Thanks for the article Cole! I'm a big fan of knot theory (I wrote an article for New Scientist a few years back about the topic).

The discovery of Kenneth Perko is a really interesting one. I got a bit tied up in knots (pardon the pun) when I chatted to knot theorist Professor Hans Boden (McMaster University) about Perko's discovery .

Apparently it is not strictly the case that the Perko pair are the same knot-- it's more correct to say that one is equivalent to the other after taking a mirror image.

Some knots are the same as their mirror images, some are not, and this isn't recorded in the knot tables. Sometimes a knot in the table refers to one and only one knot type, sometimes it refers to two possibly different knot types. Complicated stuff!

I am also duty bound to report that even though Perko is always described as an amateur mathematician, he had a PhD in maths, although I believe he worked as a lawyer. So he had the qualifications to match his legacy.

Thanks again for a great article!