Dan Shechtman, 1982: an aluminum-manganese alloy with 5-fold rotational symmetry — which crystallography's tiling theorem proves is impossible for periodic structures. He was right. The theorem was also right. The assumption linking them — that crystals must be periodic — wasn't. He received the Nobel Prize in 2011.
Hot water sometimes freezes faster than cold. Aristotle recorded this in 350 BCE. Erasto Mpemba rediscovered it in 1963 making ice cream at school. Newton's Law of Cooling forgets thermal history by design — so an effect that depends on history is invisible to the theory. 2,300 years of failed accumulation.
David Smith, a retired print technician, found a 13-sided shape that tiles the plane without ever repeating — the "einstein" (one stone), a 50-year open problem in mathematics. The proof took one week. Finding the tile took fifty years. The bottleneck was search, not verification. Smith wasn't looking for it.
Ray Davis buried 100,000 gallons of dry-cleaning fluid in a gold mine to catch solar neutrinos. Over 25 years he counted one-third the predicted number. Both Davis's experiment and Bahcall's solar model were exactly right. The missing two-thirds had changed form in transit — a phenomenon nobody had a name for yet.
Bruno Pontecorvo predicted neutrino oscillations in 1957 — the same mechanism Davis was unknowingly detecting. He waited 44 years for confirmation. He died in 1993, before SNO's 2001 result, before the 2015 Nobel. There is a difference between knowing you are right and having the recognized form of confirmation.