Recent political enquiries to get at the truth of some scandal have had to contend with witnesses that colour their testimonies by self-interest and their own perception of what is significant.
Mathematicians also want to get at the truth. They observe phenomena and patterns that they want to understand and fit into a coherent whole with a line of logic that leads from accepted facts to often deep, obscure and surprising results.
This can be done in a way that does not depend on weighing assertions according to some bias and that can command everyone's agreement. It is often possible to sculpt ideas so that the arguments can be surprisingly clear and elegant.
I will look at some "case histories" that, even though they are genuinely mathematical, do not require school knowledge and involves only the sort of wit that you might bring to any parlour game of strategy.
Notes for this lecture are available in PDF format. They currently do not include the diagrams used in the talk.