First, a quick note that Brit Richard Elwes, one of my favorite popular math writers, has a new volume out "Maths In 100 Key Breakthroughs":
I'll note that Elwes' books, published in Britain, unfortunately are not always readily available in the U.S. right away, and sometimes show up at a later date, under a different title! (but worth keeping an eye out for)
Speaking of favorite math popularizers, I've had occasion to think about Martin Gardner lately, and so will re-run one of his classic puzzles that I used here a couple years back -- am quoting it directly from his "The Jinn From Hyperspace" volume:
"Now for a final paradox. There is a certain event that I guarantee will or will not take place during the next ten minutes. You are absolutely incapable of predicting correctly whether it will or won't occur. I don't mean that it's unlikely you can predict it. I mean it is logically impossible to predict it!
"You don't believe it? Then do the following. If you think the event will occur write 'Yes' inside the blank rectangle below. If you think it won't happen, write 'No' inside the rectangle.
"The event is: You will write 'No' inside the rectangle."
A wonderful paradox/conundrum entangled with self-reference, causation/prediction, and human language and logic.
I should have a bit more to pass along about Martin in an upcoming post at MathTango, but for now you can read the current post up there about "skepticism."