Now in the math literature it is alleged that Appel & Haken proved this conjecture that 4 colors are sufficient to color all planar maps such that no two adjacent countries have the same color. Appel & Haken's fake proof was a computer proof and it is fake because their method is Indirect Nonexistence method. Unfortunately in the time of Appel & Haken few in mathematics had a firm grip on true Logic, where they did not even know that Boole's logic is fakery with his 3 OR 2 = 5 with 3 AND 2 = 1, when even the local village idiot knows that 3 AND 2 = 5 with 3 OR 2 = either 3 or 2 depending on which is subtracted. But the grave error in logic of Appel & Haken is their use of a utterly fake method of proof-- indirect nonexistence (see my textbook on Reductio Ad Absurdum). Wiles with his alleged proof of Fermat's Last Theorem is another indirect nonexistence as well as Hales's fake proof of Kepler Packing is indirect nonexistence. Appel & Haken were in a time period when computers used in mathematics was a novelty, and instead of focusing on whether their proof was sound, everyone was dazzled not with the logic argument but the fact of using computers to generate a proof. And of course big big money was attached to this event and so, math is stuck with a fake proof of 4-Color-Mapping. And so, AP starting in around 1993, eventually gives the World's first valid proof of 4-Color-Mapping. Sorry, no computer fanfare, but just strict logical and sound argument. Cover Shows four countries colored yellow, red, green, purple and all four are mutually adjacent. And where the Purple colored country is landlocked, so that if it were considered that a 5th color is needed, that 5th color should be purple, hence, 4 colors are sufficient.