[black_knight]

If this space of possible structure is real, but seemingly immaterial, how does our matter brain access it?

I think we create mathematics as thought structure in our mind. We can agree on things when we create the same structures. But this structure did not exist prior to creation.

[hackinthebochs]

I don't know what real means; I might call it real depending on one's definition. I definitely wouldn't call it immaterial (though it's not material either). We access it by construction: apply relevant rules and discover their consequences. Two people probing this structure are equally constrained by the requirements of consistency. There is no Benacerraf-style access problem.