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A question of personal interest. Is "visualization" of various types of boards and graphs helped along by competitive, tournament play? Of course, I'm assuming play beyond simply knowing how the pieces move.

Paul Burchett
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    How could the answer to this be no? – Alan Jun 23 '14 at 16:15
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    There are studies that hold playing tournament chess has no transferable skills to other domains. See the following for that discussion. http://chess.stackexchange.com/questions/5069/why-is-it-a-good-idea-to-teach-chess-in-schools/5136#5136

    Do you think tournament chess helps with math? Well at least some if you take the answer as yes. This flies in the face of some who say that chess will help with chess and nothing else.

    Phase one has been reached. Result has been labeled as trivial!

     – Paul Burchett Jun 24 '14 at 13:11
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    You said CHESS related math not just calculus or some generic math. How could knowing how to play chess, having hours of practice visualizing how pieces interact with each other, do anything other than benefit you? I was once asked a question by a calculus professor regarding a chess board and removing squares. After class I was the only one to come up to him and immediately tell him the solution. It was simple, because I play chess. The question had to do with a Knight's tour and removing two opposite corner squares. I knew the answer was impossible because sqaures were same color – Alan Jun 24 '14 at 13:26
  • Perhaps the field is only chess-related in the sense that the only skill that is required is to know how to move the pieces with no real sense for chess strategy. – Paul Burchett Jun 24 '14 at 14:11
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    I once discovered that I can solve crossword puzzles in my mind without actually writing in the words. I can keep so much stuff in my mind. This is probably the result of playing chess intensely. On the other hand, being a mathematician, I can also perform a lot of mental tasks in my mind. These are similar abilitites. There may be some neurological overlap so that training one of them helps develop the other. – MichalRyszardWojcik Jul 29 '16 at 18:11
  • It is not your question, but a book of chess/math puzzles was recently discussed (in Russian), from the Moscow Center for Continuous Mathematical Education. http://chess-news.ru/node/21860 – Post-It-Note Jul 31 '16 at 04:55
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    You assume that a chess player visualizes at all. Surely a very strong player will, but my playing can only be described as "sense of smell" (The Who, Tommy) and still, I'm a FIDE Master... – Hauke Reddmann Aug 28 '16 at 20:25

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To the extent that "chess-related math" requires any expertise in chess beyond the rules(*), tournament play is probably not as useful as solving and composing chess problems/studies. Typical positions in tournament play are too complicated to evaluate with mathematical certainty, while problems and studies should and usually do have rigorous proofs of correctness that are comprehensible to human players and problemists.

(*) Sometimes one needs no expertise beyond (say) how the Knight moves (as for questions involving the Knight's tour, or dominating the 8-by-8 board with a minimal number of Knights).

Noam D. Elkies
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To paraphrase G. H. Hardy, while chess problems can be beautiful, they are trivial. The best and most difficult mathematics is "significant" mathematics, i.e. mathematics that helps you solve other problems and impacts other fields of math. So being good at chess probably won't help you much with math. Also, at least according to Hardy, chess is a primarily psychological game, as opposed to math which is purely logical (paraphrased from his Mathematician's Apology).

Elliot Gorokhovsky
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    If they're so trivial then why are such problems rewarded with mathematics papers?

    Often it's difficult to say when one is doing math or doing chess. As mentioned above, one can abstract these problems on to any square board, rectangular board, or even consider them on beehive type boards, cylindrical boards, torus boards, etc. In fact, recently, I submitted a paper whose solution was found first by someone else without referring to chess at all, but instead an interesting linear algebra problem! Even though the problems are equivalent, would you call this a chess-related problem?

     – Paul Burchett Jun 28 '14 at 20:32
  • Correction for the fourth sentence above: an interesting = by using, problem should be erased entirely! – Paul Burchett Jun 28 '14 at 20:42
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    what is meant by chess being primarily psychological. Certainly this cannot be true. – CognisMantis Nov 16 '14 at 03:49
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    @PaulBurchett I think you're overestimating the number of such papers that are published - I wouldn't be surprised if the annual output in published, indexed math journals can be counted on two hands. – Steven Stadnicki Nov 22 '16 at 02:16
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    Wrong in the above, I think. There have been over a thousand written on the $n$-queens problem alone. Divide that by roughly 100 years of relevance, also noting they're more relevant now, more than ever. – Paul Burchett Nov 22 '16 at 10:32
  • THe contention that mathematics is reducible to logic is wrong. It misses the computational aspects of mathematics. I just noticed this part of your comment, I think.

    @Rene G

     – Paul Burchett Nov 22 '16 at 10:56
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I was a tournament player who was far better than 90% of those who play competitively. I also did 5 years of graduate school work in math. I found nothing of math value from playing chess. Your mileage may vary.

Paul Burchett
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yobamamama
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Consider this, what if playing tournament chess led to blindfold play? Then, along these lines, better blind play led one to visualize, even multi-task chess/math problems while doing routine tasks, like while driving for example. One would, at the least have more time to come up with new ideas! Did I mention I can do this?!

Paul Burchett
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