I have been toying with the idea of value for a while and came up with this question a few days ago.
I think that it is impossible to say that mathematical knowledge has intrinsic value for mathematicians for the following reason:
Although mathematicians working especially in inapplicable fields of mathematics say that they love number theory or set theory for the "sake of itself," the whole premise of this statement rests on the idea of mathematical beauty. The elegance of the equations and the identities is what affines them to work in this field. All this is good, but by the very act of attaching something to even the purer areas of mathematics, they in essence, value knowledge outside its realm or simply put they do not value the Fermat Little Theorem because it exists but because it is elegant and in doing so they have given it a further extension.
This is my argument. Please do point out any inconsistencies or generalizations and also I would love to read any counter-arguments.