We analyze, from a theoretical viewpoint, the bidirectional interdisciplinary
relation between mathematics and psychology, focused on the mathematical theory
of deterministic dynamical systems, and in particular, on the theory of chaos.
On one hand, there is the direct classic relation: the application of
mathematics to psychology. On the other hand, we propose the converse relation
which consists in the formulation of new abstract mathematical problems
appearing from processes and structures under research of psychology. The
bidirectional multidisciplinary relation from-to pure mathematics, largely
holds with the "hard" sciences, typically physics and astronomy. But it is
rather new, from the social and human sciences, towards pure mathematics