Could the universe have existed with either physics or math but not both? What would be some consequences?

Do you think it is just coincidence that mathematics contains structures which can be used to describe physical processes, or do you think mathematics and physics are linked on some deeper level?

There are still many branches of mathematics that have no apparent connection to physical phenomena. Do you think that all mathematics describes some physics and it is just a matter of time until someone sees the connection? Or do you think mathematics does have parts that are only to itself? What does either point of view suggest about the nature of Nature?