Old Babylonian “Algebra”, and What It Teaches Us about Possible Kinds of Mathematics

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

Resumé

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.
OriginalsprogEngelsk
TidsskriftGanita Bharati
Vol/bind32
Udgave nummer1-2
Sider (fra-til)87-110
ISSN0970-0307
StatusUdgivet - 2010

Bibliografisk note

Faktisk udkommet 2012

Emneord

  • Old Babylonian algebra
  • mathematical justification

Citer dette

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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.",
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Old Babylonian “Algebra”, and What It Teaches Us about Possible Kinds of Mathematics. / Høyrup, Jens.

I: Ganita Bharati, Bind 32, Nr. 1-2, 2010, s. 87-110.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

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N2 - 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.

AB - 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.

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