Mathematical proof: a research programme 11
Understanding what other elements played a part in the shaping of our nar-
rative is another way of developing our critical awareness of the narrative.
As R. Yeo has argued regarding the case of early Victorian Britain in
the publications mentioned above, the professionalization of science and
the development of the sense of a ‘scientifi c community’, as well as the
need of the practitioners to reinforce the unity of ‘science’ for themselves
and its value in the eyes of the public, can be correlated with an increase
in the size and number of publications devoted to the ‘scientifi c method’.
Th e distinctive features of the method enabled it to maintain the cohesion
of the community and enhance the value of the social group in the eyes of
the public. It shaped the social and professional status of those who were
soon to be called ‘scientists’. Philosophy of science and history of science
emerged and developed as disciplines through this historical process and
were instrumental in the pursuit of the question of method. How were the
understanding and discussion of mathematical proof infl uenced by this
global trend? In my view, this is a key issue for our topic, to which we shall
come back below but which awaits further research. 16
A consideration of the mainstream development of academic mathemat-
ics during the nineteenth century casts more light on our narrative from
yet another perspective. It also allows the perception of other elements that
may have played a part in constructing the narrative. Indeed, the approach
to proofs of the past at diff erent time periods correlates with more general
trends in the mathematics of the time. On the one hand, as we saw, in the
fi rst decades of the nineteenth century, Colebrooke was reading his Indian
16 Clearly, proof was a topic of explicit discussion within disciplinary writings, as the fi rst edition
of George Peacock’s Treatise of Algebra (1830) shows. Th e pages starting from paragraph
142, on p. 109, were devoted to the question: ‘What constitutes a demonstration?’ Further,
John Stuart Mill’s discussion of methodology, in his A System of Logic, Ratiocinative and
Inductive , fi rst published in 1843, encompassed an analysis of mathematical proof and led
him to off er an interpretation of Euclidean proofs as reliant on an inductive foundation and
their certainty as an illusion (p. 296). Th is example shows how refl ections of mathematical
proofs were infl uenced by wider discussion of methodology. By comparison, Auguste Comte’s
considerations on demonstrations were less systematic. Conversely, another question is worth
exploring: what role did ideas about and practices of mathematical proofs play in shaping the
various discourses about methodology? Even though considerations about demonstration
are pervasive in the methodological books of that period, it seems to me that this feature has
received little attention. An exception is the discussion of Whewell’s ideas regarding the various
practices of proof in the context of his wider concern for the teaching of mathematics and
physics in Yeo 1993 : 218–22. In this case, questions of method relate to pedagogic effi ciency
and tie mathematics to natural science. Hacking 1980 (reprinted as chapter 13 in Hacking
2002 : 200–13) sheds interesting light on the question of the emergence of methodology in
the seventeenth century. On the issue of mathematical proof as such, this article is updated in
Hacking 2000.