Seen and Unseen...

"We have never seen any curve or solid corresponding to my square root of minus one.  The horrifying part of the situation is that there exist such curves or solids. Unseen by us they do exist, they must, inevitably; for in mathematics, as on a screen, strange, sharp shadows appear before us. One must remember that mathematics, like death, never makes mistakes. If we are unable to see those irrational curves or solids, it means only that they inevitably possess a whole immense world somewhere beneath the surface of our life."

-- Yevgenii Zamyatin, quoted in Michael Harris's "Mathematics Without Apologies"