First, math is both discovered and invented. The relationship between a circle and its circumference is a discovery. The invented part is the formula for determining what the circumference of a circle is; the symbolic language humans invented to manipulate and make use of the relationship we discovered.
But I think what the OP might be getting at is that the relationships we're looking at exist only because of how we define the terms.
So, we define what a circle is, and can then disCover relationships between it's circumference and area. And we find that these relationships are good approximations to real world objects (only approximations, since a real world circlular object is onlt an approximation to a mathematical circle).
But then what about much more esoteric maths? Are quaternions real? You may say their relationships to other mathematical objects are real; and something we discover; but then they only have those relationships because mathematicians defined them into existence by defining the properties of a quaternions.
I guess the point is, that we can discover what the logical implications are if we define things to obey certain conditions. And we may find the objects we defined useful for modelling some aspect of the real world. But that does not necessarily mean the real world actually works in any way like the object we've defined - the similarity may break down under certain conditions.
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