Lecture 1 - Linking and knotting

Christopher Zeeman kicks off the very first Ri Christmas Lecture on Mathematics by exploring the complex properties of linking and knotting.

Across the lecture Professor Zeeman looks at a branch of mathematics called Topology, a form of geometry in which we "imagine things are made of rubber: we can bend them and twist them, but not cut or glue them".

As Zeeman states, it leads us to study "basic things like links and knots and holes and curves and surfaces and insides and outsides and surfaces with only one side (not only in 3-dimensions but also in higher dimensions)."

By looking at linking numbers, Zeeman unravels how a mathematical theorem can be used to describe the number of times two closed curves are linked. He also defines knotting numbers which are used to prove how various mathematical knots are different and takes a look at the impossibly shaped Möbius Strip.

We are also introduced to the concept of a mathematical proof and shown how to generate a 'theorem'. Zeeman demonstrates that once a theorem has been proved true, it can be used as the basis to prove further truths. Unlike science which sets out to disprove its truths, mathematical proofs stand true for all time.

Finally, if all this seemed a little abstract, Zeeman applies these concepts to the field of genetics, where mathematics has been used to provide fresh perspectives on the structure of DNA.






Sir Christopher Zeeman



All lectures in the series