ABSTRACT
Fermat ’s most famous comment (called Fermat ’s Last eorem today) is found in his marginal notes to a Latin translation of Diophantus ’ (A.D. 250) works, where Fermat wrote that the expression xn + yn = zn is true for no integer n that is greater than two. ere are many sets of numbers x, y, and z for which x2 + y2 = z2 (the Pythagorean eorem ) is true-for example 32 + 42 = 52 and 52 + 122 = 132. Fermat ’s statement was this: ere are no whole numbers x, y, and z such that when all three numbers are raised to the same power that is greater than two, the equation is true. For example, there are no integers x, y, and z for which x3 + y3 = z3. He then famously wrote, “I have a marvelous proof of this, but this margin is too small to include it.” Mathematicians tried to discover his proof (or any other proof, for that matter) for the next 350 years. Andrew Wiles at Princeton University fi nally accomplished it in 1996, leaning heavily on several discoveries that had been found in the intervening years. It is likely that Fermat ’s own proof was fl awed although his conclusion was correct: ere are no values of x, y, and z for which xn + yn = zn is true for any value of n greater than two. Since we don’t have Fermat ’s work, we can only be skeptical about the validity of his proof.
