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Original language | English |
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Pages (from-to) | 2377-2391 |

Journal | Philosophical Transactions A: Mathematical, Physical and Engineering Sciences |

Volume | 363 |

Issue number | 1835 |

DOIs | |

State | Published - Oct 2005 |

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

- mathematical proof, automated theorem proving , schematic proof, constructive omega rule

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ID: 400701