The Story of Fermat's Last Theorem

The story of Fermat's Last Theorem is actually one I have been interested in ever since I found a Numberphile video about it (link below). It began with 17th century judge Pierre de Fermat who did mathematics on his own as a hobby. He was reading a book called Arithmetica by Diophantus and wondered whether their was any whole number solutions to the equation X^n + Y^n = Z^n when n>2. Fermat believed that none existed and he wrote in Latin in the margin of the book, "I have a truly marvelous proof which this margin is too narrow to contain". Soon after, he drops dead leaving no written proof of his claim. Fermat's son discovered the book (which has many such claims) and republished it to include his father's notes. Through subsequent years, every claim Fermat made was proven to be correct. All except for the above equation, known as Fermat's Last Theorem. Into the 20th century, still no one could prove his theorem. Some believed that Fermat was cocky and did not actually have a proof. Some thought that he had a proof but since he worked alone no one checked it and found an error he must have made. Others however believed that his 'truly marvelous' proof did exist and had just eluded mathematicians for centuries. One such believer was a boy named Andrew Wiles who grew up in Cambridge. At ten years old he found a library book about this infamous theorem and was determined to prove it. He spent years asking his teachers and peers about it, learning as much as he could. When Wiles was in his late thirties he had a PhD and was teaching at Princeton yet he still lacked an answer. Around that time a link was found between Fermat's Last Theorem and an unsolved problem called the Taniyama-Shimura Conjecture. If one solved most of Taniyama-Shirmura, they would also solve Fermat's Last Theorem. Andrew Wiles secretly worked on this conjecture intensely for seven years. At the end of seven years, he suddenly realized that he had solved Taniyama-Shirmura and thus the Last Theorem. Wiles presented his proof to Cambridge and the media exploded with news of this great feat. However all  proofs must be checked for accuracy and an error was found in the proof. Wiles hoped to fix it easily but it took him one year to correct his embarrassing mistake. After a lifetime of searching, Andrew Wiles found proof that Fermat's Last Theorem, that no whole number solutions to the equation X^n + Y^n = Z^n when n>2 exists, was correct. Andrew Wiles solved a theorem that was widely believed to be unsolvable and thus made history.
http://www.numberphile.com/videos/fermat_theorem.html

The Paradoxicality