Fermat: The World’s Greatest Troll

This handsome man is the great Pierre De Fermat. Born in the 17th century, he was a lawyer by day and a mathematician by night. What’s interesting about Fermat though is that he is increasingly more notable in the math world than he is in the law world.

He didn’t publish much, if anything, but he was included in some of the day’s math circles. So he was rubbing elbows with the best of the best and yet he was just a hobbyist mathematician. In fact, if he published some of his work, we might have actually ended up calling the 2d plane we know as the Cartesian plane (after Rene Descartes) the Fermatian plane.

Still though, none of this matters in comparison to what he was immortalized for.

First, picture this. You are sitting in your living room reading your book for English class and you have a discussion tomorrow so you are writing anything you find interesting into the margins of the book. You know, when you realize that this passage infers that Hamlet is completely ego-driven, or that this passage proves that Atticus Finch is the epitome of morality, or that this sentence proves that the monster from Frankenstein is all in Victor’s head. Specifics don’t matter since this is just an example but I hope it’s pretty easy to imagine, everyone in their lifetime has probably written something into the margins of a book.

Now Fermat is like everybody else. He was reading his copy of Arithmetica and he came across something he thought was interesting:

X2 + Y2 = Z2

And well, he decided to make note of a great thought he had in the margin. He wrote something along the lines of:

It is impossible to separate a cube into two cubes, or a fourth power into two fourth powers, or in general, any power higher than the second, into two like powers. I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.

I’ll break down what he is saying and give you some background.

X2 + Y2 = Z2

What you see above is many things, but you probably know it as the Pythagorean Theorem. What’s more interesting about this is that there is an infinite amount of integers (non-decimal) numbers that can satisfy this. If you have taken Geometry you know these to be Pythagorean Triples. Stuff like:
3,4,5
9,16,25
5,12,13
Essentially, you can keep having these all the way into infinity. That means you can keep going and get larger sets like:
77893200, 128189952, 150000048

What Fermat is saying though is that it doesn’t hold true for any power greater than 2. There is no sets that can satisfy:
X3 + Y3 = Z3
X4 + Y4 = Z4
X5 + Y5 = Z5
X6 + Y6 = Z6
X1000 + Y1000 = Z1000

There is no combination of 3 non-decimal numbers AT ALL that can be put into those equations above and have them be true.

What’s so great about that? Well the second part of his margin note is his claim to have a proof that shows it, it just can’t fit into the margin. Oh and by the way it’s “truly marvelous” too.

It also couldn’t be found at all.

That’s right, Fermat wrote in the margin of his math textbook that he has one of the best proofs ever and doesn’t have the proof to back it up.

The thing is though, Fermat is completely right, and everyone knew it. The whole math community knew it. But the tough thing about math is that no work or conjecture has any value without a proof. Everything you learn in class has already been brought through lines and lines of formalized logic that satisfies the math community’s strict no-failing case standards.

So this became known as Fermat’s Last Theorem (even though this technically wasn’t his last theorem, it’s just that it was found way after he died) and it became unsolved for a whopping 400 years. Sure some people solved certain cases but nobody created a general proof that would hold true for every case.

It wasn’t until the 1990s that it was fully proved.

The implications of this are simple. Fermat, the man who wrote one of the greatest problems in the margin of his textbook, also claiming to have solved it, is the world’s greatest troll.

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