TITLE: How to appreciate Fermat's last theorem?
QUESTION [8 upvotes]: I am someone who is not a Maths major, these days (during the summer) I am attracted to Fermat's Last Theorem. I understand that there is no whole number solution to the equation $x^n + y^n = z^n$ for $n\gt 2$ but doing a simple calculation we can have a non-whole number solution?
So, my question is this: What is that the whole numbers are that important?

REPLY [3 votes]: Integer solutions of a problem are essential in many areas. You wouldn't like that the number of persons to fit in the room be $13.5$, would you ?
But besides this obvious pragmatism, it turns out that all research around integer solutions of equations, the so-called Number theory, ends-up in numerous beautiful (and difficult) extensions that make the delight of mathematicians.
Fermat's last theorem is a perfect example, having required an army of the finest minds for several centuries before the answer was found.
Interestingly, Number theory makes a heavy use of techniques drawn from the theory of real and complex variables.