David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
The computer played an essential role in the proof given by Kenneth Appel and Kenneth Henken of the Four-Color Theorem (4CT).1 First proposed in 1852 by Francis Guthrie, the four color problem is to determine whether four colors are sufficient to color any map on a plane so that no adjacent regions have the same color. Appel and Heken’s proof involves a lemma that a certain ‘avoidable’ set U of configurations is reducible. The proof of this critical lemma requires certain combinatorial checks which are too long to do by hand. The job was done by an IBM 370/168, using over 1200 hours of computer time. In 1977, Appel and Heken, assisted by John Koch, published the proof, and the 4CT has since been considered an established result. No one has seen the entire proof of the reducibility lemma. It was too long to print out; even if it had been, no one would be able to run through it step by step.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library||
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Casey Rufener (2011). The Four-Color Theorem Solved, Again: Extending the Extended Mind to Philosophy of Mathematics. Res Cogitans 2 (1):215-228.
Marian Mrozek & Jacek Urbaniec (1997). Evolution of Mathematical Proof. Foundations of Science 2 (1):77-85.
Andrew Aberdein (2006). Proofs and Rebuttals: Applying Stephen Toulmin's Layout of Arguments to Mathematical Proof. In Marta Bílková & Ondřej Tomala (eds.), The Logica Yearbook 2005. Filosofia. 11-23.
Anita Waselewska (1979). A Constructive Proof of Craig's Interpolation Lemma for M-Valued Logic. Studia Logica 38 (3):267 - 275.
Konstantine Arkoudas & Selmer Bringsjord (2007). Computers, Justification, and Mathematical Knowledge. Minds and Machines 17 (2):185-202.
Added to index2009-01-28
Total downloads80 ( #16,856 of 1,102,742 )
Recent downloads (6 months)3 ( #120,386 of 1,102,742 )
How can I increase my downloads?