Why do many math books have so much detail and so little enlightenment? (2010)
The top-rated answer is either defeatist, or just rationalization for the sentiment "I had to go through this and figure out everything myself, so you should too".<p>There is a <i>huge</i> amount of information encoded in the choice of exactly how to define thing, and which theorems people care about. This reflects a long process of trial-and-error as the field was constructed.  For a famous philosophical treatise on this using the  Euler characteristic as an example, see "Proofs and Refutations” by Imre Lakatos<p><a href="https://en.wikipedia.org/wiki/Proofs_and_Refutations" rel="nofollow">https://en.wikipedia.org/wiki/Proofs_and_Refutations</a><p>Part 1: <a href="https://math.berkeley.edu/~kpmann/Lakatos.pdf" rel="nofollow">https://math.berkeley.edu/~kpmann/Lakatos.pdf</a><p>Most of that foundational information is lost when it's not written down somewhere accessible; contrary to the answerer, only a small fraction is reconstructed by students as they learn the subject.<p>It's a huge problem, it applies to physics textbooks too, and it doesn't have to be this way.  Unfortunately, the problem has been known for decades and there's not much reason to expect things to change.  (Lakatos wrote the above in 1976.)