Editing Proofs and Refutations (section)

{{Short description|1976 book by Imre Lakatos}}
{{Infobox book
| name              = Proofs and Refutations: The Logic of Mathematical Discovery
| image             = ProofRefute.jpg
| author            = [[Imre Lakatos]]
| language          = 
| genre             = [[Philosophy of mathematics]]
| published         = 1976
| publisher         = 
| isbn              = 978-0-521-29038-8
| pub_date          = 
| editors           = 
}}

'''''Proofs and Refutations: The Logic of Mathematical Discovery''''' is a 1976 book by philosopher [[Imre Lakatos]] expounding his view of the progress of [[mathematics]]. The book is written as a series of [[Socratic dialogue]]s involving a group of students who debate the proof of the [[Euler characteristic]] defined for the [[polyhedron]]. A central theme is that [[definition]]s are not carved in stone, but often have to be patched up in the light of later insights, in particular failed [[Mathematical proof|proof]]s. This gives mathematics a somewhat experimental flavour. At the end of the Introduction, Lakatos explains that his purpose is to challenge [[formalism (mathematics)|formalism in mathematics]], and to show that [[informal mathematics]] grows by a logic of "proofs and refutations".