Fermat's Near Miss

A lot of people have heard about Fermat's last theorem. Originally proposed in the 1600s, the theorem was finally solved in the 20th century by a mathematician named Andrew WIles. 

Fermat's theorem says that there are no solutions (x,y,z) to the equation x^n + y^n = z^n for n > 2. If you've studied math or physics at a university or in some cases high school level you have likely heard of it. Today I was reminded of an example from the Simpsons which is purported to show a solution where x^n + y^n = z^n. Specifically...

There we see 3987^12 + 4365^12 = 4472^12. And if you were to plug this into a handheld calculator, it would be correct!

So what is going on? How could Homer Simpson have a counter-example to Andrew Wiles proof? In fact, these numbers are so large that most calculators round the error off and they appear to be the same! X, y, z combinations like this that "solve" Fermat's last theorem are known as near misses. I was reminded of this interesting example by this video, but have also read it in this book.

Also of note, in the holy doughnut to filled in doughnut progression along the bottom of the chalkboard, Homer is "solving" a question in topology! Unfortunately, in topology, a doughnut and a sphere do not equate...