You might like to look at the article "Making a mathematical exhibition"
http://pages.bangor.ac.uk/~mas010/icmi89.html
With regard to content we agreed that the aims were to:
suggest that the making of mathematics is a natural human activity, part and parcel of the usual methods by which man has explored, discovered, and understood the world;
present each item with a purpose and context, and not just because it was something that could be shown or demonstrated;
convey an impression of some of the key methods by which mathematics works;
show mathematics in the context of history, art, technology and other applications.
(In the end, item 4. was much too ambitious! But it led to a collaboration with John Robinson in presenting his Symbolic Sculptures.) The subject of knots is suitable for conveying things about mathematics. You can see the exhibition "Mathematics and knots" at
In this area we could present the methods of:
- Representation
- Classification
- Invariants
- Analogy
- Decomposition into simple elements (and I would also include, laws of combination)
- Applications
See also articles on my web page on "Popularisation and Teaching"
www.bangor.ac.uk/r.brown/publar.html
This experience of popularisation, and presentations to 13 year olds in Masterclasses, proved very useful when I was invited to give talks to a wide range of scientists, who are very interested in what conceptual advances are being made in mathematics (rather than solutions to "million dollar problems"). See arXiv:math/0306223 , to a conference on theoretical neuroscience.
