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2
Procrustean Marxism and Subjective Rigor: Early
Modern Arithmetic and Its Readers
Travis D. Williams
M
athematics is what its texts show it to be. This chapter presents an argument about
how to read early modern mathematics—approached here through basic arithmetic
treatises—in order to respect this maxim, and about the consequences of forgetting it.
I will concentrate on the concept of rigor, perhaps the most important consideration
in any attempt to read mathematics as a cultural practice, and one that necessarily
encompasses all the others. I will argue that there is a reciprocal correspondence
between “reading” and “rigor,” so much so that to read mathematics appropriately, thor-
oughly, and respectfully, one must do the mathematics itself.
The relation mathematics has to its enfolding culture has everything to do with how
we read or misread, or accept or reject the importance of mathematics, or even perform
arithmetic correctly or incorrectly, and whether we recognize the difference. Scholarly
work on early modern mathematics in its cultural context has ably demonstrated the
relationship between evolving protocapitalist market economies and increasingly ubiq-
uitous mathematical discourses related to mercantile activity, colonial expansion, newly
evolving coordinations of rank, class, and land ownership, and their associated forms of
power. It would be naive to assert otherwise. But this is not the whole story. The fol-
lowing argument will be a demonstration of this collection's core concern, that a data
set is already interpreted by the fact that it is a set: some elements are privileged by
inclusion, while others are denied relevance through exclusion. In the case of early
modern arithmetic books, their economic function has always been included, while
their other discourses have often been excluded, simply because they seem never to
have been read. After a brief theoretical prologue, I will reintroduce these books. My
methodology implies that, for unknown texts, description is argument; description will
elicit the variety of their discourses. The second phase of my argument will show, with
theoretical support, that this variety is irreducible by economic or other constraints.
