An exhibition should convey some flavour of the real achievements of mathematics. If instead it simply presents an assortment of, for example, strange polyhedra, and states that these are the wonderful things mathematicians study, then it will be very easy for the public to be convinced that mathematics is hard or weird or both. Each exhibit should have a mathematical point and should explain its relations with other parts of mathematics and with other disciplines. In the case of this exhibition, we felt the most surprising idea that could be conveyed in a way related to everyday experience was the analogy between knots and numbers revealed by the notion of a prime knot. It is for this reason, as well as for the needs of exposition, that we devote more than one board to this topic.
Surprising applications are also important for conveying some of the excitement of mathematics.
Key aims of mathematics are to show new perspectives, views, and order in what seems initially a tangle of unanalysable phenomena. This is one impression of mathematics that we wish to convey to the viewer. Here is where we feel we are really breaking new ground. Mathematics lacks an adequate discussion of methodology. A majority of students of mathematics do not know what they are doing or why they are doing it, they know only that they have to learn how to do certain things.