**Richard Morris
(rich@singsurf.org)University of Liverpool**

This paper was presented at the Visulisation of Mathematics Workshop
in Berlin (VizMath '95). And appears in "Visualization and Mathematics:
Experiments, Simulations and Environments", Hans-Christian Hege, Konrad Polthier (eds), Springer Verlag Heidelberg . ISBN 3-540-61269-6.

Postscript Version of the main text (gzipped postscript).

In section~\ref{tool_sec} we will look at a set of programs we have developed to tackle the basic graphical problems which occur in singularity theory. We will discuss some of the user interface issues as well as the algorithms used to create accurate representations of singular surfaces.

In section~\ref{example_sec} we will look at the role experimental results have to play in the development of mathematical proof. We will examine two cases studies which are good examples of this experimental method and illustrate some of the techniques needed for successful experimental analysis. In both cases there was a conflict between mathematical conjectures and the results generated by computer graphics. This conflict caused both the mathematics and the experimental results to be reexamined leading to a resolution of the problems. In the first case a the experimental results were shown to be correct and in the second both methods were partially correct and the final results had a much richer structure.

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