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.

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.

EditorsG++ introduction Part I Philosophy of Mathematics 1 Infinite regress and foundations of mathematics 2 A renaissance of empiricism in the recent philosophy of mathematics? 3 Cauchy and the continuum: the significance of non-standard analysis for the history and philosophy of mathematics 4 What does a mathematical proof prove? 5 The method of analysis-synthesis Part II Critical Papers 6 The problem of appraising scientific theories: three approaches 7 Necessity, Kineale and Popper 8 Changes in the problem of inductive logic 9 On Popperian historiography 10 Anomalies versus G++crucial experimentsG++ 11 Understanding Toulmin Part III Science and Education 12 A letter to the director of the London School of Economics 13 The teaching of the history of science 14 The social responsibility of science References Lakatos bibliography Indexes.