Mathematical proof: a research programme 19
a priori by reference to norms and values that would appear to us as charac-
terizing proofs in an essential way.
From this basis, the various chapters aim at identifying the variety of
goals and functions that were assigned to proof in diff erent times and places
as well as the variety of practices that were constructed accordingly. In brief,
the authors seek to analyse why and how practitioners of the past chose to
execute proofs. Moreover, they attempt to understand how the activity of
proving was tied to other dimensions of mathematical activity and, when
possible, to determine the social or professional environments within
which these developments took place.
Beyond such an agenda, several more general questions remain on our
horizon.
From a historical point of view, we need to question whether the history
of mathematical proof presents the linear pattern which today seems to be
implicitly assumed. How did the various practices of proof clearly distin-
guished in present day mathematical practice inherit from and draw on
earlier equally distinct practices? In more concrete terms, we seek to under-
stand how the various practices of proof identifi ed in ancient traditions
or their components (like ways of proceeding or motivations), developed,
circulated and interacted with one another. Th ese are some of the questions
that arise when attempting to account for the construction of proof as a
central but multifaceted mathematical endeavour that unfolded in history
in a less straightforward way than it was once believed.
From an epistemological point of view, on the other hand, we are inter-
ested in the understanding about mathematical proof in general that can be
derived from studying these early sources from this perspective.
Further lessons from historiography, or: the historical analysis
of critical editions
Th e analysis developed so far was needed to raise an awareness of the
various meanings that have overloaded – and still overload – the term
‘proof ’ in the historiography of mathematics. We brought to light how
agendas involved in this issue fettered the development of a broader
programme which would consider proof as a practice and analyse it in all
its dimensions. Before we outline how the present book contributes to this
larger programme, further preliminary remarks of another type are still
needed.
Our approach to proofs from the past is mediated by written texts. In
his contribution to the debate evoked above, wherein he described the