Nothing so esoteric — it’s written for the popular audience. But there’s a lot of “what is mathematics?” or “how do we do mathematics?” Some random highlights:

> A big part of mathematical training is becoming acquainted with different concepts and recognizing how they’re cousins to each other.

> I encourage everyone to fool around with numbers—some enthusiasts discover important patterns that way, and some famous mathematicians, like the late John Conway, made a career of it.

> When we give word problems in school, we tend to cherry-pick perfect models that have one correct answer. Rather than teach a preordained procedure, we could encourage exploration by asking students to fix more realistic models where things are slightly noisy or slightly incorrect.