Perhaps that points to our cognition being a mathematical product. Are there ways of understanding things in a non-mathematical - meaning non-cognitive - way?

Perhaps that points to our cognition being a mathematical product. Are there ways of understanding things in a non-mathematical - meaning non-cognitive - way? Is there something greater than Turing Completeness? Such an idea is silly because we're using reason to fathom the answer. When we encounter some sort of alien cognition out there which is beyond the bounds of math, it either will be understandable and expand our mathematical vocabulary as we seek to formalize it... Or it will look just like gibberish and passed off as 'too chaotic, or too self-referential', or some other unfathomable quality.