46 karine chemla
interpreted as related to the statement of rules which ground the correct-
ness of the algorithm. Proust thereby accounts for the meaning behind the
numerical display as found in Tablet A, suggesting that it made sense for its
readers in a way comparable to how an algebraic formula makes sense for us
today. For her, the numerical text enjoys a kind of transparency in regard to
the algorithm treated, making the operation of the procedure explicit. Th e
reader could thereby see why and how the algorithm worked. Th is is how
Proust argues that the numerical text bears witness to an interest in the cor-
rectness of the algorithm for computing reciprocals. Note that Proust’s argu-
ment is in agreement with what Høyrup has shown. Although they operate
in diff erent ways, they both highlight that a specifi c kind of inscription has
been designed to note down an algorithm while pointing out the reasons for
its correctness. In some sense, Proust’s thesis with respect to these tablets
concurs with Netz’s conclusions on the Arithmetics. In her view, Tablet A
bears witness to the development of an artifi cial kind of text designed to
make the algorithm surveyable. Yet, in both cases, diff erent aspects of the
working of the computations are made surveyable. Note further that, once
more, the fact that actors constructed a specifi c kind of text to make specifi c
statements with respect to algorithms means that historians have to design
sophisticated methods to argue how such texts should be interpreted and
what they mean. Here an interest in the correctness of the procedure can
only be perceived through lengthy consideration of the text itself.
Let us pause here for a while and consider what we have accomplished in
this subsection so far. We have entered the world of proving the correctness
of algorithms. As was stressed in Section ii of this Introduction, this was
precisely a part missing from the standard account of the history of proof
in the ancient world. By enlarging the set of sources and the issues about
proofs considered, we began to see the emergence of a new continent. But
there is more.
We saw above that an operation – take multiplication, for example –
computes two things: a number and a meaning. A multiplication can
produce the value which is claimed to be the product of two numbers. Or
it can be interpreted as computing the area of a rectangle. On this basis, we
see that Proust analyses texts addressing the former feature of the opera-
tion, whereas Høyrup considers texts that deal with the latter feature. In
what follows, we shall proceed in the development of this segment of the
history of proof, showing how various groups of actors have established the
correctness of algorithms.
Proust’s fi nal point about Tablet A relates to its specifi c structure, namely,
the display of an application of the algorithm followed by the display of its