Born in Colchester, Essex, England, Roger Penrose is a son of Lionel S. Penrose and Margaret Leathes. Penrose is the brother of mathematician Oliver Penrose and of chess Grandmaster Jonathan Penrose. Penrose was precocious as a child. He attended University College School. Penrose graduated with a first class degree in mathematics from University College London. In 1955, while still a student, Penrose reintroduced the E. H. Moore generalized matrix inverse (also known as Moore-Penrose inverse ) after it had been reinvented by Arne Bjerhammar (1951). Penrose earned his Ph.D. at Cambridge (St John's College) in 1958, writing a thesis on "tensor methods in algebraic geometry" under algebraist and geometer John A. Todd. He devised and popularised the Penrose triangle in the 1950s, describing it as "impossibility in its purest form" and exchanged material with the artist M. C. Escher, whose earlier depictions of impossible objects partly inspired it. In 1965 at Cambridge, Penrose proved that singularities (such as black holes) could be formed from the gravitational collapse of immense, dying stars.

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. Penrose and James Terrell independently realized that objects travelling near the speed of light will appear to undergo a peculiar skewing or rotation. This effect has come to be called the Terrell rotation or Penrose-Terrell rotation...

Roger Penrose is well known for his 1974 discovery of Penrose tilings, which are formed from two tiles that can only tile the plane nonperiodically, and are the first tilings to exhibit fivefold rotational symmetry. Penrose developed these ideas based on the article Deux types fondamentaux de distribution statistique (1938; an English translation Two Basic Types of Statistical Distribution) by Czech geographer, demographer and statistician Jaromír Kor?ák. In 1984, such patterns were observed in the arrangement of atoms in quasicrystals.. Another noteworthy contribution is his 1971 invention of spin networks, which later came to form the geometry of spacetime in loop quantum gravity. He was influential in popularizing what are commonly known as Penrose diagrams (causal diagrams). In 2004 Penrose released A Complete Guide to the Laws of the Universe, a 1,099-page book aimed at giving a comprehensive guide to the laws of physics. He has proposed a novel interpretation of quantum mechanics. Penrose is the Francis and Helen Pentz Distinguished (visiting) Professor of Physics and Mathematics at Pennsylvania State University.

Penrose is married to Vanessa Thomas, with whom he has one child. He has three sons from a previous marriage to American Joan Isabel Wedge, whom he married in 1959.

Penrose has written controversial books on the connection between fundamental physics and human (or animal) consciousness. In The Emperor's New Mind (1989), he argues that known laws of physics are inadequate to explain the phenomenon of consciousness. Penrose proposes the characteristics this new physics may have and specifies the requirements for a bridge between classical and quantum mechanics (what he calls correct quantum gravity). He claims that the present computer is unable to have intelligence because it is an algorithmically deterministic system. He argues against the viewpoint that the rational processes of the mind are completely algorithmic and can thus be duplicated by a sufficiently complex computer. This contrasts with supporters of strong artificial intelligence, who contend that thought can be simulated algorithmically. He bases this on claims that consciousness transcends formal logic because things such as the insolubility of the halting problem and Gödel's incompleteness theorem prevent an algorithmically based system of logic from reproducing such traits of human intelligence as mathematical insight. These claims were originally espoused by the philosopher John Lucas of Merton College, Oxford.

Penrose uses a variant of Turing's halting theorem to demonstrate that a system can be deterministic without being algorithmic. (E.g., imagine a system with only two states, ON and OFF. If the system's state is ON if a given Turing machine halts, and OFF if the Turing machine does not halt, then the system's state is completely determined by the Turing machine, however there is no algorithmic way to determine whether the Turing machine stops.) Penrose believes that such deterministic non-algorithmic processes may come in play in the quantum mechanical wave function reduction, and may be harnessed by the brain.

In 1994, Penrose followed up The Emperor's New Mind with Shadows of the Mind, and in 1997 with The Large, the Small and the Human Mind, further updating and expanding his theories. Marvin Minsky, a leading proponent of artificial intelligence, responded that Penrose "tries to show, in chapter after chapter, that human thought cannot be based on any known scientific principle." In contrast, Minsky argues that humans are, in fact, machines, whose functioning, although complex, is fully explainable by current physics. Minsky maintains that "one can carry that quest [for scientific explanation] too far by only seeking new basic principles instead of attacking the real detail. This is what I see in Penrose's quest for a new basic principle of physics that will account for consciousness."

Penrose and Stuart Hameroff have speculated that consciousness is the result of quantum gravity effects in microtubules, which they dubbed Orch-OR (orchestrated objective reduction). But Max Tegmark, in a paper in Physical Review E, calculated that the time scale of neuron firing and excitations in microtubules is slower than the decoherence time by a factor of at least 10,000,000,000. The reception of the paper is summed up by this statement in Tegmark's support: "Physicists outside the fray, such as IBM's John A. Smolin, say the calculations confirm what they had suspected all along. 'We're not working with a brain that's near absolute zero. It's reasonably unlikely that the brain evolved quantum behavior'". Tegmark's paper has been widely cited by critics of the Penrose-Hameroff position. It has been claimed by Hameroff to be based on a number of incorrect assumptions (see linked paper below from Hameroff, Scott Hagan and Jack Tuszy?ski), but Tegmark in turn has argued that the critique is invalid (see rejoinder link below). In particular, Hameroff points out the peculiarity that Tegmark's formula for the decoherence time includes a factor of T^2 in the numerator, meaning that higher temperatures would lead to longer decoherence times. Tegmark's rejoinder keeps the factor of T^2 for the decoherence time.

Phillip Tetlow, although himself supportive of Penrose's views, acknowledges that Penrose's ideas about the human thought process are not widely accepted in scientific circles, citing Minsky's criticisms and quoting science journalist Charles Seife's description of Penrose as "one of a handful of scientists" who believe that the nature of consciousness suggests a quantum process.

Penrose does not hold to any religious doctrine. In the film A Brief History of Time, he said, "There is a certain sense in which I would say the universe has a purpose. It's not there just somehow by chance. Some people take the view that the universe is simply there and it runs along—it's a bit as though it just sort of computes, and we happen by accident to find ourselves in this thing. I don't think that's a very fruitful or helpful way of looking at the universe, I think that there is something much deeper about it, about its existence, which we have very little inkling of at the moment."

Penrose has been awarded many prizes for his contributions to science. He was elected a Fellow of the Royal Society of London in 1972. In 1975, Stephen Hawking and Penrose were jointly awarded the Eddington Medal of the Royal Astronomical Society. In 1985, he was awarded the Royal Society Royal Medal. Along with Stephen Hawking, he was awarded the prestigious Wolf Foundation Prize for Physics in 1988. In 1989 he was awarded the Dirac Medal and Prize of the British Institute of Physics. In 1990 Penrose was awarded the Albert Einstein Medal for outstanding work related to the work of Albert Einstein by the Albert Einstein Society. In 1991, he was awarded the Naylor Prize of the London Mathematical Society. From 1992 to 1995 he served as President of the International Society on General Relativity and Gravitation.In 1994, Penrose was knighted for services to science. In 1998, he was elected Foreign Associate of the United States National Academy of Sciences. In 2000 he was appointed to the Order of Merit. In 2004 he was awarded the De Morgan Medal for his wide and original contributions to mathematical physics. To quote the citation from the London Mathematical Society:

His deep work on General Relativity has been a major factor in our understanding of black holes. His development of Twistor Theory has produced a beautiful and productive approach to the classical equations of mathematical physics. His tilings of the plane underlie the newly discovered quasi-crystals.

In 2005 Penrose was awarded an honorary doctorate (Honoris Causa) by Warsaw University and Katholieke Universiteit Leuven (Belgium), and in 2006 by the University of York. In 2008 Penrose was awarded the Copley Medal. He is also a Distinguished Supporter of the British Humanist Association and one of the patrons of the Oxford University Scientific Society.

• Techniques of Differential Topology in Relativity (1972, ISBN 0-89871-005-7)
• Spinors and Space-Time: Volume 1, Two-Spinor Calculus and Relativistic Fields (with Wolfgang Rindler, 1987) ISBN 0-521-33707-0 (paperback)
• Spinors and Space-Time: Volume 2, Spinor and Twistor Methods in Space-Time Geometry (with Wolfgang Rindler, 1988) (reprint), ISBN 0-521-34786-6 (paperback)
• Concerning Computers, Minds, and The Laws of Physics (1989, ISBN 0-14-014534-6 (paperback); it received the Rhone-Poulenc science book prize in 1990)
• A Search for the Missing Science of Consciousness (1994, ISBN 0-19-853978-9 (hardback))
• The Nature of Space and Time (with Stephen Hawking, 1996, ISBN 0-691-03791-4 (hardback), ISBN 0-691-05084-8 (paperback))
• The Large, the Small, and the Human Mind (with Abner Shimony, Nancy Cartwright, and Stephen Hawking, 1997, ISBN 0-521-56330-5 (hardback), ISBN 0-521-65538-2 (paperback), Canto edition: ISBN 0-521-78572-3)
• White Mars or, The Mind Set Free (with Brian W. Aldiss, 1999, ISBN 978-0-316-85243-2 (hardback))
• A Complete Guide to the Laws of the Universe (2004, ISBN 0-224-04447-8 (hardcover), ISBN 0-09-944068-7 (paperback))
• Cycles of Time: An Extraordinary New View of the Universe (Bodley Head (23 Sep 2010) ISBN 978-0-224-08036-1)

Penrose also wrote forewords to Quantum Aspects of Life and Zee's book Fearful Symmetry.