Are Numbers Real?

[robvalue]

The answer to the question depends on what you mean by real.

Without opening a whole new can of worms, let's just put the question like this: Is math something we create or something we discover? If it is something that we discover, then that implies it has "an existence" of sort or another, independent of our perceptions.

I suppose another way of framing the question could be: Does math make truth statements? That is, does math make objectively verifiable claims? It could be argued that it does.

We create maths. We discover ways in which particular maths has applications when applied to reality.

Remember that maths need not have any bearing on reality at all. To say that you "discover" a new mathematical system would be metaphorical only; it would be like exploring the platonic plane of abstract concepts.

Maths makes statements which are either true or false within their own framework. They are true, essentially, because we say they are true. They are a logical result of applying the rules which we say are true. Verifying they are true is a matter of making sure the rules have been correctly followed.