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.

Mathematical RecreationsPentominoes

Mathematical and playful

PentominoesGolomb’s Game

Pentominoes are mathematical objects yet Golomb's game is a perfect example of an abstract game: spot the cross-over.

Tactics and Strategieswith Fox and Hounds

Proof and ProvingNoughts and Crosses

Create your own GameJohn Conway's Phutball

Create ProblemsChess

White to play and draw

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

Tower of Hanoi

– David Hilbert

“Mathematics is a game played according to certain simple rules with meaningless marks on paper.”

“Games may have the potential to provide students with a mathematically focused activity while engaging them through a perception of fun.”

– Leicha Bragg

FALSE

TRUE