this is an awful article, but i was thinking about something similar watching a chomsky lecture a few hours ago.

there's a strain of mathematics that is essentially platonic (with roots in pythagoras) that argues that numbers have an independent existence from the human mind. a modern proponent of this would be godel, which is an apparent paradox that i simply cannot grasp.

for the most part, though, modern mathematics completely rejects the idea - drawing largely on the mathematics of godel, which *proved* that arithmetic is incomplete, if not on the philosophy of hilbert. there have been a number of developments in axiomatic systems that make it clear that, by doing mathematics, we project our own perception of the reality around us. we can't even build a coherent theory of parallelism.

it's really a question of a classical v. a modern perspective, and it connects with other fields like physics and biology. quantum physics has rejected the idea that mathematics can be used to describe reality, whereas modern evolutionary concepts (notwithstanding the regression that game theory has thrust upon us) uphold the fundamentally stochastic nature of processes that happen around us.

it's not really an issue for debate anymore: math is a human construction, and kant was completely fucking wrong.

http://www.sciencedaily.com/releases/2013/07/130715070138.htm

there's a growing consensus, even, that, in order to really break through a number of the dead ends we're approaching in empirical science, we're going to have to develop a new language to describe reality.