[donh]

Are you under the impression that pure math hasn't got it's byways and alleys where we deal with failures, natural limits of analysis, and groping around in the dark, unaided by provably formal demonstrations?

Not in pure mathematics. It is not the same as an experimental science. Axiom, definition, theorem -- if it's proven, it's right. No muss, no fuss.

You don't know what you are talking about. Much of "pure" mathematics has not been assailed by formal systems of proof, and some never can be, provably. You opinions about biology are as uninformed as your opinions about formal mathematics.

[AmishDude]

Much of "pure" mathematics has not been assailed by formal systems of proof, and some never can be, provably.

I think you don't understand what mathematics is, let alone pure mathematics. Mathematics is proof. If there's no proof, than it's something other than mathematics.