Ask HN: Do you read math & hard science books? How?

The problem with math books. Succinctness. There you have it. This is the single most annoying problem with succinctness. When you go over a line of text sometimes it is justified to spend 3 hours with it. But sometimes its not, its just something that you are not seeing. The thing with math books is you cant tell if it needs 3 hours or 2 minutes because all the lines look the same and the succinct ones kinda jump at you without warning. Succinctness is Power, but if you are facing a powerful person in combat you wont be singing the glories of origins of your foes power.

The way I go about these books is to work the theorems myself. It will take a loooong time to get through the first few chapters because that is where you are getting oriented towards that kind of thinking. The second chapter is usually the hardest! Stick with it. Do not try to calculate how long it is going to take to complete this book at this rate. Because the thing gets faster as you read it. Some kinda exponential function at work, the more you read the faster you can read since you have an intuition for the succinct parts and you can sense them from far. Many times you don't have to complete the book since the later chapters are on a need to know basis and the fundamentals are covered in the first half of the book. Also the thing gets faster once you cross the second chapter since you know the language now.

Why you should work the theorems yourself: When you read them you feel like you know them, but this is a bias. ( I use that word as an umbrella term to refer to all unintentional consequences of the way our mind works ). Once you try to reconstruct the theorem, that is when you get to understand all the gaps, holes and whole craters in your knowledge with such clarity.

Clearly knowing what you don't know is the last but one step before you know it. This is like finding the exact line in which the bug occurs, 95% of the times when I have done this the fix is immediately obvious to me. The remaining 5% of the times the bug is a consequence of the architecture (fondly referred to as a feature). To think of a parallel to this in learning: these are the times when you feel an Ah ha moment where whole areas of darkness come to light.

You need a guru by all means to guide you. Not all the information about the difficulty of a topic is captured by a book. You wont understand the consequences of a particular way of thinking unless you have spent a few years doing it wrong. So find a person who has been down that path to guide you. Also a buddy group makes the whole experience much more manageable and fun.

Yeah, this is exactly right. To a decent approximation, I spent college and grad school just basically plowing through math and physics texts. In eight or so years, with extensive help from the faculty of two universities, I grew to understand the contents of several dozen thick hard science and math books, and for my efforts they gave me two degrees.

Since quitting school I've dragged myself through a small pile of classic CS texts, and have learned a ton (and, as a side effect, become nicely employable as a programmer). It is insanely hard (and rewarding) work. If it's hard, then you're learning something; keep it up!

Yup. Hard science books take a long time to digest. But the trick to keep at it is to keep a self check: is this something you're really interested in learning? Perhaps you'll find out within a few chapters that it's not worth it. And that's ok.

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.

Textbooks are indispensable for really getting the material down, but I've found it much easier to read lectures.

Feynman has great examples of this type of work: "The Character of Physical Law" or "The Feynman Lectures on Computation" are both excellent. I've found that these books walk somewhere between textbook and popular science book. Easy to read but all the while teaching you the material.

I've found this type of work to be the crucial link between pop. science and a textbook. You learn enough that you can find your footing when you're in a textbook and and also the inspiration to actually read it.