The problem of contingency: "Why this universe and not some other?"
Tegmark considers that "some subset of all mathematical structures...is endowed with...physical existence" (M. Tegmark, Annals of Physics, 270, pp1-51, 1998). In later papers Tegmark suggests that ALL mathematical structures have physical existence and then that all finite computable structures have physical existence (Foundations of Physics, 38, pp101-50, 2008).
In my view:
Observing (interacting with) the physical world we learn/record a collection of patterns and procedures (action patterns/sequences). We learn to count, to gather objects together (form collections), to add objects to a collection (add), to remove objects from a collection (subtract), to compare collection sizes (equate), to divide collections into a number of equal size smaller sets (divide), etc., etc. Science studies the patterns we see in the world of our experience, the "physical world."
In mathematics we study patterns, both those we see in the world and any patterns that we choose to make up. We combine elementary patterns, divide them up, recombine, etc. Some of what we compose is then found to occur in the world, some is not. (We see horns in the world. We see ponies in the world. We combine these to form unicorns. We don't happen to find unicorns in the world of our experience.)
My artificial intelligence Asa H thinks in this same way.