# What is a proof?

Bundy, A. and Jamnik, M. and Fugard, Andrew J.B.
(2005)
What is a proof?
*Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences* 363
(1835),
pp. 2377-2391.
ISSN 1364-503X.

## Abstract

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 twentieth 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 defined? And can we give a logic-based account of such phenomena? We introduce the concept of schematic proofs and argue that they offer 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.

## Metadata

Item Type: | Article |
---|---|

School: | Birkbeck Schools and Departments > School of Social Sciences, History and Philosophy > Psychosocial Studies |

Depositing User: | Sarah Hall |

Date Deposited: | 14 Aug 2017 14:58 |

Last Modified: | 23 Feb 2018 10:12 |

URI: | http://eprints.bbk.ac.uk/id/eprint/19391 |

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