In 1935, Einstein, Podolsky, and Rosen (EPR) published a theoretical paper arguing that
quantum mechanics was incomplete. EPR believed the phenomenon known as
quantum entanglement could be explained by so-called
hidden variables that had yet to be discovered.
In 1964, John Bell proved that hidden variables as proposed by EPR would imply a certain
inequality. If EPR (Einstein
et al.) were right about quantum entanglement being explicable in terms of as-yet-undiscovered hidden variables, then Bell's inequality would hold.
Hundreds of experiments have shown that Bell's inequality does not hold. Therefore EPR (Einstein
et al.) were wrong.
When Einstein said "God does not play dice with the universe", he was insisting there must be some deterministic account of quantum entanglement. There is: the
Everett (or many-worlds) interpretation is deterministic. Einstein, however, thought a hidden-variables interpretation would work. He was wrong about that.
If you need to see an authority figure saying Einstein was wrong, see
Steven Hawking's lecture asking Does God play Dice? and search for the word "Einstein".