Well of the nature of mental concepts is a philosophical minefield as is the question of to what, exactly, the words we use for them refer.
In the case of mathematics the general intuitionist view is that the rules of mathematics are a human invention - Wittgenstein (or possibly Dummett) described them as a `psychological quirk' and then rather unconvincingly (in my opinion) posited a race of aliens who considered the value of an object to be it's area in contact with the ground and who saw nothing odd in an object changing it's value if you put it on its side but that is by the by.
Leaving aside the awkward question of what mental states are and how they relate to the reality beyond our senses, we can say that `red' is a fuzzy concept, a categorisation of a continuum that has no actual discrete segmentation, but which it is convenient for people to use in discourse and has. Infinity and imaginary numbers are worse than this, insofar as they refer to anything, they refer to something that definitely doesn't exist. The rules of mathematical reasoning are even harder to justify since it's difficult to even semi-convince yourself they might refer to some abstract object.
Moreover, unlike red, and its fuzziness of reference around the edges there is relatively little dispute, in practical situations, over the meaning of the terms infinite, imaginary number, rule of deduction. We rely on these terms to describe, predict and guarantee things about our environment which seems a lot of expect of a psychological quirk or a discursive convenience unless they capture some truth about the way physical reality works (much as red, admitedly imperfectly, captures some range of the light spectrum) but since these concepts have no physical reality we are forced to start talking about an abstract reality (in a way that red doesn't force us to do) and most current philosophers find that very objectionable.
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In the case of mathematics the general intuitionist view is that the rules of mathematics are a human invention - Wittgenstein (or possibly Dummett) described them as a `psychological quirk' and then rather unconvincingly (in my opinion) posited a race of aliens who considered the value of an object to be it's area in contact with the ground and who saw nothing odd in an object changing it's value if you put it on its side but that is by the by.
Leaving aside the awkward question of what mental states are and how they relate to the reality beyond our senses, we can say that `red' is a fuzzy concept, a categorisation of a continuum that has no actual discrete segmentation, but which it is convenient for people to use in discourse and has. Infinity and imaginary numbers are worse than this, insofar as they refer to anything, they refer to something that definitely doesn't exist. The rules of mathematical reasoning are even harder to justify since it's difficult to even semi-convince yourself they might refer to some abstract object.
Moreover, unlike red, and its fuzziness of reference around the edges there is relatively little dispute, in practical situations, over the meaning of the terms infinite, imaginary number, rule of deduction. We rely on these terms to describe, predict and guarantee things about our environment which seems a lot of expect of a psychological quirk or a discursive convenience unless they capture some truth about the way physical reality works (much as red, admitedly imperfectly, captures some range of the light spectrum) but since these concepts have no physical reality we are forced to start talking about an abstract reality (in a way that red doesn't force us to do) and most current philosophers find that very objectionable.