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He obtained a Ph.D. degree at the University of Toronto under the supervision of Prof. J.L. Synge in 1942, and then worked as a research associate in the Jet Propulsion Laboratory of Caltech.
In 1957, at a conference at Chapel Hill, North Carolina, appealing to various mathematical tools developed by John Lighton Synge, A. Z. Petrov and André Lichnerowicz, Pirani explained more clearly than had previously been possible the central role played by the Riemann tensor and in particular the tidal tensor in general relativity.