Summary

Mathematics is art as much as it is science. The cover picture, on the Review that this Symposium celebrates, is such an example. It is pretty and intriguing, yet it's relevant. The Review considered mathematical sciences research and advanced mathematical services in Australia for the next 15 years, until the year 2010. Fortuitously, the graph of the Kummer sum $\sum\exp\bigl(2\piin^3/2010\bigr)$ is particularly attractive:

 

`Normalisation' of these curlicues provides an interesting example of chaos. Quantum Electro-Dynamics (QED) entails that curlicues appear as a secondary diffraction phenomenon. So all this is not just a pleasantry.

Sums of the kind pictured here, arise naturally in fundamental mathematical questions. Their study is difficult, whilst modern computation, particularly a laser-printer and its PostScript$_{\hbox{\small{\tiny$\scriptscriptstyle\circledR$}}}$ language, make actually drawing these graphs almost trivial. And as always, a picture may be worth a thousand hours of intense study and calculation.

  ( PostScript$_{\hbox{\small{\tiny$\scriptscriptstyle\circledR$}}}$ is a registered trademark of Adobe Systems Inc.)