I think Gödel, Escher Bach does a good job imparting the "mathematical mindset", albeit indirectly. It's a great read even if it's quite long and a bit repetitive. Definitely worth a read if you're not already familiar with abstract mathematics and formal logic.
I have read that actually. I think it was much heavier on the 'logic' than the mathematics though, if you know what I mean. Great book though... love how it doesn't even really get started on its main topic (AI) until about three quarters in, having covered a vast range of supporting topics.
