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 &quot;I had to go through this and figure out everything myself, so you should too&quot;.<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 &quot;Proofs and Refutations” by Imre Lakatos<p><a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Proofs_and_Refutations" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Proofs_and_Refutations</a><p>Part 1: <a href="https:&#x2F;&#x2F;math.berkeley.edu&#x2F;~kpmann&#x2F;Lakatos.pdf" rel="nofollow">https:&#x2F;&#x2F;math.berkeley.edu&#x2F;~kpmann&#x2F;Lakatos.pdf</a><p>Most of that foundational information is lost when it&#x27;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&#x27;s a huge problem, it applies to physics textbooks too, and it doesn&#x27;t have to be this way.  Unfortunately, the problem has been known for decades and there&#x27;s not much reason to expect things to change.  (Lakatos wrote the above in 1976.)