# The Dictionary of Mathematical Eponymy: The Jordan Curve Theorem

### What is the Jordan Curve Theorem?

The Jordan Curve Theorem is the sort of thing I adore about mathematics. It states (I paraphrase):

A 2D loop that doesn’t cross itself has an inside and an outside (and the two are separate).

That might strike you as the kind of thing that’s obvious. Indeed, for a long while, the *whole mathematical community* was on your side: it’s so obvious, it doesn’t need to be proved.

And it *is* obvious, at least for polygons – the trouble comes when you look at loops made out of something like a Koch snowflake curve or a Weierstrass function that doesn’t behave like the kind of closed curve you’re probably imagining.

### Why is it interesting?

I think it’s interesting because it’s an example of something that’s straightforward to state, blooming *obvious* to the passer-by, yet quite difficult to prove formally. (For a long while, mathematicians didn’t think Jordan’s proof of the result was quite solid; in fact, it just left a few details to the reader.)

It can be generalised to more dimensions (a simple closed surface in 3D has an inside and an outside; a closed volume in 4D has an inside and an outside, too).

It’s a result that’s important because it reminds us that sometimes even the most obvious things still need to be proved.

### Who was Camille Jordan?

Marie Ennemond Camille Jordan was born in Lyon, France in 1838. He studied at the École Polytechnique, and worked as an engineer before becoming a teacher.

Among other things, he popularised Galois theory and studied groups generally; he was also renowned for eccentric notation. What’s not to love?

Although many things are named after Camille Jordan, some things that *aren’t* include Gauss-Jordan elimination (Wilhelm Jordan) and Jordan algebras (Pascual Jordan).

He died in Paris in 1922.