52 karine chemla
acts. Moreover, she delineates the techniques used by the commentator to
account for an algorithm.
Here, similarities with the Chinese sources appear. One of the key
techniques Bhaskara uses is to highlight how a given procedure is in fact
supported by a fundamental, general procedure, in the terms of which
the original procedure can be rewritten. Such a technique also appears
in Chinese commentaries, where a technical term ‘meaning ( yi′ )’ is used
exclusively to refer to the kind of meaning of the procedure that a proof
brings to light in this way.^59 Th is similarity between the two contexts pos-
sibly derives from the fact that the activity of interpreting a classic inspired
similar conceptions of the ‘higher meaning’ of an algorithm.
Showing that diff erent procedures can in fact be explained in the terms
of the same fundamental, general procedure is one way in which proofs
highlight relationships between algorithms which at fi rst glance might
appear unrelated. In such cases, something circulates among the proofs,
and thanks to the proofs, in a way that can be compared to the techniques
brought to light by Saito in the core corpus of Greek geometrical texts. Th is
circulation again requires a reading of the proof in and of itself, and not
merely as a means to prove the correctness of a procedure. Moreover, what
circulates between the proofs diff ers depending on the context. In Sanskrit
and Chinese sources, a procedure circulates, that is, a statement of the same
kind as the proposition to be proved. In other terms, the technique of proof
is at the same time a new statement. Again, this echoes present-day math-
ematicians’ claim that proofs are a source of knowledge for them. However,
the procedure in question is not ordinary, since the mere fact that it can be
put to such uses indicates that it is more fundamental and more general
than others. One may hypothesize that the identifi cation of procedures of
this kind formed one of the goals that motivated the interest in proving in
these contexts. 60 In this case, the historian would miss one of the epistemo-
logical expectations with respect to proving, were he to analyse it only from
the viewpoint of its ability to establish the statement to be proved.
It is also interesting that, in the context of Bhaskara’s commentary as
well as in the Chinese commentaries, fi gures were introduced for types of59 On this ‘meaning’ yi′ , see the glossary I compiled, CG2004: 1022–3.
60 For Chinese sources, there is evidence supporting the claim. Compare Chemla 1992 , Chemla
1997b. We reach a conclusion that was already an outcome of Lakatos’ analysis of the activity of
proving in Lakatos 1970. Th is convergence is not surprising: we share with Lakatos’ enterprise
a starting point, that is, that there is more to proof than mere deduction. However, the nature
of the statements produced in the contexts Lakatos studied and those we studied diff ers,
showing that one could go deeper in the analysis of how proofs yield mathematical knowledge
(concepts, statements and techniques).