i'm going to remove your links and just add a ref to the paper i linked above the unknotting problem is a very special case of the more general recognition problem which is also algorithmically decideable also the link to the blog is just a bad idea the blog post is a confused discussion of the erroneous mathworld snippet i'd spend some time giving a better description of these issues and format the refs but i'm planning on rewriting the whole article anyway got started earlier today talk