What is the Fermat's Last Theorem?

In 1637 the French mathematician Pierre de Fermat noted down, on the page of a book he was reading, that he had found a wonderful evidence for a certain theorem, but he told that the margins of the book were too small to write that. So, Fermat died without publishing that proof but he had launched the mystery which lasted more than 350 years to be solved!

Why did that theorem become so famous?

One of the reasons for the fame of the theorem is connected to the simplicity of its statement. Starting from the Pythagoras theorem: `x^2 + y^2 = z^2` which has lots of solutions. Fermat replaced the exponent `2` with `n` and he stated that in the case `n > 2`, the equation `x^n + y^n = z^n` does not have a solution. Another reason for the fame of this theorem was that throughout centuries lots of brilliant mathematicians have tried to demonstrate the truthfulness of this theorem. Some of them have devoted their lives to that. However, they have never been able to demonstrate it.

Has the Fermat’s theorem already been demonstrated?

Yes, it has. On October 1994 Andrew Wiles displayed a demonstration through more than 200 pages. Although there are few people who understand it, it has been accepted as being the demonstration of the famous theorem. Wiles has secretly devoted himself to the demonstration and has surprised the public and so he was recognised worldwide.

But... Did Fermat have a shorter demonstration?

It was thought not. In spite of have written he had a demonstration, it is believed it is not true since people had to wait centuries to display a demonstration of the famous theorem. Actually, it was only demonstrated after the appearance of computers which had unprecedented abilities of calculation. Besides that the evidence that was shown by Wiles used very elaborated techniques which were not known at the time of Fermat. Would Fermat have found a simpler method? The mystery is in the air!

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