Definitions, examples, theorems, proofs -- they all seem so inevitable. But how did they come to be that way? What is the role of counterexamples? Why are some definitions so peculiar? What good are proofs?
In this brilliant and deep -- yet easy to read -- book, Lakatos shows how mathematicians explore concepts; how their ideas can develop over time; and how misleading the "textbook" presentation of math really is.
Fascinating for anyone who has seen mathematical proofs (even high-school Euclidean geometry) and essential for anyone studying mathematics at any level.
(I wrote this review in 1996, before Amazon kept track of reviewers' names... some additional notes:)
If you'd like to read more discussion about Lakatos and the intellectual context of P&R, you'll be interested in Brendan Larvor's "Lakatos: An Introduction".