16 karine chemla
actual work seem quite diff erent and multifaceted, in fact. Some insight on
this point can be gained from the contributions to a debate that broke out
in the pages of the Bulletin of the American Mathematical Society about a
decade ago. 25 Th e paper by Jaff e and Quinn that launched the discussion
recognized the importance of ‘speculating’ – which they called ‘theoretical
mathematics’ – for the development of mathematics, in addition to proofs
which secure certainty. However, the authors expressed concerns regarding
the confusion that could arise from confounding rigorous proofs (ones that
bring certainty), insights, arguments and so on. As a consequence, they
suggested norms of publication that would distinguish explicitly between,
on the one hand, ‘theorem’, ‘show’, ‘construct’, ‘proof ’ and, on the other
hand, ‘conjecture’, ‘predict’, ‘motivation’, and ‘supporting argument’. 26 One
may venture to recognize in this opposition a divide of the type we are
examining with respect to history.
It is impossible to review the debate in detail here. However, for our
purposes, it is interesting to observe the intensity of reaction that this sug-
gestion elicited in the mathematical community. From the responses pub-
lished in the Bulletin , a much more complex image of the activity of proof
emerges, in which rigorous proofs appear to arouse mixed feelings and
cohabit with all kinds of other modalities of proof. 27 Moreover, the relation
of proof to other aspects of mathematical activity appears to be quite intri-
cate and calls for further analysis. In relation to our topic, I interpret the fact
that, ironically, many mathematicians do not fi nd it diffi cult to recognize
as proofs arguments from Chinese or Indian texts although other scholars
deny them this quality as an additional sign of this coexistence of motley
practices of proof in the mathematical community. Were further evidence
still necessary, these facts indicate that there are confl icting ideas among
mathematicians about what a proof is or should be. Why, in such circum-
stances, should historians or philosophers opt for one idea as the correct
one and civilize the past, let alone the present, on this basis?25 Some of the pieces written for this debate were already mentioned above. Here are the
references to the entire core exchange: Jaff e and Quinn 1993 , Atiyah, Borel, Chaitin, Friedan,
Glimm, Gray, Hirsch, Lane, Mandelbrot, Ruelle, Schwarz, Uhlenbeck, Th om, Witten and
Zeeman 1994 , Jaff e and Quinn 1994 , Th urston 1994.
26 J a ff e and Quinn 1993 : 10.
27 Th e relationship between the written text of the proof and the collective oral activity related to
proof that emerges from these testimonies presents a potentially worrying complexity to the
historian, whose only sources are written vestiges with a faint relation to real processes of proof
production.uniform, objective and fi rmly established theory and practice of proof ’ (p. 1.) A comparable,
yet diff erent, account of proof, which is quite critical of standard views, is provided by
Rav 1999.