### Resumé

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.

Originalsprog | Engelsk |
---|---|

Titel | History of Mathematical Proof in Ancient Traditions |

Redaktører | Karine Chemla |

Udgivelses sted | Cambridge |

Forlag | Cambridge University Press |

Publikationsdato | 2012 |

Sider | 362–383 |

ISBN (Trykt) | 9781107012219 |

Status | Udgivet - 2012 |

### Bibliografisk note

De ensbetitlede "mulige dubletter" er et preprint og et genoptryk af dette### Citer dette

*History of Mathematical Proof in Ancient Traditions*(s. 362–383). Cambridge: Cambridge University Press.

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*History of Mathematical Proof in Ancient Traditions.*Cambridge University Press, Cambridge, s. 362–383.

**Mathematical Justification as Non-Conceptualized Practice: the Babylonian Example.** / Høyrup, Jens.

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TY - CHAP

T1 - Mathematical Justification as Non-Conceptualized Practice: the Babylonian Example

AU - Høyrup, Jens

N1 - De ensbetitlede "mulige dubletter" er et preprint og et genoptryk af dette

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

M3 - Book chapter

SN - 9781107012219

SP - 362

EP - 383

BT - History of Mathematical Proof in Ancient Traditions

A2 - Chemla, Karine

PB - Cambridge University Press

CY - Cambridge

ER -