Roger Penrose

• 1. Introduction

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  Roger Penrose received half of the 2020 Nobel Prize in Physics for showing that the formation of black holes is a robust prediction of Einstein's general theory of relativity. The citation sounds like the summit of a single, tidy career. It is not. Penrose is an English mathematician, mathematical physicist and philosopher of science, and his name is attached to ideas that seem to belong in different worlds. What connects a collapsing star, an impossible staircase and the human brain? How did one person end up at the centre of all three? And why do so many specialists admire his mathematics while rejecting his claims about the mind?

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• 2. Family and Illusions

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  Roger Penrose was born on the 8th of August 1931 in Colchester, Essex, into a family crowded with talent. His mother, Margaret, née Leathes, was a physician. His father, Lionel Penrose, was a psychiatrist and geneticist.

  The grandparents ran through painting, physiology and music. J. Doyle Penrose, his paternal grandfather, was an Irish-born painter. His maternal grandfather, John Beresford Leathes, was a physiologist, and his maternal grandmother, Sonia Marie Natanson, was a concert pianist. His uncle was the artist Sir Roland Penrose.

  The siblings were just as varied. Oliver Penrose became a physicist, Shirley Hodgson a geneticist, and Jonathan Penrose a chess grandmaster. Their stepfather was Max Newman, a mathematician and computer scientist.

  The Second World War found young Roger in Canada, where his father worked in London, Ontario, at the Ontario Hospital and Western University. Back in England he studied at University College School. He then took a BSc at University College London, graduating in 1952 with First Class Honours in mathematics.

  George Gamow's Mr. Tompkins books had already set his direction. Penrose recalled that the stories' "magic was responsible, to a very considerable extent, for the great excitement" that physics held for him. He says that excitement never faded.

  In 1955, as a doctoral student, he reintroduced a generalised matrix inverse first described by E. H. Moore. Arne Bjerhammar had already reinvented it in 1951, and the result is now called the Moore-Penrose inverse. Penrose began research under the geometer W. V. D. Hodge. He took his PhD at St John's College, Cambridge, in 1957, with a thesis titled "Tensor Methods in Algebraic Geometry" supervised by John A. Todd.

  A chance encounter in Amsterdam in 1954 took him somewhere stranger. Attending a conference as a student, he stumbled on an exhibition of work by M. C. Escher. Soon he was trying to draw impossible figures himself and found the tribar, a triangle that looks like a solid object but cannot exist.

  With his father he went on to design a staircase that loops upward and downward at once. They described the triangle as "impossibility in its purest form". An article followed, and a copy reached Escher. The Dutch artist answered with two of his best-known pictures, Waterfall and Ascending and Descending.

  Dennis Sciama would soon steer this young pure mathematician toward astrophysics, and the impossible figures would give way to real objects whose geometry was just as strange.

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• 3. Collapsing Stars

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  In 1964, while a reader at Birkbeck College, Penrose "revolutionised the mathematical tools that we use to analyse the properties of spacetime", according to Kip Thorne of the California Institute of Technology. That judgement points to a problem physicists had struggled with for decades.

  Until then, solving Einstein's equations explicitly had been possible only for configurations with a high degree of symmetry. Nobody knew whether those tidy cases were typical. One remedy was perturbation theory, developed under John Archibald Wheeler at Princeton. Penrose chose a more radical route. He set aside the fine geometry of spacetime and looked instead at its topology, or at most its conformal structure, which is fixed by the lay of the lightcones and so determines how light can connect one event to another.

  His paper "Gravitational Collapse and Space-Time Singularities" is summarised roughly like this. If a dying star implodes beyond a certain point, nothing can stop its gravitational field growing strong enough to form a singularity. The method mattered as much as the result, because it gave similarly general conclusions in other settings. One was the cosmological Big Bang, which he tackled with Stephen Hawking, a student of Sciama.

  The 1969 cosmic censorship conjecture was his most decisive step on gravitational collapse. It proposed that any resulting singularities would stay hidden inside a well-behaved event horizon, enclosing a region of spacetime for which Wheeler coined the term black hole. Outside, the curvature would be strong but finite. Some gravitational energy might even be extractable there through what is called the Penrose process, and matter falling inward could release energy enough to account for quasars.

  In 1979 Penrose followed his weak cosmic censorship hypothesis with a stronger version, the strong censorship hypothesis. Alongside the Belinski-Khalatnikov-Lifshitz conjecture and questions of nonlinear stability, settling it remains one of general relativity's major open problems. The same year brought his Weyl curvature hypothesis, which concerns the initial conditions of the observable universe and the origin of the second law of thermodynamics.

  A quieter result came from James Terrell, who realised independently with Penrose that objects moving near the speed of light appear skewed or rotated. This is now called the Penrose-Terrell rotation. Penrose also helped popularise the causal diagrams that bear his name.

  The singularity theorems that grew from this work earned Penrose and Hawking the 1988 Wolf Prize in Physics.

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• 4. Tiles and Twistors

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  In 1967 Penrose invented twistor theory, a scheme that maps geometric objects in Minkowski space into a four-dimensional complex space. The metric signature of that space is (2,2). Few ideas in his career are so abstract, and none was more ambitious about recasting the geometry of physics.

  Four years later, in 1971, came spin networks. They later came to supply the geometry of spacetime in loop quantum gravity, a quite different programme from the one he had in mind.

  His best-loved invention is more visual. In 1974 he discovered the Penrose tilings, built from just two tiles that can cover a plane only in a nonperiodic way. They were the first tilings to show fivefold rotational symmetry, a feature that ordinary repeating patterns cannot have.

  A decade later, in 1984, patterns of exactly this kind turned up in the arrangement of atoms in quasicrystals. Dan Shechtman is credited with the discovery of those materials, which the tilings had presaged.

  When the London Mathematical Society honoured Penrose in 2004, its citation put it plainly: "His tilings of the plane underlie the newly discovered quasi-crystals."

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• 5. Before the Big Bang

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  In 2010 Penrose reported possible evidence of an earlier universe, found as concentric circles in Wilkinson Microwave Anisotropy Probe data on the cosmic microwave background. He mentions this in the epilogue of his 2010 book Cycles of Time. The book argues, from Einstein's field equations and the Weyl curvature hypothesis, that the transition at the Big Bang could have been smooth enough for a previous universe to survive it.

  The argument rests on his conformal cyclic cosmology. Penrose proposes that at the far end of time all matter ends up inside black holes. Those black holes then evaporate through Hawking radiation, leaving a universe made only of photons.

  Photons, in this picture, "experience" neither time nor space. A universe of photons that is infinitely large is therefore indistinguishable from one that is infinitely small. So the singularity at a Big Bang and an endlessly expanded universe amount to the same thing.

  In simple terms, he treats the Big Bang singularity as only apparent. The singularity at a black hole's event horizon works the same way, because a change of coordinates removes it. Penrose proposes a different change of coordinates that would remove the one at the Big Bang.

  One consequence is that the major events at the Big Bang can be understood without first unifying general relativity and quantum mechanics. That frees the theory from the Wheeler-DeWitt equation, which disrupts time. Penrose notes that the Einstein-Maxwell-Dirac equations offer an alternative route. Some of his conjectures about the Weyl curvature have since been proved by other researchers.

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• 6. Mind and Machine

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  The Emperor's New Mind, published in 1989, won the Royal Society Science Books Prize and set out Penrose's views on physics and consciousness. His claim is that the known laws of physics cannot explain consciousness. He sketches what the missing physics might look like, including a bridge between classical and quantum mechanics that he calls correct quantum gravity.

  A thought experiment with Turing machines carries much of the weight. Picture a system with two states, ON and OFF, where ON means a given Turing machine halts and OFF means it does not. The system is fully determined by the machine, yet no algorithm can say in advance which state it will take.

  Penrose concludes that a process can be deterministic without being algorithmic. He suspects such processes enter the quantum mechanical reduction of the wave function, and that the brain may harness them. Computers, being algorithmically deterministic, could not on this view be truly intelligent.

  The philosopher John Lucas of Merton College, Oxford, first advanced the underlying claims about the halting problem and Gödel's incompleteness theorem. Their combined form is known as the Penrose-Lucas argument. Mathematicians, computer scientists and philosophers have criticised it, and many experts say it fails, though they attack different parts.

  Marvin Minsky, a leading proponent of artificial intelligence, was especially sharp. He wrote that Penrose "tries to show, in chapter after chapter, that human thought cannot be based on any known scientific principle." Minsky held the opposite view, that humans are machines whose workings current physics can fully explain.

  Penrose answered in 1994 with Shadows of the Mind and in 1997 with The Large, the Small and the Human Mind. In those works he drew on the anesthesiologist Stuart Hameroff. Together they argued that consciousness arises from quantum gravity effects in microtubules, a proposal they named Orch-OR, for orchestrated objective reduction.

  Max Tegmark attacked it in a paper in Physical Review E. He calculated that neuron firing and microtubule excitations run slower than the decoherence time by a factor of at least 10 billion. IBM's John A. Smolin said the numbers confirmed long-held suspicions: "It's reasonably unlikely that the brain evolved quantum behavior."

  Phillip Tetlow, though sympathetic, concedes that Penrose's picture of thought is a minority view. He cites the science journalist Charles Seife, who called Penrose "one of a handful of scientists" who think consciousness suggests a quantum process.

  In January 2014 Hameroff and Penrose said that Anirban Bandyopadhyay of Japan's National Institute for Materials Science had found quantum vibrations in microtubules, supporting Orch-OR. An updated version of the theory appeared in the March 2014 issue of Physics of Life Reviews, alongside critical commentary and debate. Penrose has also discussed consciousness with Ted Honderich on In Our Time.

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• 7. Teaching and Travel

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  In the academic year 1956-57, Penrose was an assistant lecturer at Bedford College, now Royal Holloway, University of London. He then became a research fellow at St John's College, Cambridge. During that post he married Joan Isabel Wedge in 1959.

  A NATO Research Fellowship for 1959-61 took him first to Princeton University and then to Syracuse University. He spent 1961-1963 at King's College, London, and 1963-64 as a visiting associate professor at the University of Texas at Austin. Later visiting posts came at Yeshiva University, Princeton and Cornell, during 1966-67 and 1969.

  In 1983 the Rice University provost, Bill Gordon, invited him to teach in Houston, and Penrose worked there from 1983 to 1987. His doctoral students include Andrew Hodges, Lane Hughston, Richard Jozsa, Claude LeBrun, John McNamara, Tristan Needham, Tim Poston, Asghar Qadir and Richard S. Ward.

  In 2004 he published The Road to Reality: A Complete Guide to the Laws of the Universe, a 1,099-page survey of the laws of physics. It includes an explanation of his own theory, the Penrose Interpretation. That proposal links quantum mechanics and general relativity by holding that a quantum state stays in superposition until the difference in space-time curvature reaches a significant level.

  Penrose is now Emeritus Rouse Ball Professor of Mathematics at the University of Oxford and an emeritus fellow of Wadham College.

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• 8. Honours and Beliefs

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  In 1971 the American Astronomical Society and the American Institute of Physics gave Penrose the Dannie Heineman Prize for Astrophysics. He became a Fellow of the Royal Society in 1972. In 1975 he and Hawking were jointly awarded the Eddington Medal of the Royal Astronomical Society.

  The Royal Society awarded him its Royal Medal in 1985. Over the next years came the Dirac Medal and Prize of the British Institute of Physics in 1989, the Albert Einstein Medal in 1990 and the Naylor Prize of the London Mathematical Society in 1991. From 1992 to 1995 he was President of the International Society on General Relativity and Gravitation.

  Penrose was knighted for services to science in 1994, and in 2000 he was appointed a Member of the Order of Merit. The London Mathematical Society gave him its De Morgan Medal in 2004. The Royal Society's Copley Medal followed in 2008, and ETH Zürich's Richard R. Ernst Medal in 2012.

  Honorary degrees arrived from institutions across the world. They include the University of Bath in 1994, Glasgow and Essex in 1996, Warsaw and Leuven in 2005, and Cambridge in 2020. In 2025 he received the Golden Plate Award of the American Academy of Achievement.

  The other half of his 2020 Nobel Prize went to Reinhard Genzel and Andrea Ghez, for the discovery of a supermassive compact object at the centre of our galaxy.

  Penrose and Joan had three sons. He is now married to Vanessa Thomas, a director of academic development at Cokethorpe School in Witney, Oxfordshire. She was formerly head of mathematics at Abingdon School, and they have one son.

  On BBC Radio 4 on the 25th of September 2010, Penrose said: "I'm not a believer myself. I don't believe in established religions of any kind." He regards himself as an agnostic. He is also a patron of Humanists UK.

  Yet in the 1991 film A Brief History of Time he said that the universe has a purpose and is not "just there by chance". Treating the cosmos as something that merely computes, he added, is not a fruitful view: "there is something much deeper about it."

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