Pierre de Fermat was a French Mathematician. Not what we might call the 'best' mathematician, he is probably only really the one to raise this particular problem to peoples attention.He owned a copy of "Arithmetica", the famous mathematical text written by Diophantus. This book was composed of 130 algebraic problems. One of which consisted of the following:
We are all aware of the Pythagorean Theorem, a^2 + b^2 = c^2, where c is the length of the hypotenuse and a and b are the lengths of the other two sides in a right angles triangle.
With this equation, you can get numerous whole number solutions, for example:
3^2 + 4^2 = 5^2
9 + 16 = 25
5^2 + 12^2 = 13^2
25 + 144 = 169
These are called Pythagorean Theorems, and there are infinitely many of these, where a, b and c are all whole numbers.
However, in Arithmetica, Diophantus conjectured this:
for a^n + b^n = c^n when n is bigger than 2, is there any whole number solutions?
In this book, Fermat made a lot of marginal notes. In a lot of these, he claimed he had a proof for the problems, however it seems that we have never found any proofs that he did for the problems. All the problems he says he had proofs to, do have proofs. However, they were all solved by other people later on. It is called Fermat's "Last" theorem, because is was the last of the problems that Fermat claimed to have a proof to, to be proven.
With all honesty, I am unable to see how Fermat could have solved this problem. He was an amateur mathematician. Andrew Wiles, the man who had eventually solved the problem dedicated 7 years of his life towards the problem, going to the best schools, colleges and universities, and an amateur mathematician in the 17th century was able to solve it? In the marginal note, Fermat said that "The proof was to large to put in the margin". Andrew Wiles' proof was over 150 pages long. Oh 'really' Fermat? The proof is 'too big' to put in the margin? Additionally, the mathematics used in the proof for the theorem was not really available to Fermat at the time. And I highly doubt there is an easier way to solve the problem, that we are failing to see, when Wiles spent 7 years on the problem.
Although, credit to Fermat, no one would of really cared about the problem as much as they do if Fermat didn't bring it to peoples awareness by pretending he could solve them.
