Ho Math Chess Research and Articles > Do Chess and Math Have Anything in Common?

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9 Mar 2007

Do Chess and Math Have Anything in Common?


Frank Ho


Ho Math and Chess Learning Center




Chess has many math characteristics that mostly are learned in elementary schools. There are other math related topics such search tree of a possible moves etc., which are high level thinking math and is related to artificial intelligence.  Definitely chess and math are related in various math subjects and areas. My research area is in elementary mathematics and chess so I would like to talk about how chess and elementary math have something in common and perhaps also touch on topics on the areas that are unique in their own way. In other words, they are totally not in common.


Chess deals with whole number system so it is very comfortable for a young child to learn chess and at the same time to learn our whole numbering system. The chessboard is normally square in shape and players use chess notation, this definitely is “borrowing” the concept of coordinates from math, but it only serves to benefit child. Image a 5 year old is learning the X and Y coordinate system math concept by learning chess?


The concept of relative values of chess pieces is similar to the concept of using unknowns in the algebra, and yet the chess values are very meaningful to children. Why a queen could be numerically substituted by a value of 9? This constant value is the most beautiful concept that we could use to teach a child to learn the concept of substitution and function while they having fun.


Chess provides a conduit to lead a child to learn some math concepts without any hard pressure. They practice their critical thinking skill while pondering the next best move; considering all the pros and cons; weighing all the possible moves. This process of thinking involves data gathering, analyzing, synthesizing and integrating which is all critical thinking skills.


The benefits of using chess as a means of developing critical thinking while other teaching “tools” are not readily available is a child can constantly get feedbacks from opponent while they socialize and entertain each other. The wrong moves could get penalized by the opponent – an immediate feedback of their critical thinking skill, no other critical thinking training course could provide such an instant response and so much entertainment value.


The checkmate and check pattern is just amazing and there are no other substitutes which could be used to train youngsters this kind of patter recognition and spatial relation. A number of 3 added to another number of 5 is just plain 8 in math workbooks. In chess, this calculation is not just a vertical 3 plus 5 or horizontal 3 plus 5 we see most of the time in worksheets. It could involve a rook and knight attacking the same piece and the directions are multi-direction and the way to solve this type of question involves spatial relation and pattern visualization.


The chess pattern and math pattern is so different that I have not been able to find anything in math pattern which could replace the ”cause and effect” pattern in chess since the chess position has a purpose that is to check or checkmate or attack, defend etc., but this kind of pattern does not exist in math.


The distance of some chess moves does not make sense at all from math point view. How could a knight takes more moves to reach a closer square than a far away square? This is intriguing. How could a pawn reach the last rank takes the same number of moves to reach it from its diagonal, isn’t the slant line longer than a straight line, this does not make sense at all. But it all works out beautifully in chess and it even becomes a famous counting square problem in chess.


Chess players are constantly looking for the mate position by coordinating chess pieces in cross lines, isn’t this what a student is trying to find for the solution of a system equations in math? This is also the concept of set theory.


How many symmetry lines can a square have? This is the answer of how a queen moves. A knight really moves in L shape? What happens when knight is looking for the next move? It is really looking out directions almost like a circle. Chess really is not a game of rank and file, it is a game of circle (movements) and square (chessboard).


Many interesting mathematical problems could be created if one truly appreciates the beauty of math concept built in chess. The math and chess integrated problems not only advances a child’s chess knowledge, it also improves a child’s ability in problem solving, critical thinking, logic, and visualization.


Ho Math and Chess learning Center has created the world’s first commercially available math and chess integrated workbooks and more details can be found by visiting www.mathandchess.com.   

Frank Ho