Why do many math books have so much detail and so little enlightenment? (2010)
Honestly, every time that a discussion on mathematics comes up in HN I feel the same way: people seem to think that mathematicians are some kind of elitist people that don&#x27;t know how to explain concepts, and that mathematics would be like coding (note: projecting everything into the tech world is not the best way to understand the world) if it weren&#x27;t because mathematicians don&#x27;t explain things well. But the reality is way different:<p>* We know that teaching mathematics is difficult. But, contrary to what most people think, there is no magic pill to solve it. Motivation and intuition are important, yes, but so are definitions and formality. Also, even when giving them to the students, they might not be useful: sometimes each person needs a different motivation of a concept, sometimes the intuition relies on more advanced concepts...  Furthermore, things don&#x27;t usually click the first time you are exposed to them, but only after you have worked with them for some time. Don&#x27;t think that just because you are given a motivation and intuition behind the concepts everything is just going to become easy to understand. Even motivations and intuitions need work to be understood.<p>* The mathematics people study in high school and first-year engineering courses is very different from the mathematics that mathematicians study. Funnily enough, most mathematicians I know don&#x27;t like the approach of mathematics as a tool for other disciplines, mainly because it focuses on things that are hardly interesting (here&#x27;s the 123th trick for how to solve this weird integral that we are teaching you only because you will need it to solve some engineering equation) and avoids proofs that, despite being hard, most of the time helps understanding the concepts.<p>* Related to the last points, an important number of math books are written not for laypersons but for mathematicians. They go straight to the point, avoid long motivations&#x2F;intuitions that are not specially useful and assume familiarity with a lot of concepts. Sometimes they are written as reference books for people that already know the ideas. That, of course, makes them hardly approachable by non-mathematicians, but there are already books that do that. Just because a book or a way to teach math is not of your liking does not mean it needs to be changed.<p>* Not all mathematical concepts need to have a direct application. Sometimes, things are studied just because they seem interesting or beautiful. Searching for motivation needlessly in these cases tends to be a waste of time. It&#x27;s like reading a novel or solving a puzzle: you don&#x27;t need to know &quot;why&quot;, just enjoy it. If you&#x27;re lucky applications can appear later, but there&#x27;s nothing wrong if they don&#x27;t.