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