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What are numbers?
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12/3/2014 7:36:52 AM Posted: 2 years ago We use numbers every day, but taking a step back, what are they, really " and why do they do such a damn good job of helping us explain the universe (such as Newtonian laws)? Mathematical structures can consist of numbers, sets, groups, and points " but are they real objects, or do they simply describe relationships that necessarily exist in all structures? Plato argued that numbers were real (it doesn't matter that you can't "see" them), but formalists insisted that they were merely formal systems (welldefined constructions of abstract thought based on math). This is essentially an ontological problem, where we're left baffled about the true nature of the universe and which aspects of it are human constructs and which are truly tangible. (Source: io9.com)

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12/3/2014 9:52:26 AM Posted: 2 years ago Numbers, and all mathematics for that matter, are all derivatives of logic.
So where does logic come from? Clearly logic does not come from the physical realm, so this would imply that it is a metaphysical concept. If this is correct, then numbers exist in the metaphysical realm but can be used by our mind to gain understanding of the physical realm. I may be wrong, but this was my initial reaction when reading your question :) 
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12/3/2014 11:24:58 AM Posted: 2 years ago Speaking from a physics point of view numbers and maths in general are just a tool to help with understanding. So I rarely stop to think about the nature of numbers.
I might be wrong but I think it was Shaw who tried to define numbers in an independent and consistent way. I think this led to defining numbers as collections of the null set. But does having a definition for each number tell us anything about them? I am not sure. A common debate between physicists is how the universe relates to maths and numbers. Does maths describe the universe or is there a deeper connection. Is the essence of the universe encapsulated in maths. Some physicists think it is a deep connection because it is so successful at making accurate predictions about the nature of matter and energy, some of which are very surprising such as antimatter. Personally I feel there is a reality to numbers, that they exist in our absence. This is based on the assumption that the universe is not just in my imagination but exists separately from me and that I can trust my senses to tell me the truth about it. The universe is described accurately by numbers and runs without me watching it so numbers continue without me. But perhaps that is a naive view. Let's hope "the truth is out there" cos there is bugger all round here. 