There's much in recent mathmatics that is of interest to the non-specialist - if you know the right place to look. In A Mathematical Tourist: snapshots of modern mathematics
, Ivars Peterson, a sicence journalist, investigates some of the recent discoveries and finds all sort of fascinating topics to report on. There are prime numbers and their use in cryptography together with higher dimensional objects and how they apply to managing businesses. The chapter on Twists of Space
looks at soap films, topology, new types of crystals and knot theory, with a description of how chemists have tried to create knotted molecules. And there's plenty on fractals, chaos, cellular automata, and a lot more besides.
The book is getting on for 20 years old (I read the 1988 edition), and a lot more mathematics has been done in that time, but I didn't feel that the book was particularly dated. Since Peterson's itinerary in mathland is pretty packed, I'm not sure that the book is for the total novice. On the other hand, if you've got a bit of mathematical experience then you shouldn't find the book too difficult - and there are plenty of pictures to help the journey along. I feel that it'sthe sort of book which will stimulate the reader to try to find out more about the topics covered.