We began in Chapter 1 with two general problems: Wren's switch of interests from astronomy to architecture; and the relation between his architecture and his early work in natural philosophy. The mathematical sciences tradition in England has helped to explain the domain he accepted for his work and to show that there was no fundamental shift in intellectual terms, even though the change had far-reaching professional implications for Wren. The same tradition is relevant to understanding the character of Wren's work in both professions.

We have seen clearly how fundamental was the role which mathematics, as it was understood within the mathematical sciences, played in Wren's natural philosophy. Its influence can be traced in the forms of abstract regulative criteria, direct mathematical formulation, and practical maths-based technology. Echoing the creeds of early practitioners like Recorde or Digges, Wren wrote that:

Yet the kinds of theories Wren formulated were not mathematical derivations from some high-level principles but, rather, were generalized accounts of observations, expressed in a mathematical formalism or as a geometrical model and constrained by certain pre-theoretical assumptions of neatness, elegance or symmetry.