Mathematics and the mind reflect each other. 🙂
The fields ofand both use quite a bit of mathematics.
The answer hangs on what is meant by the word “mimic” in the question. One way to interpret the question is this: Will ideas about cognition mirror ideas about abstract mathematical concepts? From one perspective you could say this is necessarily the case: since human minds produce mathematics, the structures of mathematics must conform to the constraints of the structures of human thought.
Going in the other direction, mathematics is a key tool for understanding the natural world, and so if we study the mind/brain using methodologies derived from physics, chemistry and engineering, we will no doubt find ourselves using mathematical terminology, analogies, and concepts to describe mental processes.
This blog post I wrote gives an overview of the theoretical and mathematical approaches to the mind/brain:
And this book may be of interest in exploring the psychological roots of mathematical concepts:
Image: Drawing Hands by MC Escher.