KNOTS IN a shoelace or a length of twine can be a nuisance but they have proved an inspiration for mathematicians.
The study of knots has been a rich source of important discoveries for those using maths to describe them, explained one of the world’s leading theoretical physicists.
Prof Edward Witten of Princeton’s Institute for Advanced Study was in Dublin yesterday to deliver the annual Hamilton Lecture at Trinity College Dublin.
He explained the obvious simplicity but also the hidden complexity of knot theory in a presentation entitled “The Quantum Theory of Knots”.
Knot theory really is linked to actual physical knots and not just imaginary ones. Using the maths can help answer questions such as whether a knot can be untangled, explained Prof Witten before the lecture. “A knot is what you think it is, a tangled bunch of string.”
Knots are interesting because they are a real world object that can be described in the real world’s three dimensions. “Geometry started by dealing with things you can see,” he said before his talk. “In the beginning people were just curious about knots, “ he said. “They started with knots because they could see them like the Greeks could see plane geometry,” he said.
Mathematicians began delving into the subject, however, and started making interesting discoveries. “Knots sound like playthings but it turned out mathematicians in the 20th century developed deep theories of knots,” Prof Witten said.
Early interest including his own was fuelled by an insight related to knot theory known as the Jones polynomial, developed by Vaughan Jones in 1983.
Knot theory gained prominence again just over a decade ago after work by mathematician Mikhail Khovanov.