Is the Universe comprehensible?

As Einstein said, “The most incomprehensible thing about the world is that it is comprehensible”. But is it really comprehensible?

Let’s suppose that the Universe is, at the end, a sort of mathematical structure (as supposed by Max Tegmark). The question is, can we know this structure? That would mean that this mathematical structure allows to contain a description of itself, written in its own “language”. As Humans, we are a part of this structure. If we understand this structure, that means that we have a description of it inside our brain. Our brain is a physical object, and any information inside it is encoded as physical processes. In fine, this description is encoded in terms of the fundamental structure itself.

Is it possible? Does mathematical structures that allow to encode a complete description of themselves do really exist? This seems to be a very Gödelian question!