My favorite "math author" is Sherman Stein. I have a couple of his books, both of which I recommend. The first one I read is called Strength In Numbers, and the second is How The Other Half Thinks. I met Stein one time at his home, and also went to a book signing he did once. A retired math professor, he was exceedingly able not only to talk about math, but also to explain it to people for whom math does not come easily.
How The Other Half Thinks is a book that, in a clear and interesting way, explains mathematical thought processes to "words people". I had a reverse "How The Other Half Thinks moment" today.
In my pre-calculus class we are beginning trigonometry, and today we discussed (among other things) the topic of coterminal angles. If it's been awhile since you studied angles, an example of coterminal angles would be a 30 degree angle and a 390 degree angle--angles that are a revolution (or multiple revolutions) apart, but both have the same sine, the same cosine, the same tangent, etc. One girl was having a difficult time with the concept, and then the lightbulb seemed to go on. "So, in words, they're kind of like synonyms?"
That's one of the awesome-est non-math explanations of a math concept I've ever heard!