### Abstract

Until recently, Old Babylonian algebra (mostly identified simply as Babylonian)

either looked very much like recent equation algebra in presentations of the

history of mathematics, or it was characterized as empirical, a collection of

rules found by trial and error or other (unidentified) methods not based on

reasoning. In the former case, the implicit message was a confirmation of the

status of our present type of mathematics as mathematics itself. The message

inherent in the second portrait is not very different: if mathematics is not of

the type we know, and whose roots we customarily trace to the Greeks, it is

just a collection of mindless recipes (a type we also know, indeed, from teaching

of those social classes that are not supposed to possess or exercise reason)—

tertium non datur!

More precise analysis of Old Babylonian mathematical texts—primarily

the so-called algebraic texts, the only ones extensive enough to allow such

analysis— shows that both traditional views are wrong. The prescriptions turn

out to be neither renderings of algebraic computations as we know them nor

mindless rules to be followed blindly; they describe a particular type of geometric

manipulation, which like modern equation algebra is analytical in character,

and which displays the correctness of its procedures without being explicitly

demonstrative.

The paper explains this, adding substance, shades and qualifications to the picture, and then takes up the implications for our global understanding of

the possible types of mathematics.

either looked very much like recent equation algebra in presentations of the

history of mathematics, or it was characterized as empirical, a collection of

rules found by trial and error or other (unidentified) methods not based on

reasoning. In the former case, the implicit message was a confirmation of the

status of our present type of mathematics as mathematics itself. The message

inherent in the second portrait is not very different: if mathematics is not of

the type we know, and whose roots we customarily trace to the Greeks, it is

just a collection of mindless recipes (a type we also know, indeed, from teaching

of those social classes that are not supposed to possess or exercise reason)—

tertium non datur!

More precise analysis of Old Babylonian mathematical texts—primarily

the so-called algebraic texts, the only ones extensive enough to allow such

analysis— shows that both traditional views are wrong. The prescriptions turn

out to be neither renderings of algebraic computations as we know them nor

mindless rules to be followed blindly; they describe a particular type of geometric

manipulation, which like modern equation algebra is analytical in character,

and which displays the correctness of its procedures without being explicitly

demonstrative.

The paper explains this, adding substance, shades and qualifications to the picture, and then takes up the implications for our global understanding of

the possible types of mathematics.

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

Tidsskrift | Ganita Bharati |

Vol/bind | 32 |

Udgave nummer | 1-2 |

Sider (fra-til) | 87-110 |

ISSN | 0970-0307 |

Status | Udgivet - 2010 |

### Bibliografisk note

Faktisk udkommet 2012### Emneord

- Old Babylonian algebra
- mathematical justification

### Citer dette

Høyrup, J. (2010). Old Babylonian “Algebra”, and What It Teaches Us about Possible Kinds of Mathematics.

*Ganita Bharati*,*32*(1-2), 87-110.