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# An Analysis of the Last Mathematical Theorem by Pierre de Fermat

Fermats Last Theorem is a mathematical enigma that has stumped mathematicians for hundreds of years According to Andrew Wiles The definition of a good mathematical problem is the mathematics it generates rather than the problem itself Singh 163 Pierre de Fermat see diagram one a seventeenth-century French civil servant and judge and amateur mathematician first introduced it His greatest love was number theory httpwww-groupsdcsst- andacuk-historymathematiciansFermathtml Number theory is concerned with the study of whole numbers the relationships between them and the patterns they form He also developed the main ideas of calculus But his Last Theorem was by far his greatest challenge httpwww-groupsdcsst-andacuk7EhistoryHistTopics Fermats lasttheoremhtml To understand Fermats theorem one must first understand Pythagoras equation His equation states that In a right-angled triangle the square of the hypotenuse is equal to the sum of the squares on the other two sides see diagram two In symbols x2 y2 z2 z is the length of the hypotenuse the longest side and x and y are the lengths of the other two sides Such an example would be 32 42 52 therefore 9 16 25 25 25 Fermat considered the cubed version of this equation x3 y3 z3 Eventually he also considered if these equations would have a solution x4 y4 z4 x5 y5 z5 and so on He wondered if there could be a solution to any of these equations and came to the conclusion that there was none So Fermats Last Theorem is xn yn zn has no whole number solution when n is greater than 2 httpwwwmerseyworldcomgrogers While Fermat was reading about Pythgoras Theorem in his copy of the book Arithmetica by Diophantus see diagram three he wrote in 1637 I have discovered a truly marvelous proof of this which however the margin is too small to contain Aczel p9 This message was

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