I like to look and compare chess and mathematics in terms of possible propadeutics for future studies in school and life. Propaedeutics (from the Greek. Propaideio – will go before) – a short course that introduces the study of a subject – is to prepare the listener for the successful perception of the basis of the material in teaching him some of these skills and competencies and creating an intuition that would contribute to more successful and a thorough knowledge of the substantive content of the course.
As we know, the entrance to the Academy of Athens was decorated with the inscription: “Let None But Geometers Enter Here”(Plato). In the Gymnasium the role of geometry was assigned as propaedeutics of philosophy which was studied in the Academy. We are offering the role to chess. Not o the game of chess, but to use the specific set of properties chess has as educational tool.
Presenting a remarkably intuitive, and therefore relatively easy to master and consistent framework, based also on a clearly formulated forms of axioms (rules of the game), so far the game of chess, as propaedeutics, has – in comparison with the previously used propaedeutics as geometry and different types of logic has a number of fairly obvious advantages. The critical advantage of the game of chess to the geometry or logic lies in the fact that today it can successfully fulfill the role as a universal intellectual propaedeutics, contributing, if used correctly, education of students of many qualities and competencies, as needed in their life ahead.
For the talented person with a right mindset, a chess game can become a constant source of creative intuition, because once acquainted with this amazing structure, people usually have never forgotten it completely at all, – unlike, many of the things taught us by our school teacher. Studying chess you can more easily transfer the learning.
You can not really learn chess. There are too many different positions to remember. Mathematics you can learn- simply remembering the formulas. However chess teaches you that this is not the solution. There is not so many chess-mathematics problems. I like to present two of them.
1.There is an Euler problem. The Knight supposed to move all around chess board and hit every square only once. Euler proved that it is possible. Now the problem is the following.
Prove that if the Knight starts the journey at the square a1 he can not end up at the square h8 hitting all other squares once.
Hint. You need to use odd and even number properties.
2. Can we prove that in a game of chess White never loses.
We can not, but lets change the rules so, that White and Black can make two moves in a row instead of one.
Prove that in this case White never loses.
Hint. Proof by Contradiction.
There is a conference in London Chess and Mathematics
I sent the following poster to the confererence and you may download it here as well.