My friend has a theory about 'instantiation' of numbers, they believe that every time we think of a number we create an 'instance' of it in our own heads, it's the same idea, but each time we think, another instance is created, and the previous one eliminated and he believe mathematical expressions are more about using these 'instances' than the objects themselves, for example:
1+2=3 means to him that 1+2 is an instance of 3 as it is equal to another instance of 3 and + is a sort of 'combining' operation between the instances of 1 and the instance of 2, giving an instance of 3 where equality implies they are 'qualitatively identical' as opposed to 'numerically identical' as we talk about most mathematical objects in standard mathematics.
I asked him whether he's referring to a particular instance, and he said it's general like a chemical formula where Co2+H20 refers to 'any molecule of each element, you reference the element, but in the context you mean 'any molecule of', in the same way, if you combine 'any instances 1+2 you get another instance of 3 in 1+2 which will be equal to any other instance of 3'. Perhaps, in the context of chemical formulas we can consider the + and the arrow as operators on the elements themselves to form mappings (such as element A's molecules for chemical bonds with element B), which eliminates any 'implied' context to it.
Of course this is all non-standard and made up, but is there any useful part of it, could we from an entirely philosophical perspective view it like this, what really are the 'referents' in a mathematical expression, do we only ever refer directly to the 'types' (numbers) or could we see it in an alternative way like this?