### Abstract

at first based on what I shall speak of as “the locally obvious”, that is,

presuppositions which the interlocutor—or, in case of writing, the imagined or

“model” reader—will accept as obvious; next in its interaction with critique, investigation

of the conditions for the validity of the seemingly obvious as well as the limits

of this validity. This is done, in part through analysis of material produced within late

medieval Italian abbacus culture, in part from a perspective offered by the Old

Babylonian mathematical corpus—both sufficiently distant from what we are familiar

with to make phenomena visible which in our daily life go as unnoticed as the air

we breathe; that is, they allow Verfremdung. These tools are then applied to the development

from argued procedure toward axiomatics in ancient Greece, from the midfifth

to the mid-third century bce. Finally is discussed the further development of

ancient demonstrative mathematics, when axiomatization, at first a practice, then a

norm, in the end became an ideology. The whole is rounded off by a few polemical

remarks about present-day beliefs concerning the character of mathematics.

Original language | English |
---|---|

Title of host publication | Interfaces between Mathematical Practices and Mathematical Education |

Editors | Gert Schubring |

Place of Publication | Cham |

Publisher | Springer VS |

Publication date | 2019 |

Pages | 27-46 |

ISBN (Print) | 978-3-030-01616-6 |

ISBN (Electronic) | 978-3-030-01617-3 |

Publication status | Published - 2019 |

Series | International Studies in the History of Mathematics and its Teaching |
---|---|

ISSN | 2524-8022 |

### Cite this

*Interfaces between Mathematical Practices and Mathematical Education*(pp. 27-46). Cham: Springer VS. International Studies in the History of Mathematics and its Teaching

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*Interfaces between Mathematical Practices and Mathematical Education.*Springer VS, Cham, International Studies in the History of Mathematics and its Teaching, pp. 27-46.

**From the Practice of Explanation to the Ideology of Demonstration: An Informal Essay.** / Høyrup, Jens.

Research output: Chapter in Book/Report/Conference proceeding › Book chapter › Research › peer-review

TY - CHAP

T1 - From the Practice of Explanation to the Ideology of Demonstration: An Informal Essay

AU - Høyrup, Jens

PY - 2019

Y1 - 2019

N2 - The following discusses the practice of mathematical argument or demonstration—at first based on what I shall speak of as “the locally obvious”, that is,presuppositions which the interlocutor—or, in case of writing, the imagined or“model” reader—will accept as obvious; next in its interaction with critique, investigationof the conditions for the validity of the seemingly obvious as well as the limitsof this validity. This is done, in part through analysis of material produced within latemedieval Italian abbacus culture, in part from a perspective offered by the OldBabylonian mathematical corpus—both sufficiently distant from what we are familiarwith to make phenomena visible which in our daily life go as unnoticed as the airwe breathe; that is, they allow Verfremdung. These tools are then applied to the developmentfrom argued procedure toward axiomatics in ancient Greece, from the midfifthto the mid-third century bce. Finally is discussed the further development ofancient demonstrative mathematics, when axiomatization, at first a practice, then anorm, in the end became an ideology. The whole is rounded off by a few polemicalremarks about present-day beliefs concerning the character of mathematics.

AB - The following discusses the practice of mathematical argument or demonstration—at first based on what I shall speak of as “the locally obvious”, that is,presuppositions which the interlocutor—or, in case of writing, the imagined or“model” reader—will accept as obvious; next in its interaction with critique, investigationof the conditions for the validity of the seemingly obvious as well as the limitsof this validity. This is done, in part through analysis of material produced within latemedieval Italian abbacus culture, in part from a perspective offered by the OldBabylonian mathematical corpus—both sufficiently distant from what we are familiarwith to make phenomena visible which in our daily life go as unnoticed as the airwe breathe; that is, they allow Verfremdung. These tools are then applied to the developmentfrom argued procedure toward axiomatics in ancient Greece, from the midfifthto the mid-third century bce. Finally is discussed the further development ofancient demonstrative mathematics, when axiomatization, at first a practice, then anorm, in the end became an ideology. The whole is rounded off by a few polemicalremarks about present-day beliefs concerning the character of mathematics.

M3 - Book chapter

SN - 978-3-030-01616-6

SP - 27

EP - 46

BT - Interfaces between Mathematical Practices and Mathematical Education

A2 - Schubring, Gert

PB - Springer VS

CY - Cham

ER -