Fermat's Last Theorem/Historical Note

Fermat's Note
As himself put it, sometime around $1637$:

Nobody managed to find such a proof, until it was finally proved by in $1994$.

It is seriously doubted that actually had found a general proof of it.

It is almost impossible that he found ' proof, since it uses areas of mathematics that were not yet invented in 's time.

himself left an outline of the proof for $n = 4$.

provided the full proof for $n = 4$ and also a proof for the more difficult case $n = 3$.

The cases for $n = 5$ and $n = 7$ were proved by, and  and others.

The case for $n = 7$ was proved by in $1840$.

At the time ' proof was published, the theorem had been established as true for all numbers up to $125 \, 000$.

Furthermore, where $n$ does not divide any of $x$, $y$ or $z$, it had been proved for all $n$ up to $253 \, 747 \, 889$.

In the words of :
 * Before beginning I would have to put in three years of intensive study, and I haven't that much time to waste on a probable failure.

, in the introductions to early editions of his, introduced Fermat's Last Theorem as an example of a $50$ point exercise, that is, a research problem.

In later editions, that is, those published after $1994$, it was downgraded to a $45$ point question.