These are books that capture something about the "mathematical experience" without getting into the subject matter. The hope is to give a sense of what "doing mathematics" feels like. My target is somebody who doesn't really get why mathematicians do what they do, but wants to understand better.

In a very real sense, this is an impossible task. How can you understand what being a mountain climber is like if you've never even thought about climbing a mountain? There is little you can do about translating most of the direct experience. However, there have been several skilled writers who have successfully conveyed important aspects of mountain climbing, such as the motivations and emotions and aspirations, which even somebody who has never seen a mountain in person can understand. I'd argue that mathematics is a lot more accessible than mountain climbing in this regard, as it is something that we encounter and unconsciously use everyday.

To keep the list's length reasonable, my criteria is that the book should be about mathematics in this larger sense, but whose main topic is not mathematics or mathematicians per se. In particular, no popularizations of mathematics nor biographies of mathematicians. However, as I am looking for accounts of the mathematical experience, a few of these are written by mathematicians who talk about technical mathematics. But in these exceptional cases, understanding said mathematical content is inessential. You should be able to skip over any and all such mentions without missing the main point.