Posts Tagged ‘rook polynomial’

The Math of Chess

September 16, 2008
"Excelsior" by Sam Loyd

White to move, mate in 5. (Sam Loyd, 1861)

It probably comes as no surprise to anyone that knows me that I enjoy playing chess. Indeed, chess is a common hobby among mathematicians (as are Go, juggling, and magic). But I was still amazed to see that a book I was reading, Chess Endings for the Practical Player by Ludek Pachman, was translated by someone named Hardy, and edited by someone named John E. Littlewood. I thought, “No way.” Hardy and Littlewood do chess? The same two that gave us this?

Well, I was right. The Hardy is Otto Hardy, not G.H. Hardy, and the Littlewood is John Eric Littlewood, not John Edensor Littlewood. But wow, close huh?

Had I been wrong — had the Hardy and Littlewood actually worked together on the book — it still shouldn’t have been shocking. It is fairly common to find mathematicians that study and/or play chess. Former chess world champion Max Euwe had his Ph.D. in mathematics, as do GMs John Nunn and Jon Speelman. (Nunn is also a GM chess problem solver – one of only three in history.) Noam Elkies (the youngest full tenured professor in the history of Harvard – at 26!) has published several papers on the mathematics of chess, and earned his solving GM title in 2001.

Math and chess have long been associated with one another. Some famous problems include the Knight’s Tour (any early version of which appeared in the Sanskrit poem Kâvyâlankâra by Rudrata ca. 900):

An open knight's tour.

the Eight Queens Problem, and the Mutilated Chessboard Problem (posed by Martin Gardner). There’s even a book called Mathematics and Chess.

Not all mathematical study of chess is purely recreational. The so-called rook polynomials have found applications in matrix theory and number theory. There’s even a Rook Reciprocity Theorem!

Check out Wikipedia’s Chess and Mathematics category for even more connections between the two, and also see Mathworld’s pages related to chess and math. Finally, no discussion of chess would be complete without a reference to xkcd’s comic that inspired these amazing photos.