Do numbers exist independently of human perception? Or are they just illusory mental objects? Here are some thoughts for your consideration.
The Universe is composed of energy, so everything in it is necessarily composed of energy. Numbers can be manipulated; therefore numbers exist in some form, and therefore numbers are composed of energy. Energy is real, numbers are real. Hopefully that gets us past the philosophical speculations and we can ask more interesting questions:
Real numbers exist, so how do they manifest themselves? What are they? Where are they?
Perception, and in using that term I am including rational thinking, divides energy into forms called ideas; more accurately, because ideas require other ideas for their definition, it divides energy into IdeaContexts ("ICs" for short, integrated circuits structured by analogy, but that's a story for another day). ICs have relative sizes: God is the largest IC, and domain, phyla, and species, along with battleships, yachts and canoes, not to mention 3,2,1, are smaller ICs within the God IC.
This approach describes a perceptual landscape of power relationships. Bigger, smaller, equal ICs sorted by rational – ratio – thinking, which is a procedural embodiment of the greater including/influencing the lesser. Now we can consider two additional questions:
Do power relationships exist in the Universe? If so, did any of those relationships exist prior to human perception? If you answer yes to both questions, then what we call numbers, the Universe calls power relationships.
I think the lawyers call that a distinction without a difference.
Many thanks for your time.