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https://chess.stackexchange.com/questions/5199/does-playing-tournament-chess-help-one-in-the-field-of-chess-related-math

I often wonder whether the visualization of the various types of chess-related graphs is helped along by playing competitively. This would seem to fly in the face of a recent peer-reviewed study in the sense that there would be a high-level benefit (ie teaches skills that can be transferred to other domains) to chess if this line of thinking is correct, namely in the field of chess-related math.

http://people.brunel.ac.uk/~hsstffg/preprints/chess_and_education.PDF

On the other hand, the study seems to be very thorough and is one of the few peer-reviewed articles available on the subject. One would expect if there were some high-level gain to playing competitively then the test that shows this would be repeatable. However, there has been mixed results, as the above article claims. Perhaps the field of chess-related math is only chess-related in that the only skill that transfers is knowing how the pieces move, without any regard for strategy. What do you think?

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    $\begingroup$ Playing <foo> competitively does take a lot of time, so it presumably takes time away from getting proficient in <bar> (whatever <foo> and <bar> might be). $\endgroup$
    – vonbrand
    Jun 24, 2014 at 18:07
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    $\begingroup$ There are a lot of studies about these connections. What level of mathematics are you interested in, and do you mean specifically tournament chess or experience playing chess more generally? $\endgroup$
    – Benjamin Dickman
    Jun 24, 2014 at 21:53
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    $\begingroup$ @vonbrand - I'm certain competitive chess takes time. However, if it is beneficial one would expect that some could reach a happy medium between competing, living, and doing math. $\endgroup$
    – Paul Burchett
    Jun 25, 2014 at 0:06
  • $\begingroup$ @BenjaminDickman - I mean chess-related mathematics - for example problems like the Knight's tour, Independent queen's problem, domination problems, etc. Also, I meant this to be a general investigation as to what skills learned in chess might help one in the field of chess-related math. Some of the skills I'm considering, like for example blind play, are believed to be facilitated greatly by tournament play. Thus, the question about tournament play. In other words, what skills learned from chess, besides simply knowing how to move the pieces, facilitate the mathematics noted? $\endgroup$
    – Paul Burchett
    Jun 25, 2014 at 0:09
  • $\begingroup$ I'd really like to start a conversation about proof of the exceptional isomorphism between E8 and D62 It is, groups, all chess movement I would love to say this article matematicheskoi $\endgroup$
    – LoculoSoft
    Jun 30, 2014 at 8:32

2 Answers 2

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While I don't have a deep knowledge of peer-reviewed literature on transfer of skills from playing tournament chess, I am an experienced tournament chess player as well as a math educator. Based on my knowledge of what tournament chess players actually do, I find it very unlikely that tournament chess would provide any significant boost to mathematical skills that could not be gained by other means. Sure, the mental discipline and working memory development can't hurt, but those things are hardly specific to chess.

The simple reason is that playing a game of chess, even at the highest levels, doesn't involve thinking processes anything like those of graph theory and the Knight's tour, or even mathematics in general. A low-level tournament player will have thought processes centered around tactical calculations a few moves into the future, e.g., "If I capture on e4, then he captures with the bishop, then I recapture with the queen, ..." A mid-level player will add positional thinking such as "If I make him recapture on c3, his pawn structure will be weak." The strong players will be adept at choosing the right broad plan, such as "I'll spend a few moves locking up the queenside, then I'll start a pawn storm on the kingside before he can get in position to defend."

I don't see any way that a task analysis of any of these thought processes gets even close to chess math problems such as the Knight's tour, or to any problems of higher math in general. The thought processes involved in tournament chess are very domain-specific. So-called chess math problems such as the Knight's tour may appear to be superficially related to chess, but being entirely divorced from real chess considerations such as pawn structure, capturing pieces, etc., there is little reason for even a grandmaster to have any special insight or advantage in such problems.

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  • $\begingroup$ I"m a mathematics educator as well. I tutor. I also played scholastically for 12 years! My claim, which I really haven't invested much in until recently, is that there is a small amount of chess specific knowledge that facilitates both mathematics, computer science, and other fields. Take, for example, captures. Tactics teaches one to not only count attackers vs defenders when capturing, but also the order which captures take place. This fact is also used when considering certain properties of dominating sets. I don't think it's overly helpful though, as others can use other visual aids. $\endgroup$
    – Paul Burchett
    Aug 7, 2015 at 18:31
  • $\begingroup$ Btw, I'm not saying the typical GM (if there is such a thing), under most circumstances has any special insight into mathematics. It's only when mathematical ability is combined a healthy attitude towards the game that one can draw from the game in this way. Most GMs I don't think have both of these, although there are certainly exceptions (people like Lasker, Euwe, etc.). Simply think of the representation chess provides for these problems as a visual aid. Others visual aids exist for these problems, however, the medium of chess provides another perspective with its own advantages. $\endgroup$
    – Paul Burchett
    Aug 7, 2015 at 18:47
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Playing tournament level chess results in high-level, transferrable, cognitive skills. These skills lie partially in the field of maths. For example a Knight's Tour is a graph theory problem. Many other aspects of chess lie in the fields of discrete geometry and game theory.

But all these aspects never cover any of these theories or sub-theories in a whole. And they mostly don't cover their basics.

Consequently, it only helps understanding or doing math better, but it cannot convey math on its own. The ultimate abstraction even in elementary math goes much further than the abstraction in chess: just remember that chess is finite.

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    $\begingroup$ You certainly might be right that chess holds high-level, transferrable skills, however, that seems to be an opinion in light of recent evidence. Actually aspects of chess can be seen in many places. I recently submitted a paper whose central problem was in the field of linear algebra. While someone beat me to the punch, so to speak, the problem could've easily been asked using chess terms. In fact, that's the way I came across the problem; by using Dr Doug Chatham's separation problems on the rook's graph. The problem is equivalent to a soon to be published, Linear Algebra paper! $\endgroup$
    – Paul Burchett
    Jul 15, 2014 at 3:34
  • $\begingroup$ @PaulBurchett Yes, but you won't understand graph theory or linear algebra from this aspect of chess alone, I guess. $\endgroup$
    – Toscho
    Jul 16, 2014 at 11:22
  • $\begingroup$ Learning how to move the pieces will at least provide a potential visual aid from among others. What help that has on understanding "chess-related" math is unknown, and is opinion based. However, given the recent push for proofs without words, some would certainly argue the use of another visual aid results in more mathematical creativity. Who ultimately knows?! $\endgroup$
    – Paul Burchett
    Jul 16, 2014 at 11:30
  • $\begingroup$ I'd say any specialty would be difficult to master through any one type of visual aid. However, many are aware of at least how the pieces move and I'd say it is a valuable visual aid for discrete mathematics! The paper is Brualdi, Kiernan, Meyer, Schroeder, "Patterns of Alternating Sign Matrices", Linear Algebra and its Applications 438 Issue 10 (2013) 3967=3990 This problem can be viewed as a separation independence on the rook's graph. Zeros are open squares, ones are rooks and negative ones are pawns. $\endgroup$
    – Paul Burchett
    Aug 12, 2014 at 9:48
  • $\begingroup$ Just to add, Dr Doug Chatham is one of many that have written on separation problems. I mentioned him as he has authored and/or coauthored many of these types of papers. $\endgroup$
    – Paul Burchett
    May 8, 2016 at 9:29

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