Until the first quarter of the seventeenth century there
was a great deal of agreement about
the nature of mathematical practice. Mathematicians, as well as their patrons
and clients,
viewed all possible aspects of their work, both theoretical and practical,
as being included
within their discipline. Although the mathematical sciences were a fairly
recent foreign
import to England, which can barely be traced back beyond the mid-sixteenth
century, by
the beginning of the seventeenth century there was a large and growing
body of
practitioners with a unified view of their subject's identity. Divisions
began to appear,
however, and they were often framed in terms of the proper mixture of theory
and practice
in mathematical education.
One early sign of the emergence of this tension is the kind of accusation
made in the
priority dispute between William Oughtred and Richard Delamain taking place
around
1632. Their bitter conflict began over who first invented the Horizontal
Quadrant, a form
of sundial, and the Circles of Proportion, a logarithmic calculating device
that can be
considered a precursor of the slide rule, and ended in a dispute over what
constituted
proper mathematical practice. Oughtred accused Delamain of making his students
‘only
doers of tricks, and as it were Juglers’ by teaching them
the use of instruments without any
theoretical foundation. Instruments, Oughtred claimed, could only be used
with
understanding by students who had a proper theoretical foundation. He advocated
postponing their use until after the theoretical foundations of a subject
had been
thoroughly mastered. Delamain, on the other hand, was perfectly willing
to teach practical
instrumental operations without insisting upon a theoretical grounding.
This paper will
use the dispute between Oughtred and Delamain to investigate the breakdown
of
consensus over internal mathematical boundaries, the rhetoric and strategies
involved in
attempts to gain authority by mathematical practitioners, and the extent
to which their
roles were negotiated, both with other practitioners, and with their patrons
and students.