Proofs and Refutations: Facts, Discussion Forum, and Encyclopedia Article

Proofs and Refutations

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	Topics Proofs and Refutations Topic Home Proofs and Refutations is a book by the philosopher Imre LakatosImre Lakatos Imre Lakatos was a philosopher of mathematics and of science. ... expounding his view of the progress of mathematicsMathematics Mathematics is the discipline that deals with concepts such as quantity, structure, space and change.... . The book is written as a series of Socratic dialogueSocratic dialogue Socratic dialogue is a genre of prose literary works developed in Greece at the turn of the fourth century BCE, preserved to... s involving a group of students who debate the proof of the Euler characteristicEuler characteristic In algebraic topology, the Euler characteristic is a topological invariant, a number that describes one aspect of a topologi... defined for the polyhedronPolyhedron A polyhedron is a geometric shape which in mathematics is defined by three related meanings.... . A central theme is that definitionDefinition A definition delimits or describes the meaning of a concept or term by stating the essential properties of the entities or ... s are not carved in stone, but often have to be patched up in the light of later insights, in particular failed proofMathematical proof In mathematics, a proof is a demonstration that, assuming certain axioms, some statement is necessarily true.... s. 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 counterexampleCounterexample In logic, and especially in its applications to mathematics and philosophy, a counterexample is an exception to a proposed g... 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.