Is mathematics about truth or validity
From the very beginning I will suggest that when I discuss mathematics and its truth and validity, I will not simply be objectively reporting on its nature. In some ways I can not really say exactly what mathematics say, I have to report what I think it is. At least in the case of mathematics there is widespread agreement about its nature, what do people think about it. ... Moreover, we need to be careful, the reality about which physicists speak is something that most of us believe has real, material nature. Mathematics is an abstract structure. ... When we use mathematics in application, we go beyond mathematics itself. While it may be possible to speak with confidence about this theorem, that definition and even a certain proof, to know mathematics is not to be able simply to recite a list of statements, we have to take in our minds that mathematics is based on axioms that can not be truth or false.