The Evolution of Mathematics in Ancient China: From the newly discovered 數 Shu and 算數書 Suan Shu Shu Bamboo Texts to the Nine Chapters on the Art of Mathematics

The history of ancient Chinese mathematics and its applications has been greatly stimulated in the past few decades by remarkable archaeological discoveries of texts from the pre-Qin and later periods that make it possible to study in detail mathematical material from the time at which it was written. By examining the recent Warring States, Qin and Han bamboo mathematical texts currently being conserved and studied at Tsinghua University and Peking University in Beijing, the Yuelu Academy in Changsha, and the Hubei Museum in Wuhan, it is possible to shed new light on the history of early mathematical thought and its applications in ancient China. Also discussed here are developments of new techniques and justifications given for the problems that were a significant part of the growing mathematical corpus, and which eventually culminated in the comprehensive Nine Chapters on the Art of Mathematics. What follows is a revised text of an invited plenary lecture given during the 10th National Seminar on the History of Mathematics at UNICAMP in Campinas, SP, Brazil, on March 27, 2013.