12 karine chemla
sources with mathematical analysis in mind. His comparisons were with
Wallis or D’Alembert. On the other hand, at the end of the nineteenth
century, when Greek geometry overshadowed all other evidence for the
early history of proof, the value of rigour had been growing in signifi cance
for some decades, and academic mathematics was witnessing the begin-
ning of a new practice of axiomatic systems which would soon become the
dominant trend in the twentieth century. 17
Th ese arguments suggest that diff erent factors brought about the shift
in historiography outlined above and could account for the outline of the
now-standard narrative of the early history of proof. Some of these factors
clearly relate to the state of mathematics at a given time, both institutionally
and intellectually, but others are not directly related to it. Th e infl uence of
some of these factors may be felt at the present day and could explain the
lingering belief in this narrative as well as the signifi cance widely attached
to it. However, the same arguments invite us to look at this narrative with
critical eyes: the narrative belongs to its time and the time may have come
that we need to replace it.Dissatisfactions: overemphasizing certainty
For more than three decades now, some historians of mathematics have pub-
lished articles and books arguing that the Chinese, Babylonian and Indian
sources on which they were working contained mathematical proofs. 18
17 It would be interesting to document these correlations in greater detail. See e.g. I. Toth’s
work on the history of axiomatization. Other changes in the mathematics of the nineteenth
century also probably had an impact on the historiography in exactly the same way such
as the increasing marginalization of computing and the division between pure and applied
mathematics, which were soon perceived as two distinct pursuits and to be carried out in
separate institutions. Th ibaut’s critical remarks, mentioned above, on the practical orientation
of the mathematics in the Sulbasutras are probably an echo of the latter trend and illustrate
a typical motif of nineteenth- and twentieth-century historical publications. Regarding the
marginalization of computing and its impact on historiography, I refer to the forthcoming joint
publication by Marie-José Durand-Richard, Agathe Keller and Dhruv Raina.
18 For the Chinese case, let us mention the fi rst research works on the topic published in
English: Wagner 1975 , Wagner 1978 , Wagner 1979. One must also mention the fi rst works
in Chinese systematically addressing the issue: the 8th issue of the journal Kejishi wenji
(Collection of papers on the history of science and technology), in 1982; the 11th issue of the
journal Kexueshi jikan (Collected papers in history of science); Wu Wenjun 1982. Since then,
the publications are too numerous to be listed here. Th e reader can fi nd a more complete
bibliography in CG2004. Th e fi rst publication on the topic of proofs that could be read in the
Mesopotamian sources is Høyrup 1990. Since then, Høyrup has continued exploring this issue,
and other specialists of the fi eld have joined him to support and develop this thesis. A synthesis
of the outcomes of this research programme, the results of which were widely adopted by the
narrow circle of specialists of Mesopotamian mathematics, was published: H2002. As for the
Indian case, we can refer the reader to H1995: 75–7, Jain 1995. Th ese were followed more
recently by Patte 2004 , Srinivas 2005 , Keller 2006 , among others.