Knot Sliceness

Every single knot has to bound a disk in four dimensional space. The question is, how nice is the disk? And this is really what comes about when you talk about sliceness. In particular, there is this knot called the conway knot that was due to john conway when he was tabulating the knots. He needed to figure out whether or not this particular knot, this new knot that was a mutant of the other knot, was smoothly sliced.