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Friday, December 28, 2007

The Four Color Theorem

Theorem: A plane separated into regions can be colored by no more than four colors such that regions which share a common boundary do not have the same color.

Conjecture first made by Francis Guthrie

1879: Alfred Bray Kempe provided a proof for the conjecture and received great acclaim

1890: Percy John Heawood showed that Kempe's proof was wrong.

1976: Four color conjecture becomes four color theorem for a second time. Four Color theorem proven by Appel and Haken, using a computer.

Hence, the first computer assisted proof was born. The four color theorem cannot be verified by other mathematicians without the use of a computer.

Point.

Is it ok for mathematicians to put their faith in computers? Can such proofs be accepted? (By the way, Mathematicians have already accepted it.)

Small point.

Mathematicians can make mistakes. Maths can't be true all the time. (see what happened to Kempe)

Sources:
http://www.mathpages.com/home/kmath266/kmath266.htm
http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/The_four_colour_theorem.html.
http://mathworld.wolfram.com/Four-ColorTheorem.html

:Noted:

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