Pocono conference
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Followup to the Shelter Island Conference, this is where Julian Schwinger and Richard Feynman exposed their theories to explain the experiments of the previous conference.
Julian made a formal presentation that took until the afternoon and bored everyone to death, though the mathematics avoided much questioning.
Feynman then presented his revolutionary approach, which he was unable to prove basic properties of, but which gave correct results, and people were not very happy.