Computer Proof
Edited by Jordan Bohall (University of Illinois, Urbana-Champaign)
About this topic
Summary | Computer proofs are those proofs in mathematics that have been at least partially and, sometimes, completely proven by computer. The landmark Appel and Haken proof of the Four Color Theorem in 1976 used a large scale exhaustion-style proof method carried out partially by computer. Shortly before the Appel-Haken proof and up to the present, computer proofs have proven useful both in pure mathematics and areas such as artificial intelligence and machine learning. However, the proof-by-exhaustion methods are contentious in that they represent deductions which are not surveyable by humans in a reasonable amount of time. So, questions for computer proof involve what counts as mathematical proof, are empirical methodologies acceptable in pure mathematics, and do we have certainty that the theorem, etc. proven by computer are indeed proven. |
Key works | Tymoczko 1979, Burge 1998, Manders 1989 |
Introductions | Gowers 2008 |
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Related categories
Siblings:
- Godel's Theorem (119)
- Probabilistic Proof (11)
- Undecidability (44)
- Mathematical Proof, Misc (56)
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David Bourget (Western Ontario) David Chalmers (ANU, NYU) Area Editors: David Bourget Gwen Bradford Berit Brogaard Margaret Cameron David Chalmers James Chase Rafael De Clercq Ezio Di Nucci Esa Diaz-Leon Barry Hallen Hans Halvorson Jonathan Ichikawa Michelle Kosch Øystein Linnebo JeeLoo Liu Paul Livingston Brandon Look Manolo Martínez Matthew McGrath Michiru Nagatsu Susana Nuccetelli Giuseppe Primiero Jack Alan Reynolds Darrell P. Rowbottom Aleksandra Samonek Constantine Sandis Howard Sankey Jonathan Schaffer Thomas Senor Robin Smith Daniel Star Jussi Suikkanen Aness Kim Webster Other editors Contact us Learn more about PhilPapers |