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Title:What is a proof?
Authors: Alan Bundy ; Mateja Jamnik ; Andrew Fugard
Date:Oct 2005
Publication Title:Phil. Trans. R. Soc A
Publication Type:Journal Article
Volume No:363(1835) Page Nos:2377-2392
To those brought up in a logic-based tradition there seems to be a simple and clear definition of proof. But this is largely a 20th century invention; many earlier proofs had a different nature. We will look particularly at the faulty proof of Euler's Theorem and Lakatos' rational reconstruction of the history of this proof. We will ask: how is it possible for the errors in a faulty proof to remain undetected for several years - even when counter-examples to it are known? How is it possible to have a proof about concepts that are only partially de ned? And can we give a logic-based account of such phenomena? We introduce the concept of schematic proofs and argue that they over a possible cognitive model for the human construction of proofs in mathematics. In particular, we show how they can account for persistent errors in proofs.
2005 The Royal Society All Rights Reserved
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Bibtex format
author = { Alan Bundy and Mateja Jamnik and Andrew Fugard },
title = {What is a proof?},
journal = {Phil. Trans. R. Soc A},
year = 2005,
month = {Oct},
volume = {363(1835)},
pages = {2377-2392},
doi = {10.1098/rsta.2005.1651},
url = {,4,13;journal,15,146;linkingpublicationresults,1:102021,1},

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