The Colossal Book of Mathematics

These fall more in the "pop-sci" realm, but I think are really good at trying to convey what kinds of things working mathematicians actually think about: - Colossal Book of Mathematics by Martin Gardner: Uses games and recreational math to introduce areas like group theory and topology. - Finding Moonshine by Marcus Du Sautoy: Tells the story of the unexpected connection between two areas of math that, on the surface, seem to be completely unrelated. - The Great Mathematical Problems by Ian Stewart: Does a good job explaining several of the major open problems in math today.

I second this! Gardner would be something more recreational and fun than a lot else out there. The Colossal Book of Mathematics is a good way to get a lot in one place. The Night is Large is also great but less math-focused. I don't see any recommendations for Smullyan yet. The Lady or the Tiger is the classic I think, but I really loved Forever Undecided.