Mathematicians
Kenneth Appel
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American mathematician who, with Wolfgang Haken at the University of Illinois at Urbana-Champaign, proved the four color theorem in 1976, the first major theorem proved with essential computer assistance. The proof checked roughly 1,900 unavoidable configurations for reducibility, using about 1,200 hours of computer time, and could not be verified by a human reading it line by line. Appel later chaired the mathematics department at the University of New Hampshire.
Facts
BirthplaceBrooklyn, New York, United States 2 Death PlaceDover, New Hampshire, United States 2 Nationality / Culture Defining ContributionWith Wolfgang Haken, proved the four color theorem in 1976 using an unavoidable set of reducible configurations checked by computer, the first major theorem proved with essential computer assistance. 1 Notable WorkEvery planar map is four colorable, Part I: Discharging and Part II: Reducibility (Illinois Journal of Mathematics, 1977, with Wolfgang Haken); Every Planar Map Is Four Colorable (American Mathematical Society, 1989, with Haken) 1 AwardFulkerson Prize, American Mathematical Society, 1979 (shared with Wolfgang Haken) 3 Cross-Tradition Connections
Sources
1. MacTutor History of Mathematics Archive
University of St Andrews, School of Mathematics and Statisticshttps://mathshistory.st-andrews.ac.uk/Biographies/Appel/Quote, https://mathshistory.st-andrews.ac.uk/Biographies/Appel/
Kenneth Appel was an American mathematician best-known for his part in proving the four-colour theorem.
2. Kenneth Appel (Wikipedia)
Wikimedia Foundationopening paragraphQuote, opening paragraph
Kenneth Ira Appel (October 8, 1932 - April 19, 2013) was an American mathematician who in 1976, with colleague Wolfgang Haken at the University of Illinois at Urbana-Champaign, solved the four-color theorem, one of the most famous problems in mathematics.
2. Kenneth Appel (Wikipedia)
Wikimedia FoundationBiography sectionQuote, Biography section
He died in Dover, New Hampshire, on April 19, 2013, after being diagnosed with esophageal cancer in October 2012.
3. Celebratio Mathematica, Wolfgang Haken, A Biographical Sketch
Thomas, The Four Color Theorem (Faculty Reference Page)
Robin Thomas, Georgia Institute of Technology, School of MathematicsProofs Credited: Four Color TheoremView the Source Dissenting Readings (1 dissenting reading)
Proofs Credited: Four Color Theorem
Robin Thomas, who with Neil Robertson, Daniel Sanders and Paul Seymour published a simplified but still computer-assisted proof of the theorem in 1997, has written that part of the Appel-Haken proof uses a computer and cannot be verified by hand, and that even the part that is supposedly hand-checkable is extraordinarily complicated and tedious. The objection is not that the theorem is false, every attempt to verify it independently, including a fully machine-checked formal proof by Georges Gonthier in 2005, has confirmed it, but that a proof containing a step no human can read and check line by line changes what counts as mathematical justification, a question the philosopher Thomas Tymoczko raised in a 1979 paper in the Journal of Philosophy that remains cited in discussions of the theorem's significance.
A dissenting reading, from Robin ThomasRobin Thomas, Thomas, The Four Color Theorem (Faculty Reference Page), Georgia Institute of Technology, School of Mathematics
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