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This paper uses a book, "Proofs and Refutations: The Logic of Mathematical Discovery," as an example of Lakatos's use of dialogue. The book was originally adapted from his dissertation and influenced by Polya and Popper. His discussion of the Euler conjecture is summarized. Three purposes for choosing the dialogue form for the book were that it helped to achieve the polemical intent, that it accurately reflected the role of criticism in the growth of knowledge, and that it modeled how mathematics education might be conducted. One disadvantage of the writing style is that the book evokes an emotional reaction from readers, such as delight or disgust. Another disadvantage is that the dialogue itself often veils Lakatos's own position. (YP)