Now, you might think it strange that in a lecture on biology, I will be talking a lot about mathematics ... um ... If r may digress a bit ... When I was a student, mathematics, the language of clear abstraction, had nothing to do with life sciences like biology, the sphere of messy organic forms, cutting up frogs in the lab, and so on ... um ... In fact, I started doing biology precisely to avoid matl1s and physics. So, I've had a lot of catching up to do. We are all aware of how the sciences have come to inter-relate more and more, and not only will mathematics impinge more and more on biology but also, I am told, in the 21" century, the driving force behind mathematics will be biology. This is partly because mathematicians are always on the look out for more areas to conquer. But a far greater reason is that the subject has been boiled down to physics and chemistry - obvious attractions for mathematicians. A number of mathematical fields can be applied to biology. For example, knot theory is used in the analysis of the tangled strands of DNA, and abstract geometry in four or more dimensions is used to tell us about viruses. Again, neuroscience appears to be maths-friendly and equations can also explain why hallucinogenic drugs cause the users to see spirals.