alt Hacker NewsI think Hardy would be very much on the same page with me, as well as Godel and many others. Mathematical truths exist independently from our feelings and processes to discover them. People do and should argue about which truths are interesting to pursue and refine, but all of them are out there to be discovered... or not.
Whatever philosophy you prefer, math is about establishing objectively valid logical results, completely independent of the human process used to arrive at them.
Axioms don't exist independently from our feelings and processes, we pick axioms we feel are good, and axioms defines mathematics.
Mathematicians even argue which axioms we should have, it isn't objective in the slightest, mathematics is therefore very closely linked to our feelings and intuition. Remove that and you just have formal logic, a very different field.