Math IAFFour Color TheoremMatt ReedFour Color TheoremI. IntroductionSince the beginning of travel and exploration, maps have helped people record the specifics of new and unexplored regions of the Earth. Early maps were crudely hand-drawn and were rough estimates of geographic area based on interpretation of the terrain. Once people began to color maps, to designate divisions within regions, the problem arose regarding the number of colors needed to color a map.II. History The theorem was first proposed by August Ferdinand Moebius in 1840. However, the problem was ignored until 1856. In 1856, Francis Guthrie proposed the conjecture to his brother Frederick who then took the problem to the attention of his advisor; Auguste De Morgan. From this point on, a series of mathematicians sought to prove that it takes a minimum of four colors to color each region of a map without adjacent regions being the same color.III. The theorem The theorem developed in a series of stages between the 1840s and the 1980s. Multiple false proofs and conjectures were proclaimed in the 1850s. However, they were all eventually refuted. A precursor to the proof, written in 1890 by Heawood, details the use of five colors to shade regions of a map. However, the proof involving four colors was ultimately not proven until the 1970s. This proof was one of the first ever proven by a computer, which caused a revolution in the solutions of mathematical conjectures. Although imperfect, Kempe's purported original proof of the four-color theorem provided some of the basic tools later used to prove it. Kempe's argument is as follows. "First, if the planar regions separated by the graph are not trian...... middle of paper..., many interpretations of the proof have been refuted and constructed. Additionally, the four-color theorem was the first proof to be solved using a computing device, creating controversy over its legitimacy as a proof of its time. However, now that computers have been integrated into our daily lives, they have become evidence in their own right that will continue to be used as long as new places to map are discovered. Works Cited O'Connor, JJ and EF Robertson. “The four color theorem”. The four color theorem. Np, September 1996. Web. February 04, 2014.Rogers, Leo. “The four color theorem”. : Nrich.maths.org. Np, and Web. January 8, 2014.Thomas, Robin. “An Update on the Four Color Theorem.” AMS.org. Np, August 1998. Web. January 5, 2014. Wilson, Robin J. Four Colors Are Enough: How the Card Problem Was Solved. Princeton, New Jersey: Princeton UP, 2002. Print.