do you do this? Recently I subscribed to the arxiv RSS (astro-ph.co, gr-qc), there's lots of papers uploaded daily, but most don't look very interesting, so 15 interesting ones would be ~1 weeks worth for me.

That's an interesting list on distributed computing, thanks.

As regards how often I do this: I go through periods where I do it a lot (sometimes several times in a week), and then months where I don't do it at all. I do it thematically (i.e., with closely related papers), so I've never tried doing something like what you suggest with the arXiv's recent papers. They're usually not all that closely connected.

I approach this in the same pattern. There are some technological tricks that have recently made it much easier, though.

In addition to Arxiv and preprints I can find online, there's Google Scholar and Amazon Previews (I'm still missing many journal articles, especially in engineering, due to a lack of university access, luckily they're often compiled in journals on Amazon). By flipping through Amazon's book previews using the search feature, I can read an arbitrary number of pages in any given book, and the world's library is at my lap. I can then 'photocopy' the relevant/interesting sections using ctrl-shift-command-4 on my Mac, and paste them into my Evernote. In this way I can locate and collate a large number of papers and texts, and organize them along the way without even dipping into LaTeX. After that, I can past those copies into Mathematica, which has a very workable equation typesetter, with the additional advantage of the equations being computable.

Lately I make a lot of use of Evernote, however, which I can pretty much paste anything into, and I can 'photocopy' any part of a text on the computer by using ctrl-shift-command-4 on my Mac.

I think that especially with the Internet not bounding paper lengths any longer, authors should write more comprehensive versions of their papers (or at least include an appendix).

In most cases, the succintness of the papers is what makes them difficult to read, both in terms of skipping steps in proofs and in terms of hidden assumptions of the reader's knowledge.

Psyklic, our UW QSE group felt the same way, and to remedy these problems we wrote a 96-page "Practical Recipes" article on quantum simulation, which appeared this month in the (open source) New Journal of Physics.

This length permitted our QSE Group to explain practical methods for quantum system engineering at a mathematical level that was well-matched to our quantum system engineering students.

On the other hand, the peer review of articles of this length is a lot of extra work for all concerned---reviewers, editors, and authors ... to say nothing of the effort demanded of the readers.

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