As a mathematics student at University College, London, Penrose discovered a theorem concerning eight conics in a plane, for which three well-known theorems turned out to be special cases. He received a Bachelor of Science degree in 1952 and a Ph.D. from Cambridge in 1957, writing his dissertation on algebraic geometry. As a student, Penrose rediscovered and developed mathematician E. H. Moore's generalized inverse matrix, a method of solving equations that involves rectangular arrays of numbers. At St. John's College, Cambridge, Penrose heard lectures by Paul Dirac on quantum mechanics and by Hermann Bondi on the theory of relativity, and became interested in relating quantum mechanics and space-time structure.
Beginning as a research fellow at St. John's College from 1957 to 1960, Penrose pursued a career of research and teaching at major universities in England and the United States. He was a North Atlantic Treaty Organization (NATO) research fellow at Princeton, Syracuse, and Cornell universities from 1959 to 1961. In the 1960s he had visiting appointments at the University of Chicago, Yeshiva University in New York, the University of Texas in Austin, the University of California at Berkeley, and King's College and Bedford College in London.
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