When the Higgs boson was confirmed in 2013, it marked the end of a nearly 50-year journey -- physicists Robert Brout and François Englert, Peter Higgs, Gerald Guralnik, C. Richard Hagen, and Tom Kibble, writing in three separate papers in 1964, suggested the existence of a particle that affected other particles' masses. But that's not the record.
Paul Dirac's 1928 equation predicted the existence of certain subatomic particles also. One of the equation's solutions suggested the existence of the positron, an "antiparticle" to the more commonly-known electron. The positron was discovered in 1932.
But other possible solutions to Dirac's equation existed, and they also predicted the existence of certain subatomic particles that had not been found at the time scientists worked with Dirac's idea. One solution, from German mathematician Hermann Weyl, predicted the existence of massless particles. Weyl's solution was published in 1929, and no massless particles were known to exist at the time, which led to a hunt for "Weyl fermions." "Fermion" and "boson" are the names for two different classes of subatomic particles.
When neutrinos were discovered, they were thought to be massless and seemed like a good candidate for a Weyl fermion, but recent experiments suggest they actually do have mass. However, scientists at Princeton and at MIT and Zhejiang University in China believe they have found evidence of Weyl fermions through different experiements. Their measurements and findings have to be reviewed and confirmed, so it's possible that this is another false lead. But if not, then Paul Dirac and Hermann Weyl predicted something in 1929 that wasn't found for about 85 years.
Probably one of the reasons real science never gets boring. Not only are you finding things about the world today, there's a whole bunch of stuff mathematicians may have dreamed up about the same time that sound began to be used in movies, still waiting to be checked out.