# OddThinking

A blog for odd things and odd thoughts.

### Colouring History

Every now and again, when I think I am working on something terribly esoteric and pointless, I am heartened by considering the lifetime work of Camille Jordan. (Actually his name was Marie, but he called himself by one of his middle names – Camille. Perhaps the fact that his wife’s name was Marie-Isabelle had something to do with that.)

To understand the genius of this well-regarded French mathematician, we need to do a little experiment together.

Posit a simple closed curve, C, in the plane R2… oh err… sorry. Please permit me to start again.

Take out a pencil and a sheet of paper. Start drawing a swirly line, around the page and, without lifting the pencil and without letting the line cross, make sure you finish up at the same point you started, to form a curvy loop. With me so far? What you just drew is called a Jordan Curve after our hero Monsieur Jordan.

The next step is to take out a felt-tipped pen and colour in the inside of the loop. Still with me?

If you are, you clearly do not have the genius of Jordan, because he was the first person to say “Whoa! Wait a moment! You can’t just assume that such a loop has an inside and an outside! That’s something you need to prove first!” (Of course, he probably said it in French, which probably made it sound more geniusy.)

Legend has it, he then spent much of the rest of his life trying to prove that you could colour the inside of a Jordan Curve. He thought he had succeeded at one stage, but his proof turned out to be incorrect. It wasn’t until after Jordan’s death that Oswald Veblen managed to finally prove the Jordan curve theorem, and colourers-in around the world could finally nod in relief, and break out the Derwents.

So, if what you are working on seems rather pointless, remember Jordan. Remember his esoteric, pointless and ultimately futile goal in life made him famous enough to have a curve, an asteroid and an institute named after him.