A mathematican walks into a bar accompanied by a dog and a cow. The bartender says, “Hey, no animals are allowed in here.”

The mathematician replies, “These are very special animals.”

“How so?”

“They’re knot theorists.”

The bartender raises his eyebrows and says, “I’ve met a number of knot theorists who I thought were animals, but never an animal that was a knot theorist.”

“Well, I’ll prove it to you. Ask them them anything you like.”

So the bartender asks the dog, “Name a knot invariant.”

“Arf! Arf!” barks the dog.

The bartender scowls and turns to the cow asking, “Name a topological invariant.”

“Mu! Mu!” says the cow.

At this point the bartender turns to the mathematican and says, “Very funny.” With that, he throws the three out of the bar.

Outside, sitting on the curb, the dog turns to the mathematican and asks, “Do you think I should have said the Jones polynomial instead?”

Notes. The dog is, of course, referring to the Cahit Arf-invariant of knot theory, while the cow is referring to the Milnor mu-invariant of algebraic topology.