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I think/hope this is okay for MO.

I often find that textbooks provide very little in the way of motivation or context. As a simple example, consider group theory. Every textbook I have seen that talks about groups (including some very basic undergrad level books) presents them as abstract algebraic structures (while providing some examples, of course), then spends a few dozen pages proving theorems, and then maybe in some other section of the book covers some Galois Theory. This really irks me. Personally I find it very difficult to learn a topic with no motivation, partly just because it bores me to death. And of course it is historically backwards; groups arose as people tried to solve problems they were independently interested in. They didn't sit down and prove a pile of theorems about groups and then realize that groups had applications. It's also frustrating because I have to be completely passive; if I don't know what groups are for or why anyone cares about them, all I can do is sit and read as the book throws theorems at me.

This is true not just with sweeping big picture issues, but with smaller things too. I remember really struggling to figure out why it was supposed to matter so much which subgroups were closed under conjugation before finally realizing that the real issue was which subgroups can be kernels of homomorphisms, and the other thing is just a handy way to characterize them. So why not define normal subgroups that way, or at least throw in a sentence explaining that that's what we're really after? But no one does.

I've heard everyone from freshmen to Fields Medal recipients complain about this, so I know I'm not alone. And yet these kinds of textbooks seem to be the norm.

So what I want to know is:

Why do authors write books like this?

And:

How do others handle this situation?

Do you just struggle through? Get a different book? Talk to people? (Talking to people isn't really an option for me until Fall...) Some people seem legitimately to be able to absorb mathematics quite well with no context at all. How?

2Community wiki? – Akhil Mathew – 2010-01-27T01:59:22.043

13I found myself thinking the exact same as you on multiple occasions. I find it most annoying in proofs to be honest: the solution is pulled out of a hat and then checked, with no insight about how the solution was found. It's as if someone was explaining how to come up with elliptic curves of high rank just by giving an example by Elkies and checking that it is of high rank. – Sam Derbyshire – 2010-01-27T02:01:27.253

4Why did the comments go away? – Mariano Suárez-Álvarez – 2010-01-27T06:16:38.767

7We decided that a discussion of the merits of Bourbaki was not a good use of the comments box (it had drifted far from the topic at hand), so we killed them. – Andy Putman – 2010-01-27T06:33:09.733

4Two possible reasons why: 1) such books are easier to write 2) the books you want becomes very long, and , very often, surprisingly, more difficult to read. – kjetil b halvorsen – 2012-09-22T19:02:10.003

A lot of people have offered seemingly math-specific answers, but I don't see any problem here that's specific to math. Bad physics textbooks (i.e., most physics textbooks) tend to offer equations without interpretation. Bad history textbooks (i.e., most history textbooks) tend to describe events without giving interpretations that might offend, e.g., Italian-American parents who don't want to see Columbus painted as a scumbag. Textbooks are this way because students are usually happiest when fed facts to memorize, techniques to master. Students are unhappy when asked to do critical thinking. – Ben Crowell – 2012-09-23T02:21:04.337

2Most history textbooks? Where? Why are all questions and answers happening in the USA? – Yemon Choi – 2012-09-23T09:10:04.587

3The fact that this question was closed is itself an answer to the question. There are perhaps as many who do not understand the need for contextualization in math discourse, as those who are pained by the start lack of it. – ctpenrose – 2017-05-15T04:45:24.573

1@ctpenrose, this should be the accepted answer – Eric – 2017-05-15T12:37:53.560