Universiteit Leiden

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A mathematical shoe-tying award

Knots come in all shapes and sizes: mariners and scouts can vouch for this. Sjabbo Schaveling will obtain his PhD on 1 September for a mathematical method to distinguish between all these knots. ‘I flatten them to a pretzel.’

You have done research on knots. What kinds of knot should I imagine?

‘It really is about the knots that you come across in everyday life. The knot you use to tie your shoelaces or the way that the earbuds for your phone get tangled up. It’s a separate branch of mathematics that arose at the end of the nineteenth century. Physicists at the time thought that each atom was a different knot, so they wanted to classify all the possible atoms. That’s how knot theory as we now know it developed.’

What did you discover about knots?

‘I came up with what is known as an invariant. That’s a kind of algorithm that you can use to distinguish between and classify all the different types of knot. Our invariant is the most effective way to do that at present. I only have to do the calculation for the most complex knots because they require an incredible amount of processing power.’

Is this knowledge only of interest to sailors?

‘No, definitely not. Mathematical knowledge about knots is really important nowadays, for instance if you want to research the intertwining of atom lattices. These lattices form superconductors, for example, which are used in all sorts of applications such as MRI scanners. Knowledge about knots could help improve these superconductors.’

How exactly do you go about your work?

‘I do most of the work on a big blackboard. I begin with a specific knot, for example the simple overhand knot. Then I flatten this like a pretzel and draw it on the blackboard. This helps me see how many times the rope crosses. With an overhand knot that is three times. I then give each crossing point its own label, you could call it a kind of number. I then multiply these numbers, which gives each specific knot its own value.’

Do you do everything on a blackboard or do you sometimes resort to rope?

‘Sometimes! Before you draw a knot it can be useful to tie it yourself. When I was young my parents gave me a book of knots, which I still have now. It’s proven very useful in my current work because some knots are extremely complicated.’

Text: Merijn van Nuland

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