id: 06490090
dt: b
an: 2016a.00015
au: Høyrup, Jens
ti: Algebra at the time of Babylon. When mathematics was written on clay. With
a preface by Karine Chemla. (L’algèbre au temps de Babylone. Quand
les mathématiques s’écrivaient sur de l’argile.)
so: Inflexions. Paris: Vuibert/Adapt-SNES (ISBN 978-2-311-00001-6/pbk;
978-2-35656-016-2/pbk). xiv, 162~p. (2010).
py: 2010
pu: Paris: Vuibert/Adapt-SNES
la: FR
cc: A30
ut: Babylonian algebra; quadratic equations; sexagesimal system; cuneiform
ci: Zbl 0086.00208; Zbl 0052.24402; Zbl 1191.01003; Zbl 1326.01004; Zbl
1326.01008
li:
ab: The mathematical achievements of the Babylonians are, as a rule,
underrated, although (or because?) much of what they did can be
understood with a solid background in high school mathematics.
Textbooks devoted to Babylonian mathematics suitable for the general
reader are still rare: examples are [{\it K. Vogel}, Vorgriechische
Mathematik. II: Die Mathematik der Babylonier (German). Hannover:
Hermann Schroedel Verlag KG (1959; Zbl 0086.00208); {\it E. M. Bruins},
Fontes Matheseos. Grundzüge des vorgriechischen und griechischen
mathematischen Denkens (Dutch; Flemish). Leiden: Brill (1953; Zbl
0052.24402); {\it R. Caratini}, Les mathématiciens de Babylone
(French). Paris: Presses de la Renaissance (2002; Zbl 1326.01004); {\it
P. S. Rudman}, The Babylonian theorem. The mathematical journey to
Pythagoras and Euclid. Amherst, NY: Prometheus Books (2010; Zbl
1191.01003); {\it P. Yuste}, Matemáticas en Mesopotamia (Spanish).
Madrid: Dykinson (2013; Zbl 1326.01008)]. The present book by one of
the leading experts in this area is a welcome addition to this set. The
introduction presents the sexagesimal system, as well as operations
such as addition, subtraction, multiplication, division, squaring and
taking square roots. The first chapter covers equations of the first
degree by discussing problems from the cuneiform tablets TMS XVI \# 1
and TMS VII \# 2. The subsequent chapters present equations of the
second degree from BM 13901, more involved equations of the second
degree, e.g., from AO 8862, as well as applications to geometry (VAT
8512). The rest of the book deals with the question whether we may talk
about Babylonian algebra in the first place. In the appendix, the
author presents several examples of transliterations that the readers
are invited to study. The author has taken part in improving the
interpretation of Babylonian texts during the last 30 years, and he is
aware that he is standing on the shoulders of giants: on p. 10, for
example, he writes that “the interpretation of these texts made in
the 1930s appears as a true heroic deed and remains an excellent first
approximation”. This compares favorably with the attitude of other
historians of mathematics who look down upon the pioneers of their
field of expertise as “mathematicians who produced largely
anachronistic accounts of ancient mathematics”. I fear that only
very few high school students will pick up a book like this and study
it on their own; but with some guidance they will discover a whole new
world, a new way of looking at the mathematics they know. I strongly
urge teachers to become familiar with this material ‒ there is more
to be learned from, e.g., this book than from the whole literature on
didactics of mathematics in this century.
rv: Franz Lemmermeyer (Jagstzell)