Sir Roger Penrose (born 8 August 1931) is an English mathematician, mathematical physicist, philosopher of science and Nobel Laureate in Physics. 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.

Penrose has contributed to the mathematical physics of general relativity and cosmology. He won the Royal Society Science Books 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". He shared the 1988 Wolf Prize in Physics with Stephen Hawking for the Penrose–Hawking singularity theorems, and the 2020 Nobel Prize in Physics with Reinhard Genzel and Andrea Ghez "for the discovery that black hole formation is a robust prediction of the general theory of relativity".

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 Russian Jew. 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.

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.