Problèmes et démonstration de la correction d'algorithmes en Chine ancienne

Abstract : Most of the themes of the problems that we find in the mathematical manuscripts recently discovered in China, in graves dating from the last centuries B.C.E., present a striking continuity with those that have come down to us in The Nine Chapters on the Mathematical Procedures (1st century CE), with their layers of commentaries indissociable from the text itself. This fact suggests that these books are related to a same tradition, concerning the use of problems in the context of proofs of the corectness of algorithms that they state. Whereas historians of mathematics have been more interested in the latter, we argue here that the problems played a key role in the ancient practice of proofs to which the commentaries bear witness. The idea that a problem and its associated procedure form a general proposition, no matter how they are formulated, sheds light on two aspects of this role : resorting to a problem to embody one of the steps to be performed in the step by step creation of an algorithm, and the use of the situation and values presented in the statement of a problem in order to interpret the meaning of the procedure's operations.
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Submitted on : Tuesday, March 12, 2013 - 11:44:44 AM
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Karine Chemla. Problèmes et démonstration de la correction d'algorithmes en Chine ancienne. Moyens de validation et de preuve dans les différentes disciplines, Mar 2010, France. pp.33-50. ⟨halshs-00799461⟩



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