Mathematics for April Fool's Day
In his April (1975) column in Scientific American, Martin Gardner claimed that this 110region map required five colors and was thereby a counterexample to the fourcolor "theorem" (at most four colors are needed to color any planar map whose regions share a common boundary but do not share the same color).
I remember being caught up in the attempts to color in the regions...I even gave it to my middle school students to play with as extra credit. Then, in a subsequent issue, Martin Gardner confessed that his entire April (1975) column was an April Fool's joke on his readers.
In fact, Stan Wagon, mathematics professor at Macalester College, produced a coloring that shows only four colors are needed to color Gardner's map.
It is now interesting (around this year's April Fool's Day) to look back at this hoax and how Martin Gardner introduced it:
As a public service, I shall comment briefly on six major discoveries of
1974 that for one reason or another were inadequately reported to both the scientific
community and the public at large. The most sensational of last year's
discoveries in pure mathematics was surely the finding of a counterexample to
the notorious fourcolormap conjecture. That theorem, as all readers of this
department must know, is that four colors are both necessary and sufficient
for coloring all planar maps so that no two regions with a common boundary are
the same color. It is easy to construct maps that require only four colors, and
topologists long ago proved that five colors are enough to color any map.
Closing the gap, however, had eluded the greatest minds in mathematics.
Most mathematicians have believed that the fourcolor theorem is true and
that eventually it would be established. A few suggested it might be Godelundecidable. ]
H.S.M. Coxeter, a geometer at the University of Toronto, stood
almost alone in believing that the conjecture is false.
Coxeter's insight has now been vindicated. In November 1974 William
McGregor, a graph theorist of Wappingers Falls, N.Y., constructed a map of
110 regions that cannot be colored with fewer than five colors.
McGregor's technical report will appear in 1978 in the Journal of Combinatorial
Theory, Series B.
William McGregor is an actual person, who created the map and gave Gardner permission to use it as an April Fool's prank. In the followup column, Martin Gardner seemed almost apologetic:
I never dreamed anyone would take it seriously, yet it produced more than
a thousand letters from readers who did not recognize the column as a hoax.
