This is a story book. It chronicles a series of high school lessons about crystal shapes called polyhedra. The class spend the whole book in a lively, wryly humorous and immensely readable dialogue with their teacher, trying to find a mathematical definition that makes sense. The reader is drawn in to the characters, their arguments and the way the plot develops.
Along the way you find that you are discovering how to do maths. I don't mean the nuts-and-bolts, how to do the boring stuff like equations, but the interesting things that make you wonder, like why, whether, what is it anyway and, most significant of all, how to do better next time. Oh, and what a polyhedron is not, too - you'll be amazed at how many lousy definitions mathematicians have nailed their flag to over the years. But that's the point Lakatos is making, maths is not some dead library catalogue that grows and grows, it is forever being torn up, burned and rewritten better than ever.
The most frightening thing about this book is its title. Get past that and you are in for a truly enjoyable ride, with no more visible maths than a few simple and well-illustrated geometrical ideas to absorb.
There are some rather more heavyweight appendices, but you don't have to plough through those unless you want to.
Lakatos' book is a real classic and serves as an excellent introduction to the philosophy of mathematics.
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