Before Watching
Let students explore the equation x^{n} + y^{n} =
z^{n} by substituting different values for n. Have them begin
with n = 2, resulting in the familiar Pythagorean Theorem,
x^{2} + y^{2} = z^{2}. Then have students change the
value of n to numbers greater than 2 to see whether they can find
solutions that will result in a balanced equation with a positive integer
answer for z.
To be sure that x^{n} + y^{n} = z^{n} has no
solutions when n is a positive integer greater than 2, every value for n
needs to be checked—a nearly impossible feat, even with the aid of a
computer. A proof is needed. Review with students the concept of theorem,
a mathematical statement that can be proved, or awaits proving. Then ask
them to describe ways that things can be proved in nonmathematical contexts,
such as in law, mystery novels, or in their everyday lives. How do these types
of proofs compare to mathematical proofs?
After Watching
Ask students to list the traits Anderw Wiles needed to solve Fermat's Last Theorem.
Which traits seem most important? Which seem least important?

