David Wells
The connections between chess and mathematics
Chess and Mathematics Conference, London,6th December 2014
Connections❖ Philosophical
❖ Mathematical Recreations
❖ Tactics and Strategy
❖ Proof and Proving
❖ Creativity
❖ Complete Analysis
Philosophical
It is much like a piece in chess - its nature is defined by simple rules
What is the number 2?
If the whole class learn chess, they will all move the pieces in the same way: total agreement.
When they master elementary arithmetic they will all operate with integers in the same way.
PentominoesGolomb’s Game
Pentominoes are mathematical objects yet Golomb's game is a perfect example of an abstract game: spot the cross-over.
Complete AnalysisCorner Game
The rook can only move up or right - any number of squares
Move here to win
Take turns to move rook
Corner GameShirley Clarke (1988)
'This kind of maths is so exciting for children. As Jermaine was writing his 'ideas for new rules', Nicholas was compulsively trying out his own ideas'.
"[this] theory about games seems to be true! The children started off by experimenting to test their theories but, in playing the game, it gradually dawned on them that there were mathematical reasons behind what was happening; they had moved on to the idea of proof."
Jermaine and Nicholas
Children’s observations"We were testing to see if the person who played first won.
As we were testing we found that if the player moved the rook onto the diagonal line you will always win.
Now we know this, the test is over because if you move first the other player will win because they go straight to the diagonal line."
Not interested in playing once the game was solved
Children’s Ideas for New Rules
Move only one square at a time or two squares
at a time.
Start only on white
Change the piece to bishop, king, queen, knight
You don’t have to move nearer to the
target square