"Epistemology of Maths: Some Common Views are Wrong"
Here is a nexus of views not uncommon among philosophers of mathematics:
“Mathematics is an a priori science, in which proofs play a central role. This is largely because thinking through an argument warrants high confidence in its conclusion only if the argument is a proof. If, in thinking through an argument, visual experience has a role which is not merely enabling, the argument is not purely a priori but contains an a posteriori element, and for that reason is not a proof.”
I will cast doubt on all of this, apart from the claim that proofs play a central role.