1 Videnskabsstudier, Department of Communication and Arts, Roskilde University2 The Department of Culture and Identity, Roskilde University
Those Greek philosophers who write about mathematics consider demonstration as central to it. Grosso modo, what Aristotle writes about the topic is congruent with what Euclid does. Demonstration was thus not only practised but also an explicit concern for Greek mathematics. Other early mathematical cultures do not speak about mathematics involving demonstration. However, Old Babylonian mathematical texts (c. 1800–1600 BCE) reveal both aspects of mathematical demonstration as we know it for instance from the ancient Greeks: arguments showing why the steps undertaken do lead to the required result; and “critique” (in Kantian sense) investigating the presuppositions behind and limits of these arguments. This is argued on a sample of characteristic but relatively simple texts in translation. Critique plays a minor role only in Old Babylonian mathematics; still, the Babylonian example shows that mathematical proof may be present in a mathematical culture even if unsupported by extra-mathematical philosophy or ideology.
History of Mathematical Proof in Ancient Traditions, 2012