Brendan W. Sullivan. Everything You Always Wanted To Know About Mathematics. Pittsburgh, Department of Mathematical Sciences Carnegie Mellon University , 2013.

How do you know whether something is true or not? Surely, you've been told that the angles of a triangle add to 180°, for example, but how do you know for sure? What if you met an alien who had never studied basic geometry? How could you convince him/her/it that this fact is true? In a way, this is what mathematics is all about: devising new statements, deciding somehow whether they are true or false, and explaining these findings to other people (or aliens, as the case may be). Unfortunately, it seems like many people think math-ematicians spend their days multiplying large numbers together; in actuality, though, mathematics is a far more creative and writing-based discipline than its widely-perceived role as ever-more-complicated arithmetic.