 Fragrance of geometry is a new branch of mathematics that describes the world as it is, rather than acting as though it's made of straight lines and cubes. Nearly everything in the human body is fractal. Everything from your nervous system, to your breathing system, to your blood supply system, to the arrangement of skin cells on the surface of the body. These things are always fractal. Why? Because they are developed by repeating patterns that evolve and grow tree-like structures or branched structures. The most important thing that's happened over the last 30 years is the transition from thinking about smooth spheres, smooth processes that have been very powerful in science, to thinking about rough processes and non-differentiable and broken processes. We have the mathematical tools to start to describe these rough objects. The formula for this teapot is no more complicated than a formula for something like a sphere. It looks rough and sort of random, but it's very precise. Every single wrinkle and dinkle in it is all part of the same fractal deformation, represented by a tiny formula. It opens up a whole new way of analyzing signals, for example, to do with signals that the body gives out. Basic idea is the following. Here is a complicated signal, such as a radio signal or my voice, and you can break it apart into its respective sum of components. When you look at it very closely, it becomes boring. It looks like a little bit of straight line. This one is very complicated. It comes out of your brain, and if you look at it very closely, well, it still looks like very complicated. Fractal Fourier, exciting advance. So you're able to not just model the boring old stuff, you can model the new stuff with exactly the same types of precision and error estimates. Vierstraß, 1878, Berlin. He came up with a function that was a nightmare to everyone. It's called the Vierstraß Nowhere Differentiable Function, and guess what it looks like? Well, it turns out that if you take a collection of Vierstraß functions with different scalings, you can take them and add them up just like we added up those ones to make arbitrary signals. That have the same complexity. It's just a good piece of mathematics as the formula for a sphere and the work of Euclid. There is now a modern geometry that handles beaches and seas and skies and clouds. ANU is the centre for the mathematics behind the description of these new structures. It's time to start thinking about fractals and stop thinking about spheres.