Gregory's Server@dadakopf - Antimatter is an interesting case.
Dirac's theory of the electron predicted that it had a positively charged antiparticle of the same mass. He chickened out and suggested this was the proton. The mathematician Weyl said essentially "come on, Dirac, that doesn't have the same mass as the electron!" Then Dirac got brave enough to predict the electron had a positively charged antiparticle of the same mass. Then the experimentalists saw it!
But the funny part is, the experimentalists had already been seeing this antiparticle in photographic plates, spiraling the opposite way from the electron in the Earth's magnetic field. But they didn't believe that was possible, so they though someone had accidentally flipped those plates over.
@johncarlosbaez I have this vague memory that somewhere in Wittgenstein, he says that if you were walking down the street and there was something there utterly foreign, or unknown to you, that you wouldn’t see it. Maybe there has to be some sort of psychological twist to make the unseen seen or something. Dark matter is dark because we don’t know how to see it and thus we don’t know what it looks like. Can math function as a corrective lens to focus our eyes on what’s out there?