Euclid has at least three different ways to state mathematical facts. As
Theorems, to be demonstrated, as problems to be constructed, and numbers
to be found (the latter are limited to Books VII - IX of the Elements, on
"numbers"). These are distinctions within the mass of mathematical
propositions in the Elements, not distinctions among propositions, some
of which are "mathematical" and some of which are not (compare e.g.
Descartes' Geometrie which is all about problems - no theorems - and
Hilbert's Foundations of Geometry - which is all theorems and no
problems).
There are modern versions of these dichotomies that one could cite (see eg
L. Dickey's preface to his book on integrable systems). There are few
mathematicians who have formulated their mathematics in a fashion which
includes all of these formats- but it can be done. Mathematics does not
have to be bifurcated into algorithmics and theorematics...
David Reed