Full Idea
We could not discover irrational numbers by physical measurement. The discovery of the irrationality of the square root of two was an intellectual achievement, not at all connected to sense experience.
Gist of Idea
The irrationality of root-2 was achieved by intellect, not experience
Source
James Robert Brown (Philosophy of Mathematics [1999], Ch. 1)
Book Reference
Brown,James Robert: 'Philosophy of Mathematics' [Routledge 2002], p.5
A Reaction
Brown declares himself a platonist, and this is clearly a key argument for him, and rather a good one. Hm. I'll get back to you on this one...