The Nine Chapters on the History of Chinese Mathematics

This article explores Chinese mathematics from the first archeological evidence of numbers on oracle bones (14th century BC) to the time Chi-nese mathematics became a part universal mathematics (halfway the 19th century AD). First a concise overview of Chinese history and in philosophy is given. The ethical oriented Confucianism was the dominant philosophy and con-sequently little attention was given to the natural world, hindering the development of natural sciences and mathematics. Due to historical and philosophical reasons, Chinese mathematics took quite a different path than its Western counterpart: Chinese mathematics was focused on alge-bra and practical applications instead of geometry and theoretical reason-ing. The Nine Chapters on the Mathematical Art (ca. 1st century AD) is by far the most influential work: it would shape Chinese mathematics for centuries to come. Between the 3rd and the 11th century AD, Bud-dhist and Indian ideas got a firm grip on China, yet curiously Chinese mathematics is barely influenced. In the ‘Chinese Renaissance ’ and the subsequent Mongol occupation between the 12th and 14th century Chinese mathematics will reach its zenith. In the 15th and 16th centuries mathematical development waned and important achievements were forgotten. Only after the arrival of Eu-ropean missionary-scientists at the end of the 16th and during the 17th century mathematics made progress again. The Opium Wars of the 19th century mark the end of the classical China and the indigenous Chinese mathematics would be assimilated by universal mathematics. Two conclusions are reached: (i) war seems to be good for mathe-matical progress and (ii) from the 15th century on Chinese mathematics passed away in particular due ot the lack of a general algebraic structure, which prevented structural insight