The Go board, like the chess board, has stimulated thinking about mathematical problems.

The Italian scholar G. Vacca first noticed an entry in the Meng Xi Bi Tan (Dream Pool Essays) by Shen Gua, which was published in 1086. Under the title "A problem of the mathematician Yi Xing" (1) he quotes and discusses an early attempt at calculating permutations.

Yi Xing(672-717) was a Buddhist monk who specialisied in mathematics and astronomy. He made great contributions to the then important science of calendars, to the extent that he is still remembered even though his written works have been lost. In particular he made the Da Yan calendar for the go-mad emperor Xuan Zong. He was famous also for his feats of memory.

Shen Gua(1030-1093) was Chancellor of the Hanlin Academy with an advanced interest in engineering, medicine, astronomy and cartography, and the Dream Pool Essays was an encyclopaedic collection of notes on most of the then known sciences. On this matter he says:

"The story is told that the Tang dynasty monk Yi Xing once calculated the total number of possible positions on a go board and was able to discover all of them.
I thought about this problem. It is easy but the numbers are large and cannot be expressed with the commonly used words for numbers. I will briefly indicate the numbers that have to be used.
On a 2x2 go board, using four pieces, there are 81 different positions.
On a 3x3 board, using nine pieces, there are 19,683 positions.
On a 4x4, using 16 pieces, there are 43,046,721 positions.
On a 5x5 board, using 25 pieces, there are 847,288,609,443 positions.
On a 6x6 board, using 36 pieces, there are 150,094,635,296,999,121 positions.
On a 7x7 board or greater there are no names for the numbers involved.
To write the number of positions on a go board of 361 points we will have to use the word 'ten thousand' 52 times."

(Chinese counts large numbers in units of 10,000 and has different words for 10,000 and 10,000x10,000, but then gets stuck. It is rather as if we said: million, billion, trillion, er....)

Shen Gua then goes on to explain Yi Xing's method, but points out that only mathematicians calculate in that way! Even so, Vacca points out, there is a large error in what Shen Gua says: the number of positions is 3 to the power of 361 (points can be black, white or empty), which number has 173 digits and so requires 'ten thousand' only 44 times.

Joseph Needham discusses the same passage. He says the study of permutations and combinations was extremely rare in Europe before Abraham ben Ezra (c. 1140) and in India before Bhaskara (c. 1150), and no real progress was made until the time of Pacioli. The first book was by Bernouilli in 1713.

(1) Vacca, G: "Note Cinesi", Rivista degli Studi Orientali, Rome 1915-15, Vol. 6, pp. 131-142 (only pp. 135-7 relate to go)
(2) Needham, J.: Science and Civilisation in China, Cambridge University Press, 1959, Vol. 3, Section 19: Mathematics, p. 139