In this video, Dyson describes the moment on a Greyhound bus in 1948, when he was struck by lightning (to use a suitably vivid metaphor) which eventually gave rise to a Nobel prize in physics for Feynman, Schwinger and Tomanaga, but not himself.
It was the unification of quantum mechanics (QM) with Einstein's special theory of relativity. Unification with the general theory of relativity (GR) still eludes us, and Dyson heretically argues that it may never happen (in another video). Dyson's other significant contribution to physics was to prove (along with Andrew Leonard, in 1967) how the Pauli Exclusion Principle stops you from sinking into everything you touch.
I learned only a year or so ago that Dyson believes that QM is distinct from classical physics, contrary to accepted wisdom. A viewpoint I've long held myself. What's more, Dyson argues that QM can only describe the future and classical physics describes the past. Another view I thought I held alone. In his own words:
What really happens is that the quantum-mechanical description of an event ceases to be meaningful as the observer changes the point of reference from before the event to after it. We do not need a human observer to make quantum mechanics work. All we need is a point of reference, to separate past from future, to separate what has happened from what may happen, to separate facts from probabilities.
Addendum: I came across this excellent obituary in the New York Times.
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