Penrose graduated with a first class degree in mathematics from University College London. In 1955, while still a student, Penrose reinvented the generalized matrix inverse (also known as Moore-Penrose inverse, see Penrose, R. "A Generalized Inverse for Matrices." Proc. Cambridge Phil. Soc. 51, 406-413, 1955.) Penrose earned his Ph.D. at Cambridge (St John's College) in 1958, writing a thesis on tensor methods in algebraic geometry under the well known algebraist and geometer John A. Todd. In 1965 at Cambridge, Penrose proved that singularities (such as black holes) could be formed from the gravitational collapse of dying immense stars. (Ferguson, 1991: 66).
In 1967, Penrose invented the twistor theory which maps geometric objects in Minkowski space into the 4-dimensional complex space with the metric signature (2,2). In 1969 he conjectured the cosmic censorship hypothesis. This proposes (rather informally) that the universe protects us from the inherent unpredictability of singularities (such as the one in the centre of a black hole) by hiding them from our view behind an event horizon. This form is now known as the weak censorship hypothesis; in 1979, Penrose formulated a stronger version called the strong censorship hypothesis. Together with the BKL conjecture and issues of nonlinear stability, settling the censorship conjectures is one of the most important outstanding problems in general relativity. Also from 1979 dates Penrose's influential Weyl curvature hypothesis on the initial conditions of the observable part of the Universe and the origin of the second law of thermodynamics.
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