The thought process began thinking all mathematical equations can be translated to English and vice versa. There must be a shared structure to language and math, or an isomorphism at the least. The effectiveness of mathematics then is more about its conciseness, not that it says anything new about the world we don't have with language.
One "natural" idea is that both our internal representations and external reality depend on spatio-temporal relations. Through sptatio-temporal relations a sound might hit our left ear before our right, or that we have a memory of the past and not the future. Noticing these relations are what are brain is good at, because it too is spatio-temporally laid out. We could then imagine from this base set of relations we construct language and math, to capture them.
But, and I hate to sound cliche, quantum mechanics might be showing relations beyond this picture of spacetime. Does math and language need to add some new relations to its repertoire to capture entanglement and wavefunction collapse? Or can it get there with its current structure? It kind of depends on what QM really is telling us. But how to get there... If math and language were built from only relations our brain and body could sense, maybe we are in danger of making empirically-refutable mathematics. How would that even look I have no idea. I have come across philosophy of mathematics essays saying math is our most global framework, able to accommodate any and all structure thus far, but still open the possibility of empirical refutation.
I don't want to get too "out there", but QM did spell the end for our classical picture of the world. Math gives us the precise statistics (e.g. wavefunctions), but does not tell us the causal story of QM. There are current-mathematics causal stories of QM (bohmian, etc), but they too disrupt our conception of spacetime and relativity. If the world is not spacetime limited, then doesn't that call into question our senses and language and math if they came about in the above method? I'm not entirely sure how the classical picture fits with math and language, but they seem connected to a large degree.
