There are so many connections between games and maths that it is no wonder that many mathematicians play chess or Go or Bridge, or that so many abstract game players are into mathematics.

The presence of rules or underlying assumptions, the fact that expert chess players can play games in their heads, just as most people can do at least some calculations in their heads and maybe visualise a cube sliced symmetrically into two parts; the fact that there are tactics and strategies for solving problems in chess and mathematics; the confidence that we – often but not always! – feel that our conclusions are correct, that we can prove them, and the reliance of the chess player and mathematician on patterns and structure – these shared features all point to deep underlying connections between mathematics and abstract games. Let's start with perhaps the most remarkable of all – that they can both ‘in theory’ be done in the mind.

Games and mathematics can be analysed in the head . . .

. . . provided we make allowances for limitations of memory and visualisation. Few of us have Euler’s phenomenal memory. On the other hand, even first-school children are expected by their teachers to do simple sums by ‘mental arithmetic’ and all strong chess players can informally discuss a game they have just played with limited recourse to the board.