Proofs and Refutations is essential reading for all those interested in the methodology, the philosophy and the history of mathematics. Much of the book takes the form of a discussion between a teacher and his students. They propose various solutions to some mathematical problems and investigate the strengths and weaknesses of these solutions. Their discussion (which mirrors certain real developments in the history of mathematics) raises some philosophical problems and some problems about the nature of mathematical discovery or creativity. Imre Lakatos is concerned throughout to combat the classical picture of mathematical development as a steady accumulation of established truths. He shows that mathematics grows instead through a richer, more dramatic process of the successive improvement of creative hypotheses by attempts to 'prove' them and by criticism of these attempts: the logic of proofs and refutations.
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'For anyone interested in mathematics who has not encountered the work of the late Imre Lakatos before, this book is a treasure; and those who know well the famous dialogue, first published in 1963–64 in the British Journal for the Philosophy of Science, that forms the greater part of this book, will be eager to read the supplementary material … the book, as it stands, is rich and stimulating, and, unlike most writings on the philosophy of mathematics, succeeds in making excellent use of detailed observations about mathematics as it is actually practised.' Michael Dummett, Nature
'The whole book, as well as being a delightful read, is of immense value to anyone concerned with mathematical education at any level.' C. W. Kilmister, The Times Higher Education Supplement
'In this book the late Imre Lakatos explores 'the logic of discovery' and 'the logic of justification' as applied to mathematics … The arguments presented are deep … but the author's lucid literary style greatly facilitates their comprehension … The book is destined to become a classic. It should be read by all those who would understand more about the nature of mathematics, of how it is created and how it might best be taught.' Education
'The whole book, as well as being a delightful read, is of immense value to anyone concerned with mathematical education at any level.' C. W. Kilmister, The Times Higher Education Supplement
'In this book the late Imre Lakatos explores 'the logic of discovery' and 'the logic of justification' as applied to mathematics … The arguments presented are deep … but the author's lucid literary style greatly facilitates their comprehension … The book is destined to become a classic. It should be read by all those who would understand more about the nature of mathematics, of how it is created and how it might best be taught.' Education
Book Description
Proofs and Refutations is essential reading for all those interested in the methodology, the philosophy and the history of mathematics. Imre Lakatos shows that mathematics grows through a process of the successive improvement of creative hypotheses by attempts to 'prove' them and by criticism of these attempts: the logic of proofs and refutations.
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The dialogue takes place in an imaginary classroom. Read the first page
Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
The dialogue takes place in an imaginary classroom. Read the first page
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Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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11 of 11 people found the following review helpful
By A Customer
Format:Paperback
One should start right off admitting that this is a book about different approaches to what a mathematical proof is and should be. However, for some weird reason, it is hard to put down - more fun and fascinating than seems credible. It is dramatized, but still - in rather donnish style and all the characters (a teacher and a bunch of students) are named after letters of the Greek alphabet. In short, an anomoly - but one you must read.
11 of 11 people found the following review helpful
By A Customer
Format:Paperback
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?
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.
8 of 10 people found the following review helpful
By A Customer
Format:Paperback
Probably the best philosophical book I have read. The book is both deep in its ideas, yet easy to read and comprehend.
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