The great mathematician G.H. Hardy wrote a slim book that is great for mathematicians and non-mathematicians alike. Best of all
As fifty or more years have passed since the death of the author, this book is now in the public domain in the Dominion of
So yes, you can get it for free, here.
I highly recommend it. (Did I mention it is a great read for non-mathematicians, too. It really is.)
Thanks to @anitleirfall on twitter for pointing this out.