2025 Joint Mathematics Meetings
Mikael Vejdemo-Johansson
Artists
Statement
In my mathematical art I seek to reify the abstract, to make mathematical concepts and shapes available to touch, to trace, to twist and turn. To create physical artifacts meant for interaction to bring the complex closer and make the abstract concrete. Over many years, I have primarily worked with computer assisted techniques - laser cutting and 3d printing, but I have come to enjoy how closely the physical manipulation of wire, chain or cable can get to the abstractions mathematicians regularly work with. This has led me to a new interest in shaping metal, in wire-wrapping, and in silver wire as an artistic medium.
Artworks
In this art work, working in argentium silver wire, the Knot Table up to 7 crossings is reproduced: each horizontal of the necklace carries one of these categories, with adjacent knots sharing the same degree of complexity, and as you go down you find simpler and simpler knots.
This part of the knot table has been known since the late 1800s. However - that has not been the case for the next few layers after the necklace ends: in 1973, Kenneth Perko found a duplicate in the 10-crossing knots. This duplicate - two versions of a knot whose diagrams are different enough to have gone unnoticed for almost a century - is known as the Perko Pair and accompanies the Knot Table necklace as a pair of earrings, hanging from subtle silver studs.