Five years ago, Tsinghua University in Beijing received a donation of nearly 2,500 bamboo strips. Muddy, smelly and teeming with mould, the strips probably originated from the illegal excavation of a tomb, and the donor had purchased them at a Hong Kong market. Researchers at Tsinghua carbon-dated the materials to around 305 BCE, during the Warring States period before the unification of China.
     Each strip was about 7 to 12 millimetres wide and up to half a metre long, and had a vertical line of calligraphy painted in black ink. Historians realised that the bamboo pieces constituted 65 ancient texts, and recognised them to be among the most important artefacts from the period.
     "The strips were all mixed up because the strings that used to tie each manuscript together to form a scroll had long decayed," says Li Junming, a historian and palaeographer at Tsinghua. Some pieces were broken, others missing. "21 bamboo strips stand out from the rest as they contain only numbers", says Feng Lisheng, a historian of mathematics at Tsinghua.
     When the strips are arranged properly, says Feng, the table can help multiply any whole or half integer between 0.5 and 99.5. "Such an elaborate multiplication matrix is absolutely unique in Chinese history," Feng adds.
     The oldest previously known Chinese times tables, dating to the Qin Dynasty between 221 and 206 BCE, were capable of only much simpler multiplications. The ancient Babylonians possessed multiplication tables some 4,000 years ago, but theirs were in a base-60 rather than a base-10 system. The earliest-known European multiplication table dates to the Renaissance.
     "The discovery is of extraordinary interest," says Joseph Dauben, a maths historian at City University of New York. "It's the earliest artefact of a decimal multiplication table in the world."

Edited from Nature (7 January 2014)