Are the axioms of math subjective? If they are, then logically all the formal consequences that flow from them are also subjective. Thus there can be no objective mathematical facts. Someone said this: Someone then replied this: But then later made the contrasting statement: A priori knowledge is knowledge claimed to be independent of experience. So it would be "internal" in being derived by reason and yet also (it is argued) objective - ontically true rather than merely an outcome of human modelling, human construction. Of course, subjective~objective is only one way of framing this dichotomistic distinction. Others (which could be better) include immanent~transcendent. Or in more recent epistemological debate, internalist~externalist. And broadening the terminology further, these issues have been discussed in terms of the analytic~synthetic and the contingent~necessary. Or the Platonic dichotomy of chora~form. And of course, the dichotomy epistemology~ontology breaks across the same lines. The point is, subjective vs objective is not a hard and fast distinction here. But there is a broad understanding of what the distinction involves. And so the question is: are axioms subjective (as I would argue is "proven" by Godellian incompleteness)? And if so, then all maths is constructed, even if we may feel the consequences of axioms have an "objective" or a priori truth - self-evidently true in the light of what has been assumed to be true?