This year’s Nobel Prize in chemistry was awarded to Dan Shechtman for his discovery of quasicrystals. Quasicrystals, unlike traditional crystals, are aperiodic on the atomic level. Basically, their patterns don’t repeat. When Shechtman first saw this in an experiment in 1982, this was scientific heresy. Crystals were periodic, period. Shechtman must have made a mistake. But he hadn’t, and rather than sitting around sulking about his doubtful colleagues, he worked hard to eliminate possible errors and build further evidence for the existence of quasicrystals. The tide of evidence turned in his favor, and the field of crystallography was changed forever.
In hindsight, quasicrystals are the sort of thing that seem to be too beautiful not to exist. (Which is not to say that, just because a theoretical structure is beautiful, it always turns out to exist—it doesn’t.) Although it took until 1982 to find evidence of atomic patterns that were not periodic, aperiodic tilings show up on the walls of mosques as early as the 12th century.