What could mathematical cognition tell us about the actual world

Recent studies concerning mathematical cognition show that we may find mathematical cognitive capacities in young infants and monkeys. They show that we possess an innate intuition of small natural integers around the age of six month. Yet, if we speak of intuitions, they are intuitions of what? So, the target of my study is to try to clarify the role intuitions play in mathematical cognition. My claim is that the results of these studies endorse a form of mathematical structuralism; the actual world is mathematically structured.