It is an in-joke among math types....

"What do you call a person who can't tell a coffee cup from a doughnut?"

answer.. A Topologist...

... Yesterday I got the following release from Nature.com on my news link...

"A team of three has solved a 45-year-old problem in the mathematics of topology.

The Kervaire invariant problem is 'one of the major outstanding problems in algebraic and geometric topology' says fellow mathematician Nick Kuhn, at the University of Virginia in Charlottesville."

Ok, I admit, I never heard of the Kervaire problem, but that doesn't mean I am topologically stupid, and so when they showed the picture at the top, my mind jerked.. ????

Sure enough, later in the article, they had the comparison I expected, right before a rather complicated description of the details of the Kervair invariant. It said, "Algebraic topology is a way of describing the properties that objects with the same topology have in common. Topologically equivalent objects are objects that can be converted into each other by deforming but not tearing them: a sphere and an eggshell, for example, or a

**doughnut and a coffee cup**." (my emphasis).

But of course they mean a coffee cup with a handle, like this one, so that both shapes are really a form of torus (doughnut) like objects. Spheres punctured with a single hole.

Ok, not they probably told some intern to get a file picture of a doughnut and a cup of coffee, and he did, but from top science mags... you just expect a little more.

Which brings me to my final question for someone who really knows topology.... is a Mobius Strip also a Genus one object like a torus?