Mathematics is a science of method (the science of measurement, i.e., of
establishing quantitative relationships), a cognitive method that enables man
to perform an unlimited series of integrations. Mathematics indicates the
pattern of the cognitive role of concepts and the psycho-epistemological need
With the grasp of the (implicit) concept “unit,” man reaches the conceptual
level of cognition which consists of two interrelated fields: the conceptual
and the mathematical. The process of concept-formation is, in large part, a
A vast part of higher mathematics, from geometry on up, is devoted to the task
of discovering methods by which various shapes can be measured—complex methods
which consist of reducing the problem to the terms of a simple, primitive
method, the only one available to man in this field: linear measurement.
(Integral calculus, used to measure the area of circles, is just one example.)
In this respect, concept-formation and applied mathematics have a similar task,
just as philosophical epistemology and theoretical mathematics have a similar
goal: the goal and task of bringing the universe within the range of man’s
knowledge—by identifying relationships to perceptual data.