Reddit mentions of Mathematics: The Loss of Certainty (Galaxy Books)

I love "The Loss of Certainty" by Morris Kline

http://www.amazon.com/Mathematics-Loss-Certainty-Oxford-Paperbacks/dp/0195030850

Is the book about maths that I recommend to my non-mathematicians friends

Other books that I found really useful, informative, motivating and accessible in high school include Feynman's QED -- a really cool introduction to Quantum Electrodynamics that I read my senior year -- and Brian Greene's The Elegant Universe. I think somebody mentioned it already.

Mathematics, the Loss of Certainty is a really good discussion on the history of math. Also quite accessible. I read it my freshman year of college.

More tangential books that I've enjoyed include The Drunkard's Walk and Chances Are. They cover similar ground, though, and I like the latter better.

There's also some pretty good fiction that gives you the flavor of some of the mindbending concepts that can arise from physics. Robert Heinlein's Time for the Stars is a good "juvenile" book that takes a step into the Twin's Paradox. Time dilation pops up in Larry Niven's A World Out of Time as well. For solar system level astrophysics, Niven's The Integral Trees postulates a really cool alternative to planets.

I read most the fiction around the time I was in high school, with the exception of Time for the Stars. Ironically, it's the only one that I can guarantee doesn't have "adult themes." I don't know what sort of restraints your parents put on your reading, though. They're all good books.

The other thing, other than books I mean, you can do is find a mentor or club in your area that could help put you on your way. An astronomy club would be a good idea, but there may also be physics or chemistry styled mentors in your area. They're likely to act out of a local university or research center (I live in Huntsville, Alabama, where Marshall Spaceflight Center is located. I know they have outreach/mentoring programs).

Oh, and I know I'm going on, one last thing that I found really useful and fun was my involvement in summer programs. In my case, the big one was Mississippi Governor's School, a three week summer program. It was an awakening from a social standpoint. (Ten years later, a large proportion of my friends either attended it or I know via some connection to it, still.) And it had an astrophysics class, which was awesome. I know other states have programs like it (assuming you're in the US), and MGS at least is easier to get into than commonly believed. People think a counselor's recommendation is required, but it's not and you get two opportunities to attend, between sophmore and junior and junior and senior years. It's unlikely you're in MS, of course, but other places have similar programs.

Good luck with things and keep us posted. :)

A somewhat different (but still very interesting) perspective on the history of mathematics is presented by Morris Kline in his
Mathematics: The Loss of Certainty, highly recommend!