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Topic: Chess and mathematics

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Chess as mental training

Ken Whyld

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Emanuel Lasker

Jose Raul Capablanca

Chess tactic

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Euler

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Deep Blue

Bobby Fischer

	Lasker's Manual of Chess - Wikipedia, the free encyclopedia
		The Elements of Chess opens with a description of the chess board, the various rules of chess, and the relative values of the pieces.
		Lasker quickly moves on to the fundamentals of chess strategy and tactics, and ends the section with examples of some of the basic mates.
		Lasker also goes on to speculate about the mathematics of chess, the "physics of contest", and the correctness of Steinitz's theories.
	en.wikipedia.org /wiki/Lasker's_Manual_of_Chess (554 words)

	Chessville - Misc. - Trivia - Chess Quotations - Chess Is . . .
		Chess, with all its philosophical depth, its aesthetic appeal, is first of all a game in the best sense of the word; a game in which are revealed your intellect, character, will.
		Chess is first of all a game, but if any succeeds in producing a game which keeps on living and is played over and over again for many years, chess becomes an art.
		Chess is the mental torture of one's opponent, and the mental torture of oneself.
	www.chessville.com /misc/Quotes/misc_trivia_quotes_chess_is.htm (1697 words)

	The Benefits of Playing Chess!
		Chess involves an infinite number of calculations, anything from counting the number of attackers and defenders in the event of a simple exchange to calculating lengthy continuations.
		Chess provides you with plenty of opportunities to travel not only all around the country but also around the world.
		Chess is a universal language and you can communicate with anyone over the checkered plain.
	clatskaniechessclub.tripod.com /id28.html (902 words)

	List of mathematicians who studied chess - Wikipedia, the free encyclopedia
		Chess and mathematics have been pursued intellectually for centuries by many researchers and scientists, especially mathematicians.
		Naturally, the logic and symmetry in chess appeal to mathematicians.
		However, they either contributed to mathematics or used mathematics in their profession.
	en.wikipedia.org /wiki/List_of_mathematicians_who_studied_chess (119 words)

	Chess World Champions - Emanuel Lasker
		He attended a school in Berlin to develop his mathematical skills further and he later went on to study mathematics at Erlangen University.
		However, the chess world would not allow this to happen and in 1921 the match went ahead.
		Chess was never Lasker's main career and throughout his world champion reign he actively pursued his other interests in mathematics and philosophy.
	www.chesscorner.com /worldchamps/lasker/lasker.htm (780 words)

	Edutech Chess: Why Chess?
		Chess is an exercise of infinite possibilities for the mind, one which develops mental abilities used throughout life: concentration, critical thinking, abstract reasoning, problem solving, pattern recognition, strategic planning, creativity, analysis, synthesis, and evaluation, to name a few.
		As in mathematics, which might be defined as the study of patterns, pattern recognition in chess is of prime importance in problem solving.
		Chess makes a child realize that he or she is responsible for his or her own actions and must accept their consequences.
	www.edutechchess.com /whychess.html (3597 words)

	Chess and Standardized Test Scores (Site not responding. Last check: 2007-10-24)
		The purpose of this study is to document the effect of participation in a chess club upon the standardized test scores of elementary school students.
		Previous studies indicating the effects of chess on scholastic achievement have received little notice, and have been criticized for small sample size, or for chess clubs being self-selective elite groups, or for being too anecdotal.
		Chess equipment, consisting of boards and sets, have been contributed by Parent-Teacher Organizations, bought with School Activity funds (small amount), and borrowed from the high school club.
	www.successchess.com /GHJDS/SAT.html (1189 words)

	A defining moment in mathematics and the Gay Marriage decision
		I knew of no mathematics department which had a course on chess, and I didn't think any of my colleagues would agree with me that chess was a branch of mathematics.
		Mathematics was an ancient word, its history extends the length of the history of civilization.
		To insist on X as the same as mathematics would put too much restriction on the usage of the word, cutting off its informal meaning used by people with various levels of experience of mathematics seemed to me to be too big a step.
	www.math.purdue.edu /~gottlieb/Law/gaymarriage.html (1110 words)

	AntiOnline - The End of Chess?
		If two people, without the benefit of computers sit down to play a game of chess against each other, the fact that their is a mathematical formula to predict the perfect move exists, does not mean that either one of the competitors can calculate that formula in their heads.
		Chess is a highly variable game that allows for tremendous variation and innovation but it is still a bounded system.
		Chess is not at risk, it is a game that has lasted the ages due to its complexity, depth, and breadth.
	www.antionline.com /showthread.php?s=&threadid=236149 (3146 words)

	Mathematics and Chess Page
		A paraphrase from the entry under Mathematics and Chess in [5]: In 1893, a Professor Binet (of Stanford-Binet IQ test fame) made a study of the connection between mathematics and chess.
		One characteristic which was missing from mathematics was the combat, in which two individuals contend for mastery, with all the qualities required of generals in the field of battle.
		Jonathan Mestel, grandmaster in over-the-board play and in chess problem solving, is an applied mathematician specializing in fluid mechanics and is the author of numerous research papers.
	web.usna.navy.mil /~wdj/math_chess.htm (2039 words)

	Emanuel Lasker
		He was taught Chess at the age of 11 by his elder brother, Berthold Lasker.
		He attended a school in Berlin to develop his mathematical skills and he later went on to study mathematics at Erlangen University.
		He defended his Chess World Championship title 7 times in the 26 years he was the World Champion.
	www.chess-poster.com /great_players/lasker.htm (1109 words)

	Chessville - Editorials - Chess Is Cool
		Mistakes are inevitable and chess, like life, is a never-ending learning process.
		Chess develops the capability to predict and foresee consequences of actions.
		Chess provides you with plenty of opportunities to travel not only all around the country, but even around the world.
	www.chessville.com /Editorials/Chess_Is_Cool.htm (845 words)

	POP Mathematics
		Our aim is to present Mathematics to as wide as possible an audience, and to give an impression for mathematics of the objects of study of mathematics, the methodology of mathematics, the successes and applications of mathematics, the enjoyment of mathematics, and the wider context of mathematics.
		This archive is part of the Mathematical MacTutor system developed at the School of Mathematical and Computational Sciences of the University of St Andrews for learning and experimenting with mathematics.
		Mathematics Awareness Week is held in late April each year to increase public understanding of and appreciation for mathematics.
	archives.math.utk.edu /popmath (2425 words)

	Freshman Seminar 23j: Chess and Mathematics (Fall 2003)
		Here's an outline/review of algebraic notation for chess positions and moves.
		Here are glossaries of most of the technical terms from chess and graph theory that we'll use.
		October 7: Computational techniques (mostly meet-in-the-middle tricks and dynamical programming), and some chess applications (corresponding squares, etc., all of which can also be understood in the Zermelo framework).
	www.math.harvard.edu /~elkies/FS23j.03/index.html (674 words)

	Iversen Lapp on Chess (Site not responding. Last check: 2007-10-24)
		Chess meant a lot to him, but could never fill his entire life.
		Besides being world chess champion, he also had other careers: teacher, managing director in a food company, scientific consultant, director of a study center for computers and university professor.
		Scientific objectivity was his profession and was also emblematic of his exact chess style.
	www.brainsturgeon.com /iversen/000527.shtml (169 words)

	News
		Abington, Pa. -- Ira Lee Riddle, lecturer in mathematics at Penn State Abington, was the chief tournament director for the 2003 U.S. Senior Open Chess Tournament, a national-title event.
		While living in Hawaii, a neighbor of his who was a competitive chess player realized that this 4-year-old boy was able to quickly grasp the strategy involved in chess.
		He has directed plays and musicals; is a PIAA certified volleyball and track/field official; has officiated wrestling and softball; serves as a judge in the Delaware Valley Science Fairs competition; has coached wrestling, soccer and track; and has written more than 100 articles, many of them chess-related.
	www.pscfchess.org /IraRiddleNews.htm (386 words)

	The Origin of Chess
		Chess has been shown to have appeared in India at a date no earlier than the sixth century AD, and Indian scholars themselves seem to believe that the actual date was considerably more recent than even that.
		The fact that Chinese chess also has a rook, a king, a pawn and a bishop, all of which occupy the same place on the board in the starting position and have the same movement and the same name as in the known medieval predecessor of western chess, is simply ignored.
		Chess also crossed from Persia to Ethiopia, where a little known form of the game, in which both sides move simultaneously and as quickly as possible, is still played.
	www.ishipress.com /origin.htm (10221 words)

	Mathematics and Chess - Petkovic - Chess House
		Here is a splendid collection of almost 100 puzzles, some adapted and some original with the author, all built around some form of the chessboard, generally the well-known 8x8 version.
		All you need to know is the rules of the game and in some cases not even that.
		Clearly described and accurately answered, these perplexing posers will appeal not only to math and chess buffs but also to anyone who enjoys testing his or her wits against a carefully selected array of the best puzzles in recreational math literature.
	www.chesshouse.com /Mamatics_and_Chess_p/3670.htm (184 words)

	Computer generates verifiable mathematics proof \| Lambda the Ultimate
		You have a valid point about the diversity of mathematical fields, but I have to (nit)pick on your example, because I think almost the opposite is true in that particular case.
		Our requirement that our mathematical notations be explicit and precise enough that they can be interpreted automatically, as by a computer, is very effective in uncovering puns and flaws in reasoning.
		Mathematics texts often talk implicitly about functions by referring to a bunch of variables, say (y_i), that depend on another bunch, say (x_j), without making explicit the fact that y_i=f_i(x_j) for some functions (f_i).
	lambda-the-ultimate.org /node/view/661 (5391 words)

	Freedom and Space in Chess
		Chess positions with larger FREEDOM NUMBERS are more flexible and more easily changed to take advantage of new ideas and/or new problems.
		Chess positions with larger SPACE are better suited to supporting an attack on your opponent's king, which usually sits at the opposite side of the board (encircled in the figure above).
		Both FREEDOM and SPACE are more useful tools in the middle game and opening, and less useful in the endgame, when pieces are fewer and can move more easily across the board (even the king).
	math.uww.edu /faculty/mcfarlat/177free.htm (234 words)

	Orlando Chess&Games Center (Site not responding. Last check: 2007-10-24)
		If you are a teacher or an administrator, and would like to start a chess program for your school, please contact Alex Zelner at 407-248-0818.
		Simple answer: introduce chess to the school curriculum.
		During the game you are focused on only one main goalÂ—to checkmate and become the victor.
	www.orlandochess.com /page.cfm?autonumber=10 (672 words)

	[No title] (Site not responding. Last check: 2007-10-24)
		Two round tables on “Journalism and Chess,” with specialized national and international journalists.
		“Chess: Its influence on society and its presence in history, qualities and defects,” analyzed by a panel comprising a sociologist, psychologist, philosopher and historian
		“Literature and Chess,” round tables with well-known international and Mexican authors, who have used chess as the main theme in some of their literary works.
	www.moreliachess.com /eng/Cultural.asp (195 words)

	Morelia International Chess Festival (English) (Site not responding. Last check: 2007-10-24)
		We wholeheartedly apologize to the chess players that intended to participate in this event as well as to the Chess community in general for any inconvenience and disappointment this may cause.
		A large number of Mexican chess players as well as players from other countries are expected to participate.
		Many different chess related activities such as lectures on "Chess and Mathematics", "Chess in Education", "Chess and Computers", etc. There will also be chess movies, exhibitions of chess paintings, living chess games, chess in literature and more.
	www.moreliachess.com (240 words)

	What's New on the Mathematics Archives
		The George Washington University Summer Program for Women in Mathematics (SPWM) is a four-week intensive program for mathematically talented undergraduate women who are completing their junior year and may be contemplating graduate study in the mathematical sciences.
		The Institute of Statistical Mathematics (ISM) is a research institute of the Ministry of Education, Science and Culture.
		The Israel Mathematical Union is the professional association of mathematicians in Israel, which works actively to encourage advanced mathematical research and teaching.
	archives.math.utk.edu /whatsnew/feb96.html (2837 words)

	Amazon.com: Mathematics and Chess: Books: Miodrag Petkovic (Site not responding. Last check: 2007-10-24)
		This book won't help you play chess any better, or be better at math, but it will provide you with an entertaining and brain challenging pass time.
		This is an interesting book, with some good problems to solve, but I was expecting a book that would relate math to chess, instead this is a book that uses the chess board and the game of chess to solve mathematical problems, this book does nothing to help with understanding chess or improving your game.
		As far as I know, only a few books combining both mathematics and chess were written in English up to now so that this book is a real attraction and refreshment.
	www.amazon.com /exec/obidos/tg/detail/-/0486294323?v=glance (1507 words)

	Clay Mathematics Institute
		His public lecture on tilings was held on July 16, 2004 and is available in pdf form here.
		Richard Stanley is currently the Norman Levinson Professor of Applied Mathematics at M.I.T. His main research interest is combinatorics and its connection with such other areas of mathematics as algebraic topology, commutative algebra, and representation theory.
		He held a Guggenheim Fellowship and is a member of the American Academy of Arts and Sciences and the National Academy of Sciences.
	www.claymath.org /fas/senior_scholars/Stanley (182 words)

	Math Lair - Chess and mathematics (Site not responding. Last check: 2007-10-24)
		This page, which is currently under construction, will highlight a few ways in which mathematics creeps into the realms of chess:
		Combinatorics: There are about 318,979,564,000 ways of playing the first four moves of a game of chess.
		There are about 169,518,829,100,544,000,000,000,000,000 ways of playing the first ten moves of a game of chess.
	www.stormloader.com /ajy/chess.html (63 words)

	Math Forum Discussions - Historia-Matematica
		Scholarly discussion of the history of mathematics (in a broad sense).
		[HM] Iraq: the history of mathematics and the aftermath of war
		The Math Forum is a research and educational enterprise of the Drexel School of Education.
	mathforum.org /kb/forum.jspa?forumID=149&start=510 (104 words)

	History of Mathematics and Chess
		I am a historian of mathematics, trying to find out more about the role Chess played in the life of mathematician Leonhard Euler.
		I wonder if the Chess community can help me find some answers.
		Your e-mail is very interesting and since we do not have much data about Leonhard Euler, we have posted your letter in our "Read our Mail" section and hopefully some viewers may write us with answers that in turn we'll send them right to you ASAP.
	www.chess-poster.com /english/mail/mail_2003/history_of_mathematics_and_chess.htm (227 words)

	EBSCOhost (Site not responding. Last check: 2007-10-24)
		Mathematics Teaching in the Middle School; Jan2004, Vol.
		Discusses the connection between mathematics and chess game.
		Skills promoted by a chess game; Mathematical activities that can be developed through the game; Basic concepts of the game.
	www.bsu.edu /classes/robinson/Chess/ChessMath.htm (164 words)

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