Fermat's last Theorem states that: “there is no solution with non-zero integers (neither X = 0, nor Y = 0, nor Z = 0) for the equation xn + yn = zn, if n is an integer greater than 2". This theorem is one of the most famous in the history of mathematics and was envisioned by Pierre de Fermat in the year 1637, however it was considered by many illustrious mathematicians as the one that has had the most erroneous publications at the time of being verified. If you analyze a bit, you can say that this theorem was actually a conjecture, since it represents something that is believed to be true but has not yet been proven.
Finally, it could be solved by Andrew Wiles in 1995. Wiles with the collaboration of the mathematician Richard Taylor, achieved the feat of being able to prove this theorem, based on the Taniyama Shimura Theorem. If this theorem, which states that if every elliptic equation has to be modular, was incorrect, then Fermat's theorem was also false. Reaching the answer of Fermat's last theorem.
Wiles, gathered all the ideas of the problem that had seduced him since childhood, he looked for a way to show the existence of an elliptical curve associated with each modular form, when he did this, he found the Taniyama Shimura theorem, which he applied to the Fermat, and although he found a bug in his first proof, it was fixed. Wiles managed to solve one of the most complicated problems in history, becoming one of the most famous mathematicians still alive. Being awarded the Abel prize appreciated by all as the nobel of mathematics. And which is awarded by the Norwegian Academy of Sciences and Letters that annually awards this famous award in mathematics.
