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Not my line of work and I wish I fully understood all of this discussion.

There is a video, scroll down to the photo/LINK. John Conway in 1990 explaining how in high school he showed why two knots can’t cancel each other out.

THe question of the Conway knot’s sliceness was famous not just because of how long it had gone unsolved. Slice knots give mathematicians a way to probe the strange nature of four-dimensional space, in which two-dimensional spheres can be knotted, sometimes in such crumpled ways that they can’t be smoothed out. Sliceness is “connected to some of the deepest questions in four-dimensional topology right now,” said Charles Livingston, an emeritus professor at Indiana University.

What’s slice? It’s the umbrella term for two properties that this kind of mathematical knot can have. And a mathematical knot is a whole major field of study unto itself, inspired by regular knots that can exist in real life.

Imagine if you tied your shoelaces like usual, but the ends weren’t loose—instead, the laces form a circle. They’re classified by the number of crossings, counted anywhere the strand of the knot crosses itself as you do when you begin to tie any regular knot.

The results of these twisting math knots are one part Cat’s Cradle and one part M.C. Escher. And what they represent is just as abstract. The plain loop is called the unknot, and all true knots must pass a test of whether they can be untangled into an unknot.