A not philosophical answer - amplifying what was said above about the construction of “mathematics.”
Much of what we think of as “thinking” is really learned procedures, many associated with learning a language including the vasty important trick of linking a sensation (sound or sight) to a cluster of facts - symbolic representation.
Please check out this post:
Note the bit about learning that things could have a name; this comes with language.
This is one of the basic supports that “math” depends on. There are others important bits and they all come with learning a language.
To amplify on this slightly - we expect that part of the action of the forebrain to select and implement a chain of activation that results in some activation pattern along the central sulcus (motor cortex) that make the body move.
A less obvious part of this is that at an early level of this process some of the projections from the forebrain never leave the brain, they project to parts of the brain that are associated with memories of perceived objects where the WHAT and WHERE streams come together. We normally consider this as thinking. The act of learning a language trains us to use this process in certain ways. These are learned actions much like learning to walk. In this case, we are learning to communicate internal states with things like naming and elaborating goal seeking with vocal sound production instead of walking and reaching.
As you are trying to work out this basic math thing remember that there are limits to what simple local processing may be dong. It could take the coordinated actions of large number of maps to do these tasks.
Thinking of the progression of:
- Chemical messenger
- Synapse
- Dendrite
- Cell
- Mini-column
- Macro-column (or hex-grid node in my way of thinking)
- Collection of columns (or hex-grid …)
- Map
- Collection of maps
- Cortex/subcortical structure
- Sequential operations local to the brain
- Brain-body interaction
As you are trying to work out some aspect of brain operations is it critical to establish at what level(s) these are manifested at. Picking the wrong level(s) is sure to lead to dead-ends, wasted effort, and frustration.