If you are asking me if I typed it wrong, I didn’t. Andrew Wiles, an American mathematician solved a mathematics problem for 8 years. Wiles spent most of his vacant time at his attic solving the problem by hand.
In 1995, he finally succeeded.
I promised that we will not solve problems in this blog, so I will keep that promise (Kidding, I won’t be able to solve that problem in a hundred lifetimes). I will just introduce to you the problem that gave Wiles and other mathematicians headaches almost all their lives.
The problem is an extension of the Pythagorean Theorem. Recall that the Pythagorean Theorem states that in any right triangle with legs and and hypotenuse ,
Notice that we can find integers , and that satisfies the equation, or geometrically, we can find right triangles whose side lengths are integers. For example, satisfy the equation because
The problem states that there are no integers that will satisfy the equation for all integral powers (the exponents must be positive integers) greater than 2. That is,
where , are integers and any integer greater than 2. Now, Wiles needed to show that the statement is either true or false. Sounds simple right?
The problem above is the Fermat’s Last Theorem (FLT) because it was the last among Fermat’s conjectures to be proven by that time. The FLT was proposed by Pierre de Fermat in 1637. Hundreds of mathematicians have attempt to solve it for more than 350 years, but nobody succeeded. Wiles succeeded in solving the problem making him one of the greatest problem solvers in the history of mathematics.
So if the problem set given to you by your teacher or professor is difficult, think of Wiles as an inspiration.