Proofs and Refutations

Cover of Proofs and Refutations by Imre Lakatos.

Proofs and Refutations is a book by the philosopher Imre Lakatos expounding his view of the progress of mathematics. The book is written as a series of Socratic dialogues involving a group of students who debate the proof of the Euler characteristic defined for the polyhedron. A central theme is that definitions are not carved in stone, but often have to be patched up in the light of later insights, in particular failed proofs. This gives mathematics a somewhat experimental flavour.

The pupils in the book are named after letters of the Greek alphabet.

Many important logical ideas are explained in the book. For example the difference between a counterexample to a proof (local counterexample) and a counterexample to a conjecture (global counterexample) are discussed.

The 1976 book has been translated into more than 15 languages worldwide, including Chinese, Korean and Serbo-Croat, and went into its second Chinese edition in 2007.

References

• Lakatos (1976). Proofs and Refutations. Cambridge: Cambridge University Press. ISBN 0-521-29038-4