This third perspective on proof comes from a mathematician with a more traditional perspective than Borwein s. The author brings his considerable experience both in developing his own proofs and in reviewing others' to questions about the roles of proof His discussion on the roles of proof contains some interesting new ideas, such as proof as exploration and proof as justification of dl!finitions-ideas that are relevant to us as we think about how we teach mathematics. At the end he offers some

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... extended illustrations of his main points. from his experience working in topological dynamics and ergodic theory.