ESHS/HSS Annual Meeting

Édouard Chavannes: The Mystery of the Dunhuang Multiplication Table

• In Event: Recent Archaeological Excavations: New Light on Ancient Chinese Mathematics 2

English Abstract

In 1906 Aurel Stein, the Anglo-Hungarian surveyor and archaeologist, discovered a nine-nines rhyme written on a wooden board in an abandoned watchtower along a portion of the Great Wall just to the north of Dunhuang in north-eastern China. Subsequently, Stein entrusted this along with nearly 2000 items that he had acquired while at Dunhuang to the French sinologist, Émmanuel-Édouard Chavannes, for study and publication. In 1913 Chavannes published about half of these, including the fragmentary wooden board on which was written a portion of a nine-nines rhyme. The first of its kind to be published, Chavannes transcribed the text, completed what he took to be missing parts of the rhyme, but was puzzled to find that all of the multiples when added together totaled 1111, whereas the total given on the board was 1113. He was at a loss to account for this discrepancy. Why, he asked, should this nine-nines rhyme end with a total of 1113? It would not be until three more nine-nines rhymes were discovered at Liye in 2002 that further light would be shed on the situation of the nine-nines rhyme for which Chavannes was trying to find an explanation, but could not. This presentation will examine the history of nine-nines rhymes in China and suggest a possible solution to the conundrum faced by Chavannes in accounting for why the Han dynasty nine-nines rhyme he had transcribed should have given the “incorrect” total of 1113.

Author

• Joseph W Dauben, City University of New York