What is a proof?

Alan Bundy, Mateja Jamnik, Andrew Fugard

Research output: Contribution to journalArticlepeer-review

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 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
Original languageEnglish
Pages (from-to)2377-2391
JournalPhilosophical Transactions A: Mathematical, Physical and Engineering Sciences
Volume363
Issue number1835
DOIs
Publication statusPublished - Oct 2005

Keywords

  • mathematical proof
  • automated theorem proving
  • schematic proof
  • constructive omega rule

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