The Mathematics of Map Coloring :: Colors Science Essays

The Mathematics of Map ColoringThe four-color conjecture has been one of several unsolved numerical problems. From 1852 to this day, practically every mathematician has studied the problem long and hard, but to no avail. The conjecture looks as though it has been solved by Wolfgang Haken and Kenneth Appel, both of the University of Illinois. They have employ computer technology to prove the conjecture. The calculation itself goes on for about 1200 hours. The staggering length of the computation of the proof is what creates some controversy in the mathematical world. The Appel-Haken Theorem is found on numerous assumptions, that there is an overwhelmingly great probability that their method of proof must succeed. 3 It assumes that the theory itself is correct, but the theory itself is also an assumption. You can calculate why this issue has been wreaking havoc for many years. It all started back in 1852 when Francis Guthrie was coloring a map of England. He wanted to know the least bill of colors, or chromatic good turn, it would take to color the map so no two adjacent regions are of the same color. He found the chromatic number to be four. He and then studied arbitrary maps and wondered if all maps could be colored with four colors. Francis curiosity would be in the minds of all mathematicians to come. He then passed this question on to his brother, Frederick. He then submitted this to his professor Augustus deMorgan as a mathematical conjecture. deMorgan was fascinated by the Four-Color problem and wrote in a letter to his mate Sir William Rowan Hamilton the next day after seeing the conjecture. Hamilton was less enlightened by it, and never worked on it. It was through deMorgan that the Four-Color problem was made known, thus deMorgan has wrong been dubbed the originator of the problem. Eventually the hype surrounding the conjecture died down in the early 1860s. This down time, during which interest i n the problem was minimal, only lasted about twenty years. A lawyer by the name of Alfred Bray Kempe proposed a solution in The American Journal of