Sir Roger Penrose (born 8 August 1931) is an English mathematician, mathematical physicist, and philosopher of science. He is Emeritus Rouse Ball Professor of Mathematics at the University of Oxford, an emeritus fellow of Wadham College, Oxford, and an honorary fellow of St John's College, Cambridge, and University College London. He shared the 1988 Wolf Prize in Physics with Stephen Hawking for the Penrose–Hawking singularity theorems, and the 2020 Nobel Prize in Physics "for the discovery that black hole formation is a robust prediction of the general theory of relativity". He proposed the Penrose triangle and corresponded with M. C. Escher, influencing his Waterfall and Ascending and Descending. Penrose's eponymous aperiodic tiling presaged the discovery of quasicrystals by Dan Shechtman.
Penrose won the Royal Society Science Book Prize for The Emperor's New Mind (1989), which outlines his views on physics and consciousness. He followed it with The Road to Reality (2004), billed as "A Complete Guide to the Laws of the Universe".
Born in Colchester, Essex, Roger Penrose is a son of Margaret (née Leathes), a physician, and Lionel Penrose, a psychiatrist and geneticist. His paternal grandparents were J. Doyle Penrose, an Irish-born painter, and the Hon. Elizabeth Josephine Peckover, daughter of Alexander Peckover, 1st Baron Peckover; his maternal grandparents were John Beresford Leathes, a physiologist, and Sonia Marie Natanson, a concert pianist. His uncle was the artist Sir Roland Penrose, whose son with the American photographer Lee Miller is Antony Penrose. Penrose is the brother of the physicist Oliver Penrose, of the geneticist Shirley Hodgson and of the chess grandmaster Jonathan Penrose. Their stepfather was the mathematician and computer scientist Max Newman. He found inspiration in George Gamow's Mr. Tompkins books: "I remember reading (or being read) the Tompkins stories as a quite young child, and I'm sure that their magic was responsible, to a very considerable extent, for the great excitement that fundamental physics has held for me for the rest of my life."
Penrose spent the Second World War as a child in Canada where his father worked in London, Ontario, at the Ontario Hospital and Western University. Penrose studied at University College School. He then attended University College London, where he obtained a BSc degree with First Class Honours in mathematics in 1952.
In 1955, while a doctoral student, Penrose reintroduced the E. H. Moore generalised matrix inverse, also known as the Moore–Penrose inverse, after it had been reinvented by Arne Bjerhammar in 1951. Having started research under the professor of geometry and astronomy W. V. D. Hodge, Penrose received his PhD in algebraic geometry at St John's College, Cambridge, in 1957, with his thesis titled "Tensor Methods in Algebraic Geometry" supervised by the algebraist and geometer John A. Todd. He devised and popularised the Penrose triangle in the 1950s in collaboration with his father, 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. Escher's Waterfall and Ascending and Descending were in turn inspired by Penrose.
As the reviewer Manjit Kumar puts it:
As a student in 1954, Penrose was attending a conference in Amsterdam when by chance he came across an exhibition of Escher's work. Soon he was trying to conjure up impossible figures of his own and discovered the tribar – a triangle that looks like a real, solid three-dimensional object, but isn't. Together with his father, a physicist and mathematician, Penrose went on to design a staircase that simultaneously loops up and down. An article followed and a copy was sent to Escher. Completing a cyclical flow of creativity, the Dutch master of geometrical illusions was inspired to produce his two masterpieces.
Penrose spent the academic year 1956–57 as an assistant lecturer at Bedford College (now Royal Holloway, University of London) and was then a research fellow at St John's College, Cambridge. During that three-year post, he married Joan Isabel Wedge, in 1959. Before the fellowship ended Penrose won a NATO Research Fellowship for 1959–61, first at Princeton University and then at Syracuse University. Returning to the University of London, Penrose spent 1961–1963 as a researcher at King's College, London, before returning to the United States to spend 1963–64 as a visiting associate professor at the University of Texas at Austin. He later held visiting positions at Yeshiva University, Princeton and Cornell University during 1966–67 and 1969.
Dennis Sciama drew his attention from pure mathematics to astrophysics. In 1964, while a reader at Birkbeck College, Penrose, per Kip Thorne of the California Institute of Technology, "revolutionised the mathematical tools that we use to analyse the properties of spacetime". Until then, work on the curved geometry of general relativity had been confined to configurations with sufficiently high symmetry for Einstein's equations to be solvable explicitly, and there was doubt about whether such cases were typical. One approach to this issue was by the use of perturbation theory, as developed under the leadership of John Archibald Wheeler at Princeton. The other, and more radically innovative, approach initiated by Penrose was to overlook the detailed geometrical structure of spacetime and instead concentrate attention just on the topology of the space, or at most its conformal structure, since it is the latter – as determined by the lay of the lightcones – that determines the trajectories of lightlike geodesics, and hence their causal relationships. The importance of Penrose's paper "Gravitational Collapse and Space-Time Singularities" (summarised roughly as that if an object such as a dying star implodes beyond a certain point, then nothing can prevent the gravitational field getting so strong as to form some kind of singularity) was not its only result. It also showed a way to obtain similarly general conclusions in other contexts, notably that of the cosmological Big Bang, which he dealt with in collaboration with Sciama's student Stephen Hawking.
It was in the local context of gravitational collapse that the contribution of Penrose was most decisive, starting with his 1969 cosmic censorship conjecture, to the effect that any ensuing singularities would be confined within a well-behaved event horizon surrounding a hidden space-time region for which Wheeler coined the term black hole, leaving a visible exterior region with strong but finite curvature, from which some of the gravitational energy may be extractable by what is known as the Penrose process, while accretion of surrounding matter may release further energy that can account for astrophysical phenomena such as quasars.
Following up his "weak cosmic censorship hypothesis", Penrose went on, in 1979, to formulate a stronger version called the "strong censorship hypothesis". Together with the Belinski–Khalatnikov–Lifshitz 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 realised 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.
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).
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. 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 popularising what are commonly known as Penrose diagrams (causal diagrams).