44 karine chemla
such as embedding them into other algorithms or modifying their lists of
operations, could be established on the basis of problems and/or fi gures. In
the case of Diophantus, equalities were transformed qua equalities. Both
techniques were adopted in Arabic algebraic texts.
In addition to providing insights into how actors carried out interpreta-
tion for the algorithms recorded on Babylonian tablets, Høyrup suggests
that the need for understanding perhaps developed in relation to teach-
ing. In other words, he links the professional context of training scribes in
Mesopotamia to the development of certain kinds of proof. Interestingly
enough, as we shall see below, such a hypothesis nicely fi ts with A. Volkov’s
thesis regarding the use of proofs for a teaching context in East Asia.
Christine Proust’s chapter suggests capturing an interest in the correct-
ness of algorithms in another kind of Mesopotamian tablet, which contain
texts consisting of only numbers. Note that, here, the work of the exegete is
particularly challenging, since she has to argue for an interpretation of texts
that contain no words, only numbers. Th e method Proust uses to read these
traces is deeply subtle but of particular interest for us.
At fi rst sight, the tablets at the focus of Proust’s attention appear merely
to betray an interest in ‘checking’ the numerical results yielded by an algo-
rithm. Seen in that light, they recall some of the texts discussed by Høyrup,
in which a similar concern can be identifi ed. However, as we shall see, the
two types of text call for diff erent modes of interpretation.
Th e tablet VAT 8390, discussed by Høyrup, contains a ‘verifi cation’
part, comparable in some sense to the ‘synthesis’ following the ‘analysis’ in
Diophantus’ Arithmetics. Th is part of the text relies on the values produced
by the algorithm as well as on the procedure described by the statement
of the problem to show that the values obtained satisfy the relationships
stated in the problem. However, the actual function of this section in the
text should not be interpreted too hastily: as Høyrup emphasizes, it does
not merely yield a ‘numerical control’ of the solution, since the way in
which the ‘verifi cation’ procedure is written down requires the same kind
of ‘understanding’ from the reader as that attached to the text of the direct
algorithm. Th e nature and practice of the ‘verifi cation’ must thus be consid-
ered somewhat further, without being taken for granted a priori.
Textual structures of this type are characteristic of other tablets, in
which, once an algorithm has yielded a result, this result is then subjected
to another procedure, immediately appended to the original one and
which has oft en been interpreted as a verifi cation of it. Th e tablets on
which Proust focuses in her chapter display such a structure. Th e main
algorithm she examines is the one used to compute reciprocals of regular