Mathematics and chess

Chess teaches many things, including strategic thinking. Though one might think at first that this type of thinking is unrelated to mathematics, in fact, chess also teaches a type of "calculation" (see Soltis's book [S] for the exact idea).

A paraphrase from the entry under Mathematics and Chess in [Su]: In 1893, a Professor Binet (of Stanford-Binet IQ test fame) made a study of the connection between mathematics and chess. After questioning a large number of leading players, he discovered that 90% were very good mental calculators. On the other hand, he discovered that although mathematicians are often interested in chess, few become top-class players.... Professor Binet commented that both chess and mathematics have a common direction and the same taste for combinations, abstraction, and precision. 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.

This page contains information on

• which mathematicians (which we define as someone who has earned a PhD or equivalent in Mathematics) play(ed) chess at the International Master level or above (also included are those who have an IM or above in chess problem solving or composing), and
• how to get papers on mathematical chess problems.

Papers about mathematical problems in chess:

I only know of a few sources:

• Lewis Benjamin Stiller, "Exploiting symmetries on parallel architecture", PhD thesis, CS Dept, Johns Hopkins Univ. 1995 Closely related is his Games of No Chance paper, "Multilinear Algebra and Chess Endgames".
• Max Euwe, "Mengentheoretische Betrachtungen uber das Schachspiel", Konin. Akad. Weten. (Proc Acad Sciences, Netherlands), vol 32, 1929, 633-642
• Noam Elkies, "On numbers and endgames: Combinatorial game theory in chess endgames", in 1996 "Games of No Chance" = Proceedings of the workshop on combinatorial games held July'94 at MSRI. Available from MSRI Publications -- Volume 29 or Noam Elkies' site.
• Mario VELUCCHI's NON-Dominating Queens Problem or math chess problems
• Timothy Chow, "A Short Proof of the Rook Reciprocity Theorem", in volume 3, 1996, of the Electronic Journal of Combinatorics.
• Herbert S. Wilf, "The Problem of the Kings", and Michael Larsen, "The Problem of Kings", both in volume 2, 1995, of the Electronic Journal of Combinatorics.
• Papers on odd king tours by D. Joyner and M. Fourte (appeared in the J. of Rec. Math., 2003) and even king tours by M. Kidwell and C. Bailey (in Mathematics Magazine, vol 58, 1985).
• Lesson 3 in the chess lessons by Coach Epshteyn at UMBC.

References

1. [BFR] Eero Bonsdorff, Dr Karl Fabel, Olavi Riihimaa, Schach und Zahl, unterhaltsame schachmathematik, Walter Rau Verlag, Dusseldorf, 1966
2. [L] Lasker, E. "Zur theorie der moduln und ideale," Math. Ann. 60(1905)20-116
3. [K] Kunz, Introduction to Commutative Algebra and Algebraic Geometry, Birkhauser, Boston, 1985
4. [N] Nunn, J. D. M. "The homotopy types of finite H-spaces," Topology 18 (1979), no. 1, 17--28
5. [S] A. Soltis, The Inner Game of Chess, David McKay Co. Inc, (Random House), New York, 1994
6. [St] R. Stanley's Chess Problems webpage
7. [Su] A. Sunnucks, The Encyclopedia of Chess, 2nd ed, St Martins Press, New York, 1976
   

Thanks to Christoph Bandelow, Max Burkett, Elaine Griffith, Hannu Lehto, John Kalme, Ewart Shaw, Richard Stanley, Will Traves, Steven Dowd, Z. Kornin, and Noam Elkies for help and corrections on these posts (which started out as a web page).