God is the obvious one.

Arguably god is not an "aspect of nature", but in this case, how do you define an aspect of nature? Something susceptible of an exact mathematical treatment? That's circular reasoning.

If you are an atheist, god may not be in your nature, but it is impossible not to believe in some unfalsifiable idea. I mean, I assume that I am not a Boltzmann brain and that you exist and that you are a human just like me, not just a NPC in a simulation. This is not mathematically quantifiable, but it is essential to make sense of the world.

And there is Gödel's incompleteness theorem.

well, the claim that all aspects of nature are susceptible of an exact mathematical treatment, for one

consciousness

Is it a counter-example though? We currently seem not to possess the tools to model the principles of consciousness, but I think the parent was going in the direction of aspects of reality that in principle evade mathematical modelling. Thus which always would evade physics which is modelling nature using mathematics. I can not think of one.

It seems to be an article of faith that consciousness can be modeled mathematically

I was not claiming that we can, I wanted to point out that we do not know if we can not. (maybe bad phrasing). Especially, as we observe that while science progressed, aspects which looked like that they could not be modelled at some point surprisingly could.

I guess, to count it as counter-example it would be necessary to have evidence that it is an aspect of reality and to have evidence that it can not be modelled. If I did not miss something, we do not have a solid definition for consciousness. I agree, that there could be definitions of consciousness which evade mathematical modelling, but then we have to still show that this specific definition is realised in nature, correct?