WHAT WAS A MATHEMATICAL PROBLEM IN ANCIENT CHINA?

Texte d'une conférence donnée à Chicago en mai 2002Most historians of science have tended to take the mathematical problems that composed Chinese ancient texts at face value, as if the category of a mathematical "problem" was a-historical. This talk would like to offer a historical approach to determine what a mathematical problem was in ancient China for the practitioners of mathematics. I intend to show that such a problem was not the same object as what we call a mathematical problem today. Moreover, I shall argue that the practice ancient China's practitioners in mathematics developed to work out mathematics on the basis of problems was specific. In fact, problems played a key part in the conduct of proofs. These results should guard us against jumping to the conclusion, as is too often the case, that the problems contained in ancient China's mathematical texts were merely practical