The Beauty of Doing Mathematics: Three Public Dialogues

Certainly the discussions are very interesting. The interactions between Lang and the audience, comprimising mostly 'ordinary' people but also high-school and college students, set this book apart from a textbook. Lang does a fairly good job at covering the material (relating to primes, Diophantine equations, and a bit of geometry/topology) and explaining it to the non-mathematically-inclined. Of course, with this come problems - Lang only skims over the material and much of what he says is not supported by proof.

If you would like an interesting read, I would recommend this book. However, if you would actually like to learn something about Goldbach's conjecture or elliptic curves, (first and second dialogues, respectively) a textbook or book dedicated to the subject is a much better source. To compare it to an everyday situation: if you had a conversation with friends, and taped and transcribed it - reading it certainly may be interesting, but not very informative.

However, if you like material like this - I suggest you also search for "Martin Gardner" here on amazon.com; he's an excellent author for those not deeply involved with math (and even those who are).