Why do many math books have so much detail and so little enlightenment? (2010)
It&#x27;s totally cultural. The culture comes with some costs, and some benefits.<p>In physics, there are so many times where we present the same mathematical ideas in a manner that&#x27;s way more ergonomic for the minds we&#x27;re talking to-- other physicists.<p>Inexperienced mathematicians tend to see these presentations and are kind of gobsmacked, &quot;why did no-one tell me it was that simple and concrete?&quot; Experienced mathematicians tend to see these presentations and cringe, &quot;don&#x27;t they understand it&#x27;s not that simple and concrete? For instance, look at this pathological example here that contradicts everything they just said.&quot;<p>The slick presentations are great if you&#x27;re a physicist or anyone just wanting to <i>use</i> the ideas. And they&#x27;re great if you&#x27;re an inexperienced mathematician trying to get your bearings as fast as possible. But once you&#x27;re a research mathematician, trying to <i>build new ideas</i>, too many slick presentations of ideas just creates groupthink. You want as many people to generate their own mental pictures as possible.<p>That said, few people studying mathematics go on to be research mathematicians. The mathematics culture should be much, much friendlier to people whose endgame is not being a math prof. Apathy toward those whose ambitions lie outside the ivory tower is a problem endemic to most academic subcultures.<p>Finally, when reading anything generated by academia, remember <i>most of it is crap</i>. Academics are fired if they don&#x27;t make enough noise. This is truer than you think, even taking into account metrics like &quot;impact&quot;. You can make a lot of &quot;impact&quot; just by making enough noise. And you generally can&#x27;t make &quot;impact&quot; on a short timescale without making enough noise. Once your name shows up enough in a field, you&#x27;ll get known as &quot;a name&quot;, and start being cited in that field. Even when your work is drivel. If your name only shows up a couple of time in a field-- unless your work incredibly well written and you get a good dose of luck-- it&#x27;ll take years before it gets uncovered and appreciated, if it ever does.<p>Think of how much more attention you pay to what someone like maxxxxxxxx says here. Sure. He&#x27;s good. But he&#x27;s also familiar. It&#x27;s primarily his familiarity, more than his quality, that makes you feel like he&#x27;s one of &quot;names&quot; in this little subfield of the internet called hacker news.