Proofs and Refutations: The Logic of Mathematical Discovery

Category: Livres anglais et trangers,Science,History & Philosophy

Proofs and Refutations: The Logic of Mathematical Discovery Details

Imre Lakatos's Proofs and Refutations is an enduring classic, which has never lost its relevance. Taking the form of a dialogue between a teacher and some students, the book considers various solutions to mathematical problems and, in the process, raises important questions about the nature of mathematical discovery and methodology. Lakatos shows that mathematics grows through a process of improvement by attempts at proofs and critiques of these attempts, and his work continues to inspire mathematicians and philosophers aspiring to develop a philosophy of mathematics that accounts for both the static and the dynamic complexity of mathematical practice. With a specially commissioned Preface written by Paolo Mancosu, this book has been revived for a new generation of readers.

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Reviews

This is a book about mathematics in the sense that it does not really prove theorems but rather it talks about what it is like to make a theorem.The book starts with Euler's polyhedron formula. Then it goes on to search exceptions to this formula,leading to a tighter and tighter definition of a good polyhedron. The process is inspiring and you should try to find exceptions yourself instead of just reading them in the book. Each time you think the definition is waterproof, there is still some other clever monster construction that does not fit the bill. It shows how easy it is to think you have a general theorem and the value of having counterexamples.I love this book and would probably recommend it. The only thing against it is the somewhat dated style.

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