On March 11th, it was time for another lecture in a series of public lectures hosted by the Oxford Mathematical Institute. The topic of the evening was knot theory. I had heard of this particular branch of mathematics before, but I was still greatly puzzled by how knot theorists could combine maths and knots. Thus, I was eager to hear what the lecturer, Marc Lackenby, a Professor at Oxford University, had to say about the topic.
Simply put, knot theory is the mathematical study of knots. The knots studied in knot theory are the same knots you would expect to find in everyday life. The only way they differ is that the knots studied in knot theory have their ends “glued” together, so that they may not be undone.
The simplest knot is called the unknot, which really isn’t a knot at all, just a ring. As Professor Lackenby put it “From here there are no limits, that we know of, to how many crossings a knot might have, and there exist thousands of different knots with varying level of intricacy.”
Later, he explained how Peter Tait, a Scottish physicist, was the first person ever to describe this level of intricacy in a knot as the knot’s “knottiness.” In 1885 Tait published the first ever knot tables which included knots with up to 10 crossings.
The world’s knot theorists have come a long way since Tait published his tables, and today knot theory is being applied to everyday life in fascinating ways. In his presentation, Professor Lackenby focused on how knot theory is being applied to biology, more specifically genetics.
Every human cell contains when stretched out, about two meters of DNA. For this to fit into one tiny cell, only a couple of micrometers wide, one can imagine that the DNA molecule needs to be exceptionally well curled up.
The replication of DNA is essential in order for cells to divide, and during this process, the big knot of DNA needs to be untangled. This is where knot theory comes into the picture. By understanding knot theory scientists can also better understand how DNA untangles and then coil up again. This is considered valuable knowledge in many professions, especially within medicine.
Overall the lecture was very fascinating and I believe that I now have a much better understanding of both the basics and also the application of knot theory. I highly recommend anyone who is, even remotely, interested in maths to attend one of these public lectures at Oxford University.
It is an excellent way of discovering new areas of maths, and I can guarantee you will be leaving the lecture with an increased passion for mathematics.