  Objects are a centerpiece of the mathematical realm and our interaction with
and reasoning about it, just as they are of the physical one (if not more). And
humans' mathematical reasoning must ultimately be grounded in our general
intelligence. Yet in contemporary cognitive science and A.I., the physical and
mathematical domains are customarily explored separately, which allows for
baking in assumptions for what objects are for the system - and missing
potential connections.
  In this paper, I put the issue into its philosophical and cognitive context.
I then describe an abstract theoretical framework for learning object
representations, that makes room for mathematical objects on par with
non-mathematical ones. Finally, I describe a case study that builds on that
view to show how our general ability for integrating different aspects of
objects effects our conception of the natural numbers.
