
Ask HN: Do you read math & hard science books? How? - zkz
Do you buy and read math books? do you read them cover to cover or do you just use them as a reference book?<p>I typically buy a lot of math and physics, hard cs books, etc., but they take a lot of time to read so I end up collecting them, while reading them slowly (because hard science books could take months to read, at least if you don't have a lot of time for that!). Is that a typical hacker thing or is it just me?<p>I'm asking because I keep buying books about stuff I want to learn, but I also look at my library and I ask myself: "why don't I read these first?" Who knows, maybe today I want to learn something different than yesterday.
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michael_nielsen
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.

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

<http://bytepawn.com/readings-in-distributed-systems/>

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.

~~~
michael_nielsen
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.

~~~
DaniFong
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.

------
noonespecial
If they don't take a good bit of time to read, then you're not doing it right.
These are books full of tools for the mind. The best way to read them is a
little at a time, taking the parts that click in your mind and trying them out
on problems that seemed insurmountable before. The first time you open a big
box of strange tools, it won't be immediately apparent to you what they are
all for.

Finding a good math book is like stumbling into that room full of all of the
weapons on your first time through Doom...

~~~
jcdreads
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!

------
plinkplonk
In my student days, before I became a working programmer, I was desperately
poor and couldn't afford all the books I wanted to buy. So I got into the
habit of buying books when I had money in my account to avoid a future in
which I have to look longingly at a book and not have money to buy it. So, yes
your "buying a book and reading a few years later" situation is something i am
familiar with.

So anyways, I ended up having a few hundred technical books (and a couple of
thousand non technical books). The future of not having money to buy books
never came (yet, touch wood) and the biggest advantage of having this huge
collection of books is I can cross reference them to get better info on what I
am looking for. On the other hand, moving is a huge pain :-)

EDIT:(example of buying a book and then using it years later) I am now
(slowly) working through Cormen et al's "Introdcution to Algorithms" (second
edition) book. The idea is to do all the exercises and proofs and so on.
Should be done by the end of the year I think.I bought this book a few years
ago and am using it(seriously) only now. (There's a third edition out now for
anyone planning to buy. second ed is good enough for my purposes)

~~~
jlees
I studied computer science using Cormen et al., and it struck me that this
might be one way to 'use' these oft-impenetrable tomes. (Though I really found
Cormen very accessible.)

Look around for a university course that teaches using the book, and see if
you can find notes, or - better - problems based on the text. Often gives you
a sense of where to begin with the larger books.

~~~
Elcho
You can get podcasts based on this book, from the MIT's itunes page; MIT
6.046J introduction to algorithms.

Its not quite as good as seeing it on the page but it might help if your out
for a walk or in the car.

------
bluishgreen
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.

~~~
chrisduesing
This is really interesting advice. I have spent a lot of time lately
considering how I could become more effective at teaching myself math. The
community aspect is fundamental to my success as a programmer, but that is
something that I have not come across for math. Where would you suggest
someone find peers and or mentors?

~~~
bluishgreen
If you are a good programmer its very easy to become friends with math/phys/cs
profs. They typically have many projects that they are not looking at at the
moment for lack of programming power. Offer a few hours a week of your time to
a particular project that you feel interested in. You will learn crazy lots.
This is what a "Grad Student" is. But IMO this is much better than being a
grad student and suffocating through the bureau-crazy.

~~~
chrisduesing
Are you suggesting trading programming time for mentoring time, or just
programming a math teacher's projects as a means to learn?

How would you initiate something like that anyway? I would feel more than a
little awkward wandering on to a local campus and knocking on doors in the
math dept. Are there any online resources/communities?

~~~
bluishgreen
First Question: Both.

Second Question: Read online about the interests of a prof. Select a few.
Watch a few of their introductory lectures to see if you like how they explain
stuff. Select one. Look up the office hours. Wander into the room and state
your mind.

------
michael_dorfman
Basically, this is just a classic inventory control problem. If the inventory
is piling up, you need to either decrease the rate of acquisition, increase
the rate of consumption, or (preferably) both.

I can't say how typical the situation is, but it's definitely not just you. I
have quite the stack of books on my "to read" list, but I keep working my way
through them (and adding more to the pile.) So it goes.

~~~
stcredzero
I had this same inventory control problem with cookbooks. I solved it by
making a rule for myself: No new cookbooks until I cook 30% of the recipes in
all the ones I already have.

I have this same inventory control problem with computer science books. Good
textbooks are expensive. If you implement a utilization rule like this, you
can save yourself a lot of money on books you never end up reading. B&N,
Borders and their ilk have liberal return policies, as does Amazon. This will
help save lots of money. Also, the utilization rule prevents you from
disadvantageous conditioning. The retail pleasure of acquisition can drive you
to buy books faster than your actual reading rate.

 _I have quite the stack of books on my "to read" list, but I keep working my
way through them (and adding more to the pile.) So it goes._

I have the same phenomenon with Irish Trad tunes I want to learn. The list is
ever growing. (There are at least 30,000 of those.) My solution? I only learn
the tunes I _fall in love_ with. Life is short, so why waste time with
something that's just "nice?" I think I'm going to apply this to books and
other contexts.

~~~
yummyfajitas
Buy older editions of textbooks and also the "Eastern Economy" (read:
china/india printed on cheap paper) editions. You will save a pretty penny,
and thermodynamics hasn't changed much since 1975.

(Obviously this won't work for machine learning.)

~~~
samuel
Where do you buy such kind of books? I can't find them in Ebay anymore.
Probably it was not legal to export them.

------
pragmatic
I bought a Kindle b/c I don't have room for all my books. I recently had a
child and his books already fill one of my bookshelves. So I've been cleaning
out my physical books, only keeping those I really like. The Kindle DX might
be the way to go for texts. So you get unlimited space (Amazon will keep your
books online), access to all the classics for free (via gutenberg,etc) and
your books are always with you (while you carry the device anyway).

Of all the things you can spend your money on, books are the best investment
by far.

------
electromagnetic
I tend to collect lots of books, usually at times when I'm not really reading
much. However, I eventually (usually a matter of weeks or sometimes months)
get back to reading and will crunch through endless amounts of books. I've
managed to get through 500 page books in a day, every day for over two weeks
before.

As for specifically science books, I tend to read them slower so I usually
read a chapter or section of one and then read a chapter of a fiction novel.
If I keep switching I find I can get through both quite quickly as reading the
fiction novel will usually give enough motivation to read the non-fiction hard
science book quickly too.

------
jk4930
I often buy books and read some chapters that interest me. I get most out of
such books months or even years later when I can appreciate their content
better. It's good to know that I've the stuff at my hand, often there are
explanations, algorithms, concepts in a depth one rarely finds on the net.

------
twopoint718
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.

------
dinkumthinkum
Perhaps you just like the idea of reading all these books rather than the
actual reading of them.

~~~
zkz
No, I really like reading them. But it's easy to buy them faster than reading
them if reading them takes you so much time (for the hard science ones, not
divulgation, fiction, etc.).

------
Arun2009
I have the same problem. I have TONS of Mathematics (mainly) and Physics
books, but I've not really worked through most of them. I've spent a fortune
on them so far. I always keep saying that I'll take a couple of years off to
concentrate on nothing but hard science, but I know that will never happen.

I actually have a theory that good programmers are frustrated Mathematicians
and Physicists who couldn't stomach the real thing and chose the easier way
out.

------
justlearning
Thanks HN, Many times a rhetorical question is answered in ways more than i
can ask for. I have few attributes that I suspect are behind my depression.
This being one of them. I have been doing the same- but unlike the OP and
others, I get depressed that I bought a book and by not reading it completely,
I didn't give its due. I take it very personally that I have Cormen's
Algorithms and not gone past chapter1. It's like insulting the writers- i
don't know if you get it. It's like you want to be the most passionate
religious man on earth and the holy bible you really wanted to read and you
know that is what you want is lying on the shelf, while you are trying to sort
floating divs on a web page...and whenever i pick up a book, i will hit a
block where it gets difficult to understand and because i am used to reading
other books in a more casual way, i come to tell myself how dumb i am. i
convince myself this to be true when i read about everyone i follow and all
the books they have read...it's a vicious cycle that's been eating me inside
out - in almost a literal sense.

...But many a times, I will just grab a book (anything - even non technical)
and read it while sitting on the throne - read a few lines and ponder over it.
my favorite is sicp - which i have not completed after having it well over a
year. The few minutes of pondering is much more valuable compared to the
regular day, when I am less patient and I want to do some "quick fix" things.
I am so glad to find that I am not alone to read parts in between.

so @zkz, thank you for posting this question. The answers posted removed one
more attribute which added to my depression. many more to overcome. what a
day! I feel so relieved! - i would say this if I met you, so posted it here.

~~~
jlees
The throne method is surprisingly good! An ex-boyfriend of mine was a hacker
(well.. most of them have been) and one of his peculiarities was to have a
vast collection of academic and O'Reilly books next to the loo. Great for
flicking through, though often one would end up spending far too much time in
there...

------
modelic
I read all the main theorems without even reading any of the definitions and
examples for the first pass while at the same time I write down any questions
I have with a reference to the theorem it pertains. For my second pass I go
back and look at the examples to see if they answer any of the questions I
wrote down and write down more questions referencing the examples. For the
first two passes I don't try to answer any questions. I simply try to engage
the material. Finally I try to answer all the unanswered questions and work
some of the exercises and write down more questions if there are any left.

------
numberzer0
It takes me a while to read the books I have as well. I've bought lots of
books than I haven't been able to read yet and my list of books to buy and
read keeps growing as well. Another thing that adds to the amount of time it
takes me to read a book is that I'm a very meticulous reader. I like looking
up and cross referencing anything I don't understand, so for me that means
looking up lots of stuff. I wonder if other people do this as well.

------
menloparkbum
I used to buy math and science books all the time. I probably read 25% of the
books I bought. I quit buying books in general after I moved. Moving 500 books
sucks.

Now I only buy math and science books if I actually plan to work through them.
I usually try to do the problems first and only go back to the writing if I
can't figure the problems out. Other books for leisure reading, I just get
them at the library.

------
keefe
Yeah, I have a wide variety of very interesting books collecting dust on my
shelves. I don't know why really, I think maybe I spent my time in graduate
school immersed in theory and these last few years I have been completely
focused on understanding how that theory relates to practice. Maybe the
pendulum will swing the other way again once I have more free time.

------
Herring
My parents are in academia & they've each amassed a huge collection of books.
I learned very early on that I should be collecting digital books instead.

------
robryan
Definitely best to sift through them slowly, get the most out of them. No use
hammering through a good book then taking nothing from it at the end.

------
zackattack
I would try to take them cover-to-cover and then use them as reference. Also,
perhaps, if you really wanted to learn the material, you would simply check
them out of the library. There's been an article posted on the frontpage
recently about how verbalizing a goal makes it less likely to be actualized: I
think a parallel occurs with buying books (I experience the same phenomenon).

Get'em from the library, yo.

