How not to write popular math:
Cheating: spreading false math to communicate easily, spreading the false impression that some things are easy when they are not and, on the contrary, clouding behind mysteries things that could be explained. Taking short cuts which are plainly false. Appealing to magic.
Concentrating on personal stories. While it is undoubteable undoubtable that a good story is always the easiest way to keep the attention high, and that informations information on people that did math help helps in conveying some good math, I found that recently, in way too many popular math books, biographical notes are overwhelming the math content.
Let me end with an example of both. In many popular books about infinity and math stories about mental illness of Cantor or Godel abounds and are more or less explicitely explicitly linked with "devoting thoughts to infinity". This is used to shroud infinity into a cloak of misterymystery, some magic world in which one can lose his mind, and to raise attention. This is, in my opinion, doing a very bad job both in popularizing math and in writing a story.
