The History of Mathematical Proof in Ancient Traditions

15 Argumentation for state examinations:

demonstration in traditional Chinese

and Vietnamese mathematics

Alexei Volkov

Introduction

Recently a number of authors have argued, once again, that a historical
study of mathematical texts conducted without taking into consideration
the circumstances of their production and use could be fundamentally
fl awed. For instance, E. Robson claimed that a large number of cunei-
form Babylonian mathematical tablets were produced in the process of
mathematical instruction, either by students or instructors, and therefore
their interpretation as ‘purely mathematical texts’ would be inadequate. 1
Robson’s taking into consideration the educational function of the cunei-
form mathematical tablets provided additional arguments in support of a
somewhat unorthodox interpretation of the mathematical tablet Plimpton
322, hitherto believed to be one of the best-studied Babylonian mathemati-
cal texts (this interpretation was originally suggested by Bruins in 1940s
and 1950s and reiterated by other authors in the early 1980s).
In conventional historiography of Chinese mathematics the mathemati-
cal treatises compiled prior to the end of the fi rst millennium ce were oft en
tacitly assumed to be mathematical texts per se rather than mathematical
textbooks; this assumption to a large extent shaped the approaches to their
interpretation. Th e characteristic features of textbooks (i.e. texts composed
as collections of problems oft en containing groups of generic problems and
detailed descriptions of elementary arithmetical operations without expla-
nations or justifi cations of the provided algorithms) were not allotted much
attention; instead, historians oft en focused on singular ‘mathematically sig-
nifi cant’ methods and results (such as the calculation of the value of π and
the algorithm for solution of simultaneous linear equations, for instance)
thus reinforcing the image of the received Chinese mathematical treatises
as ‘research monographs’ rather than ‘textbooks’.
However, even in modern mathematics a research paper can be used
as teaching material, and, conversely, a mathematical statement from a

(^1) Robson 2001 : 171. 509