## CLASSICAL GAS --

PROOF READERS' UPDATE, JANUARY 1990: THE FOUR COLOR MAP THEOREM

In 1976, Kenneth Appel and Wolfgang Haken of the University of Illinois solved the Four Color Problem.[1] Among mathematicians, the proof was met with both jubilation - at the solution of a problem that had defied solution since Francis Guthrie first posed it in 1852 - and dismay. Many mathematicians were troubled because the proof made unprecedented use of computer computation. It was feared that the correctness of the proof could not be checked without the aid of a computer.

[Some background: The Four Color Problem is one of the few great mathematical problems that even a non-mathematician could appreciate. The problem was to prove that you would never need more than four different colors to "color in" the "countries" on a map -- any map -- so that no touching countries would have the same color.]

In 1982, I, together with my fellow members of the American Society of Proof Readers, took up the task of checking Appel and Haken's proof using only traditional means. Our work is funded by the U.S. Government's Strategic Defense Advanced Research Projects Agency. Each January, we issue a brief public statement about our progress. This is the sixth such report.

Three members of the Proof Reading team died during calendar 1989, reducing our total number to one hundred seventeen. It was decided to reduce the standard Proof Reading work week to ten hours per day, six days per week; this measure was effected primarily due to cost constraints newly imposed by the funding agency.

This year, forty-three person-years were expended in preparatory computation related to the semi-critical open subsets of phi-six that satisfy the Bend Condition.[2]

The preponderance of Proof Reading time, as in previous years, was devoted to iterative and/or recursive computation related to the introductory portions of the proof.[3]

The nature and importance of the task is at all times paramount in our thoughts. This is an exhaustive proof.

### NOTES

[1] Appel, Kenneth and Haken, Wolfgang, "Every Planar Map is Four Colorable," Contemporary Mathematics, vol. 98, American Mathematical Society, 1990. This 741 page document is a concise outline of Appel and Haken's original, computer-aided, proof.

[2] See Appel and Haken, pg 216 ff. This is the sort of task that we, and presumably Appel, would ordinarily delegate to troublesome graduate students. However, the overarching importance of this proof precludes us from delegating any portion of it, no matter how straightforward, to unproven personnel.

[3] Outlined in our annual statement issued January 1983.

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