View source for Roger Penrose

{{Short description|English mathematician, mathematical physicist (born 1931)}}
{{Use British English|date=October 2013}}
{{Use dmy dates|date=January 2021}}
{{Infobox scientist
| honorific_prefix  = [[Sir]]
| name              = Roger Penrose
| honorific_suffix  = {{post-nominals|size=100%|country=GBR|OM|FRS}}
| image             = Roger Penrose at Festival della Scienza Oct 29 2011.jpg
| caption           = Penrose in 2011
| birth_date        = {{birth date and age|1931|8|8|df=y}}
| birth_place       = [[Colchester]], Essex, England
| death_date        = 
| death_place       = 
| fields            = [[Mathematical physics]], [[tessellation]]s
| workplaces        = {{Plainlist|
* [[Cornell University]]
* [[Bedford College, London]]
* [[Princeton University]]
* [[Rice University]]
* [[Syracuse University]]
* [[King's College, London]]
* [[Birkbeck, University of London]]
* [[Wadham College, Oxford]]
* [[Polish Academy of Sciences]]
 }}
| education        = {{plainlist|
* [[University College London]] ([[BSc]])
* [[St John's College, Cambridge]] ([[PhD]])
 }}
| thesis_title      = Tensor Methods in Algebraic Geometry
| thesis_url        = https://idiscover.lib.cam.ac.uk/permalink/f/t9gok8/44CAM_ALMA21428192330003606
| thesis_year       = 1957
| doctoral_advisor  = [[J. A. Todd|John A. Todd]]
| academic_advisors = [[W. V. D. Hodge]]
| doctoral_students = {{Plainlist|
* [[Andrew Hodges]]
* [[Lane P. Hughston|Lane Hughston]]
* [[Richard Jozsa]]
* [[Claude LeBrun]]
* [[John McNamara (mathematical biologist)|John McNamara]]
* [[Tristan Needham]]
* [[Tim Poston]]
* [[Asghar Qadir]]
* [[Richard S. Ward]]
 }}
| known_for         = {{Collapsible list
 | title             = List of contributions{{nbsp}}
 | titlestyle        = font-weight: normal;
 | [[Moore–Penrose inverse]]
 | [[Twistor theory]]
 | [[Spin network]]
 | [[Abstract index notation]]
 | [[Black hole bomb]]
 | [[Spacetime|Geometry of spacetime]]
 | [[Cosmic censorship hypothesis|Cosmic censorship]]
 | [[Illumination problem]]
 | [[Weyl curvature hypothesis]]
 | [[Contributors to general relativity#P|Penrose inequalities]]
 | [[Penrose interpretation of quantum mechanics]]
 | [[Diósi–Penrose model]]
 | [[Newman–Penrose formalism]]
 | [[GHP formalism]]
 | [[Penrose diagram]]
 | [[Penrose inequality]]
 | [[Penrose process]]
 | [[Penrose tiling]]
 | [[Penrose triangle]]
 | [[Penrose stairs]]
 | [[Penrose–Hawking singularity theorems]]
 | [[Penrose graphical notation]]
 | [[Penrose transform]]
 | [[Terrell rotation|Penrose–Terrell effect]]
 | [[pp-wave spacetime]]
 | [[Schrödinger–Newton equations]]
 | [[Orch-OR]]/[[Penrose–Lucas argument]]
 | [[Free-orbit experiment with laser interferometry X-rays|FELIX experiment]]
 | [[Trapped surface]]
 | [[Andromeda paradox]]
 | [[Conformal cyclic cosmology]]
 }}
| spouse            = {{plainlist|
* {{marriage|Joan Isabel Wedge|1959|end=div.}}
* {{marriage|Vanessa Thomas|1988}}<ref name=whoswho/>
}}
| children          = 4
| father= [[Lionel Penrose]]
| relatives         =  [[Roland Penrose]] (uncle), [[Jonathan Penrose]] (brother), [[Oliver Penrose]] (brother), [[Shirley Hodgson]] (sister), [[Antony Penrose]] (cousin)
| awards            = {{Collapsible list
 | title             = List of awards{{nbsp}}
 | titlestyle        = font-weight: normal;
 | [[Adams Prize]] (1966)
 | [[Dannie Heineman Prize for Mathematical Physics|Heineman Prize]] (1971)
 | [[Fellow of the Royal Society]] (1972)
 | [[Eddington Medal]] (1975)
 | [[Royal Medal]] (1985)
 | [[Wolf Prize]] (1988)
 | [[Dirac Medal (IOP)]] (1989)
 | [[Albert Einstein Medal]] (1990)
 | [[Naylor Prize and Lectureship]] (1991)
 | [[Knight Bachelor]] (1994)
 | [[James Scott Prize Lectureship]] (1997–2000)
 | [[Karl Schwarzschild Medal]] (2000)
 | [[De Morgan Medal]] (2004)
 | [[Dalton Medal]] (2005)
 | [[Copley Medal]] (2008)
 | [[Fonseca Prize]] (2011)
 | [[Nobel Prize in Physics]] (2020)
 }}
}}
'''Sir Roger Penrose''' (born 8 August 1931)<ref name=whoswho>{{Who's Who | author=Anon| title=Penrose, Sir Roger  | id = U30531 | year = 2017 | doi =10.1093/ww/9780199540884.013.U30531 | edition = online [[Oxford University Press]]|location=Oxford}}</ref> , [[Order of Merit|OM]] is an English [[mathematician]], [[mathematical physicist]], [[Philosophy of science|philosopher of science]] and [[Nobel Prize in Physics|Nobel Laureate in Physics]].<ref>{{Cite web|url=https://www.britannica.com/biography/Roger-Penrose|title=Roger Penrose &#124; Biography, Books, Awards, & Facts|access-date=7 March 2021|archive-date=7 March 2021|archive-url=https://web.archive.org/web/20210307224416/https://www.britannica.com/biography/Roger-Penrose|url-status=live}}</ref> 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]].<ref>{{Cite web|title=Oxford Mathematician Roger Penrose jointly wins the Nobel Prize in Physics {{!}} University of Oxford|url=https://www.ox.ac.uk/news/2020-10-06-oxford-mathematician-roger-penrose-jointly-wins-nobel-prize-physics|access-date=7 October 2020|website=www.ox.ac.uk|date=6 October 2020 |language=en|archive-date=9 October 2020|archive-url=https://web.archive.org/web/20201009063427/https://www.ox.ac.uk/news/2020-10-06-oxford-mathematician-roger-penrose-jointly-wins-nobel-prize-physics|url-status=live}}</ref><ref>{{cite book| last=Ferguson| first=Kitty| author-link=Kitty Ferguson| year=1991|title=Stephen Hawking: Quest for a Theory of Everything|publisher=Franklin Watts| isbn=0-553-29895-X}}</ref><ref>{{cite book | author=Misner, Charles| author2=Thorne, Kip S.| author3=Wheeler, John Archibald| name-list-style=amp | title=Gravitation | location=San Francisco | publisher=W. H. Freeman | date=1973 | isbn=978-0-7167-0344-0}} (See ''Box 34.2''.)</ref>

Penrose has contributed to the mathematical physics of [[general relativity]] and [[physical cosmology|cosmology]]. He won the [[Royal Society Prizes for Science Books|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]],<ref>{{Cite journal |last=Siegel |first=Matthew |date=8 January 2008 |title=Wolf Foundation Honors Hawking and Penrose for Work in Relativity |url=https://physicstoday.scitation.org/doi/abs/10.1063/1.2810893 |url-status=live |journal=Physics Today |language=en |volume=42 |issue=1 |pages=97–98 |doi=10.1063/1.2810893 |issn=0031-9228 |url-access=subscription |archive-url=https://web.archive.org/web/20211207185551/https://physicstoday.scitation.org/doi/abs/10.1063/1.2810893 |archive-date=7 December 2021 |access-date=7 October 2020}}</ref> and the 2020 [[Nobel Prize in Physics]] with [[Reinhard Genzel]] and [[Andrea M. Ghez|Andrea Ghez]] "for the discovery that [[black hole]] formation is a robust prediction of the general theory of relativity".<ref name="mactutor">{{MacTutor Biography|id=Penrose}}</ref><ref name="Nobel Prize 2020">{{Cite web |title=The Nobel Prize in Physics 2020 |url=https://www.nobelprize.org/prizes/physics/2020/summary/ |url-status=live |archive-url=https://web.archive.org/web/20201006101114/https://www.nobelprize.org/prizes/physics/2020/summary/ |archive-date=6 October 2020 |access-date=6 October 2020 |website=NobelPrize.org |language=en-US}}</ref><ref name="NYT-20201006">{{cite news |last1=Overbye |first1=Dennis |last2=Taylor |first2=Derrick Bryson |date=6 October 2020 |title=Nobel Prize in Physics Awarded to 3 Scientists for Work on Black Holes |url=https://www.nytimes.com/2020/10/06/science/nobel-prize-physics.html |url-status=live |archive-url=https://web.archive.org/web/20201006102031/https://www.nytimes.com/2020/10/06/science/nobel-prize-physics.html |archive-date=6 October 2020 |access-date=6 October 2020 |work=[[The New York Times]]}}</ref>{{efn|The 2020 Nobel Prize was also awarded jointly to [[Reinhard Genzel]] and [[Andrea Ghez]] for their work on black holes.}}

== Early life and education ==
Born in [[Colchester]], Essex, Roger Penrose is a son of Margaret (née Leathes), a physician, and [[Lionel Penrose]], a psychiatrist and geneticist.{{efn|Penrose and his father shared mathematical concepts with Dutch graphic artist [[M. C. Escher]], which were incorporated into a lot of pieces, including [[Waterfall (M. C. Escher)|''Waterfall'']], which is based on the '[[Penrose triangle]]', and ''[[Ascending and Descending]]''.}} 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 [[History of the Jews in Russia|Russian Jew]].<ref>{{Cite book |last=Brookfield |first=Tarah |title=Our voices must be heard : women and the vote in Ontario |date=2018 |isbn=978-0-7748-6019-2 |publisher=UBC Press |location=Vancouver |oclc=1066070267}}</ref><ref name="Brookfield">{{Cite book|last=Brookfield|first=Tarah|url=https://books.google.com/books?id=LVlxDwAAQBAJ&pg=PA126|title=Our Voices Must Be Heard: Women and the Vote in Ontario|year=2018|publisher=UBC Press|isbn=978-0-7748-6022-2|language=en|access-date=6 October 2020|archive-date=7 December 2021|archive-url=https://web.archive.org/web/20211207185547/https://books.google.com/books?id=LVlxDwAAQBAJ&pg=PA126|url-status=live}}</ref><ref name="rsbm">{{cite journal |author=Peters |first=Rudolph |year=1958 |title=John Beresford Leathes. 1864–1956 |journal=Biographical Memoirs of Fellows of the Royal Society |volume=4 |pages=185–191 |doi=10.1098/rsbm.1958.0016 |doi-access=free}}</ref><ref name="elementy.ru">{{YouTube|id=B-EpHQ7yl9c|title=Roger Penrose. Cycles of Time: Is It Possible to Discern the Previous Universe Through the Big Bang?}}</ref> His uncle was the artist Sir [[Roland Penrose]], whose son with the American photographer [[Lee Miller]] is [[Antony Penrose]].<ref>{{Cite news|last=Hall|first=Chris|date=19 March 2016|title=Lee Miller, the mother I never knew|language=en-GB|work=The Guardian|url=https://www.theguardian.com/lifeandstyle/2016/mar/19/lee-miller-the-mother-i-never-knew|access-date=7 October 2020|issn=0261-3077|archive-date=12 November 2020|archive-url=https://web.archive.org/web/20201112020323/https://www.theguardian.com/lifeandstyle/2016/mar/19/lee-miller-the-mother-i-never-knew|url-status=live}}</ref><ref>{{Cite web|title=Illustrated Mathematics|url=https://www.farleyshouseandgallery.co.uk/exhibitions/illustrated-mathematics/|access-date=7 October 2020|website=Farleys House and Gallery|language=en-GB|archive-date=11 October 2020|archive-url=https://web.archive.org/web/20201011191035/https://www.farleyshouseandgallery.co.uk/exhibitions/illustrated-mathematics/|url-status=dead}}</ref> Penrose is the brother of the physicist [[Oliver Penrose]], of the geneticist [[Shirley Hodgson]] and of the chess grandmaster [[Jonathan Penrose]].<ref name="Roger Penrose - Biography">{{Cite web|title=Roger Penrose – Biography|url=https://mathshistory.st-andrews.ac.uk/Biographies/Penrose/|access-date=7 October 2020|website=Maths History|language=en|archive-date=8 October 2020|archive-url=https://web.archive.org/web/20201008122312/https://mathshistory.st-andrews.ac.uk/Biographies/Penrose/|url-status=live}}</ref><ref>{{cite news|last=AP and TOI staff|title=Scientist of Jewish heritage among trio to win Nobel prize for black hole finds|url=https://www.timesofisrael.com/scientist-of-jewish-heritage-among-trio-to-win-nobel-prize-for-black-hole-finds/|access-date=7 October 2020|website=[[The Times of Israel]]|date=6 October 2020 |language=en-US|archive-date=6 October 2020|archive-url=https://web.archive.org/web/20201006214254/https://www.timesofisrael.com/scientist-of-jewish-heritage-among-trio-to-win-nobel-prize-for-black-hole-finds/|url-status=live |issn=0040-7909}}</ref> 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<ref>{{cite news |last1=Ogilvie |first1=Megan |title=Just Visiting: Sir Roger Penrose |url=https://www.thestar.com/news/gta/2009/03/23/just_visiting_sir_roger_penrose.html |access-date=9 October 2020 |work=[[Toronto Star]] |date=23 March 2009 |archive-date=7 January 2021 |archive-url=https://web.archive.org/web/20210107212737/https://www.thestar.com/news/gta/2009/03/23/just_visiting_sir_roger_penrose.html |url-status=live }}</ref> and [[University of Western Ontario|Western University]].<ref>{{Cite web |title=Lionel Sharples Penrose |url=https://history.rcp.ac.uk/inspiring-physicians/lionel-sharples-penrose |website=Royal College of Physicians}}</ref> Penrose studied at [[University College School]].<ref name=whoswho/> He then attended [[University College London]], where he obtained a [[Bachelor of Science|BSc]] degree with [[First Class Honours]] in [[mathematics]] in 1952.<ref name="Roger Penrose - Biography" /><ref>[https://www.ucl.ac.uk/news/2020/oct/ucl-alumnus-professor-sir-roger-penrose-awarded-nobel-prize UCL alumnus Professor Sir Roger Penrose awarded Nobel Prize], website of the [[University College London]].</ref>

In 1955, while a doctoral student, Penrose reintroduced the [[E. H. Moore]] generalised matrix inverse, also known as the [[Moore–Penrose inverse]],<ref>{{cite journal|last1=Penrose|first1=R.|title=A generalized inverse for matrices|journal=[[Mathematical Proceedings of the Cambridge Philosophical Society]]|year=1955|volume=51|issue=3|pages=406–413|doi=10.1017/S0305004100030401|bibcode = 1955PCPS...51..406P |doi-access=free}}</ref> after it had been reinvented by [[Arne Bjerhammar]] in 1951.<ref>{{Cite web|last=Zheng|first=Wenjie|title=The 100th anniversary of Moore–Penrose inverse and its role in statistics and machine learning|url=http://www.zhengwenjie.net/pseudoinverse/|access-date=7 October 2020|website=www.zhengwenjie.net|archive-date=11 October 2020|archive-url=https://web.archive.org/web/20201011201508/http://www.zhengwenjie.net/pseudoinverse/|url-status=live}}</ref> Having started research under the professor of geometry and astronomy [[W. V. D. Hodge]], Penrose received his [[Doctor of Philosophy|PhD]] in [[algebraic geometry]] at [[St John's College, Cambridge]], in 1957, with his thesis titled "Tensor Methods in Algebraic Geometry"<ref name=pphd>{{cite thesis|degree=PhD|title=Tensor Methods in Algebraic Geometry|first=Roger|last=Penrose|oclc=71366928|website=cam.ac.uk|publisher=University of Cambridge|url=https://idiscover.lib.cam.ac.uk/permalink/f/t9gok8/44CAM_ALMA21428192330003606|id={{ProQuest| 301242962}}}}</ref> supervised by the algebraist and geometer [[J. A. Todd|John A. Todd]].<ref>{{Cite web|date=6 October 2020|title=Roger Penrose wins 2020 Nobel Prize in Physics for discovery about black holes|url=https://www.cam.ac.uk/research/news/roger-penrose-wins-2020-nobel-prize-in-physics-for-discovery-about-black-holes|access-date=7 October 2020|website=University of Cambridge|language=en|archive-date=9 October 2020|archive-url=https://web.archive.org/web/20201009072829/https://www.cam.ac.uk/research/news/roger-penrose-wins-2020-nobel-prize-in-physics-for-discovery-about-black-holes|url-status=live}}</ref> 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.<ref>{{Cite web|last=Welch|first=Chris|date=23 March 2012|title='Frustro' typeface applies the Penrose impossible triangle concept to words|url=https://www.theverge.com/2012/3/23/2898025/frustro-typeface-matrzi-hegedus-penrose-triangle|access-date=7 October 2020|website=The Verge|language=en|archive-date=26 January 2021|archive-url=https://web.archive.org/web/20210126162258/https://www.theverge.com/2012/3/23/2898025/frustro-typeface-matrzi-hegedus-penrose-triangle|url-status=live}}</ref><ref>{{Cite book|last=Baggini|first=Julian|url=https://books.google.com/books?id=rws0AgAAQBAJ&q=roger+penrose+%22penrose+triangle%22+%22impossibility+in+its+purest+form%22&pg=PT21|title=Philosophy: All That Matters|year=2012|publisher=John Murray Press|isbn=978-1-4441-5585-3|language=en|access-date=12 October 2020|archive-date=7 December 2021|archive-url=https://web.archive.org/web/20211207185548/https://books.google.com/books?id=rws0AgAAQBAJ&q=roger+penrose+%22penrose+triangle%22+%22impossibility+in+its+purest+form%22&pg=PT21|url-status=live}}</ref> Escher's [[Waterfall (M. C. Escher)|''Waterfall'']] and ''[[Ascending and Descending]]'' were in turn inspired by Penrose.<ref>{{Cite web|date=21 May 2013|title=Ascending and Descending by M.C. Escher – Facts about the Painting|url=http://totallyhistory.com/ascending-and-descending/|access-date=7 October 2020|website=Totally History|language=en-US|archive-date=29 June 2020|archive-url=https://web.archive.org/web/20200629065147/http://totallyhistory.com/ascending-and-descending/|url-status=live}}</ref>

[[file:Penrose-dreieck.svg|thumb|right|The [[Penrose triangle]] ]]
As the reviewer [[Manjit Kumar]] puts it:
{{Blockquote|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 [[Penrose stairs|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.<ref>{{cite news|url=https://www.theguardian.com/books/2010/oct/16/cycles-time-roger-penrose-review|title=Cycles of Time: An Extraordinary New View of the Universe by Roger Penrose – review| newspaper=[[The Guardian]] | author-link=Manjit Kumar| date=15 October 2010|last1=Kumar|first1=Manjit| access-date=13 December 2016|archive-date=10 January 2017|archive-url=https://web.archive.org/web/20170110122217/https://www.theguardian.com/books/2010/oct/16/cycles-time-roger-penrose-review|url-status=live}}</ref>}}

== Research and career ==
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]].<ref>{{Cite web|title=Professor Sir Roger Penrose awarded the 2020 Nobel Prize in Physics|url=https://www.kcl.ac.uk/news/professor-sir-roger-penrose-awarded-the-2020-nobel-prize-in-physics|access-date=7 October 2020|website=King's College London|language=en-EN|archive-date=22 October 2020|archive-url=https://web.archive.org/web/20201022121930/https://www.kcl.ac.uk/news/professor-sir-roger-penrose-awarded-the-2020-nobel-prize-in-physics|url-status=live}}</ref> He later held visiting positions at [[Yeshiva University]], Princeton and [[Cornell University]] during 1966–67 and 1969.

In 1964, while a [[Reader (academic rank)|reader]] at [[Birkbeck College]], London, (and having had his attention drawn from pure mathematics to astrophysics by the cosmologist [[Dennis Sciama]], then at Cambridge)<ref name="Roger Penrose - Biography"/> in the words of [[Kip Thorne]] of the [[California Institute of Technology]], "Roger Penrose revolutionised the mathematical tools that we use to analyse the properties of spacetime".<ref>{{Cite web|date=12 March 2019|title=The second Cambridge Cutting Edge Lecture: Professor Sir Roger Penrose|url=https://cambridgesocietyofparis.com/event/cambridge-cutting-edge-lecture-professor-sir-roger-penrose/|access-date=7 October 2020|website=Cambridge Society of Paris|language=en-GB|archive-date=8 October 2020|archive-url=https://web.archive.org/web/20201008185043/https://cambridgesocietyofparis.com/event/cambridge-cutting-edge-lecture-professor-sir-roger-penrose/|url-status=live}}</ref><ref>{{Cite book|last1=Thorne|first1=Kip|url=https://books.google.com/books?id=GzlrW6kytdoC&q=roger+penrose+kip+thorne+mathematical+tools+spacetime&pg=PA465|title=Black Holes and Time Warps: Einstein's Outrageous Legacy|last2=Thorne|first2=Kip S.|last3=Hawking|first3=Stephen|date=1994|publisher=W. W. Norton & Company|isbn=978-0-393-31276-8|language=en|access-date=12 October 2020|archive-date=3 February 2021|archive-url=https://web.archive.org/web/20210203044944/https://books.google.com/books?id=GzlrW6kytdoC&q=roger+penrose+kip+thorne+mathematical+tools+spacetime&pg=PA465|url-status=live}}</ref> 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.<ref>{{Cite journal|last1=Ellis|first1=George F. R.|last2=Penrose|first2=Sir Roger|date=1 January 2010|title=Dennis William Sciama. 18 November 1926 – 19 December 1999|journal=Biographical Memoirs of Fellows of the Royal Society|language=en|volume=56|pages=401–422|doi=10.1098/rsbm.2009.0023|s2cid=73035217|issn=0080-4606|doi-access=free}}</ref> 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"<ref name=Penrose1965>{{cite journal|last1=Penrose|first1=Roger|title=Gravitational Collapse and Space-Time Singularities|journal=Physical Review Letters|date=January 1965|volume=14|issue=3|pages=57–59|doi=10.1103/PhysRevLett.14.57|bibcode = 1965PhRvL..14...57P }}</ref> (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]].<ref>{{Cite web|last=Clark|first=Stuart|title=A brief history of Stephen Hawking: A legacy of paradox|url=https://www.newscientist.com/article/2053929-a-brief-history-of-stephen-hawking-a-legacy-of-paradox/|access-date=7 October 2020|website=New Scientist|language=en-US|archive-date=5 October 2020|archive-url=https://web.archive.org/web/20201005145715/https://www.newscientist.com/article/2053929-a-brief-history-of-stephen-hawking-a-legacy-of-paradox/|url-status=live}}</ref><ref>{{Cite web|title=Roger Penrose|url=https://www.newscientist.com/people/roger-penrose/|access-date=7 October 2020|website=[[New Scientist]]|language=en-US|archive-date=11 October 2020|archive-url=https://web.archive.org/web/20201011180710/https://www.newscientist.com/people/roger-penrose/|url-status=live}}</ref><ref>{{Cite web|last=Wolchover|first=Natalie|title=Physicists Debate Hawking's Idea That the Universe Had No Beginning|url=https://www.quantamagazine.org/physicists-debate-hawkings-idea-that-the-universe-had-no-beginning-20190606/|access-date=7 October 2020|website=Quanta Magazine|date=6 June 2019|language=en|archive-date=5 October 2020|archive-url=https://web.archive.org/web/20201005235915/https://www.quantamagazine.org/physicists-debate-hawkings-idea-that-the-universe-had-no-beginning-20190606/|url-status=live}}</ref>

[[file: CNRSblackhole.jpg|thumb|300px|right|Predicted view from outside the [[event horizon]] of a [[black hole]] lit by a thin accretion disc]]
It was in the local context of gravitational collapse that the contribution of Penrose was most decisive, starting with his 1969 cosmic censorship conjecture,<ref>{{cite arXiv|last=Fernandez|first=Rodrigo L.|date=21 July 2020|title=Cosmic Censorship Conjecture violation: A semiclassical approach|class=gr-qc|eprint=2007.10601}}</ref> 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]].<ref name="Curiel 2020">{{Citation|last=Curiel|first=Erik|title=Singularities and Black Holes|date=2020|url=https://plato.stanford.edu/archives/sum2020/entries/spacetime-singularities/|encyclopedia=The Stanford Encyclopedia of Philosophy|editor-last=Zalta|editor-first=Edward N.|edition=Summer 2020|publisher=Metaphysics Research Lab, Stanford University|access-date=7 October 2020}}</ref><ref>{{Cite journal|title=1979ApJ...229...46K Page 46|url=http://adsabs.harvard.edu/full/1979ApJ...229...46K|access-date=7 October 2020|journal=The Astrophysical Journal|bibcode=1979ApJ...229...46K|last1=Kafatos|first1=M.|last2=Leiter|first2=D.|year=1979|volume=229|page=46|doi=10.1086/156928|archive-date=7 December 2021|archive-url=https://web.archive.org/web/20211207185549/https://adsabs.harvard.edu/full/1979ApJ...229...46K|url-status=live}}</ref><ref>{{Cite web|title=Penrose process|url=https://www.oxfordreference.com/view/10.1093/oi/authority.20110810105604640|access-date=7 October 2020|website=Oxford Reference|language=en|archive-date=2 February 2021|archive-url=https://web.archive.org/web/20210202201151/https://www.oxfordreference.com/view/10.1093/oi/authority.20110810105604640|url-status=live}}</ref>

Following up his "weak [[cosmic censorship hypothesis]]", Penrose went on, in 1979, to formulate a stronger version called the "strong censorship hypothesis". [[File:Roger Penrose 1978.jpg|thumb|Penrose in 1978]]Together with the [[BKL conjecture|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]].<ref>{{cite conference |author=Penrose |first=Roger |date=1979 |editor-last=Hawking |editor-first=Stephen W. |editor2=Israel |editor2-first=W. |title=Singularities and Time-Asymmetry |conference= |publisher=Cambridge University Press |pages=581–638 |book-title=General Relativity: An Einstein Centenary Survey |editor=}}</ref> 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.<ref>{{Cite journal |first=James |last=Terrell |date=1959 |title=Invisibility of the Lorentz Contraction |journal=[[Physical Review]] |issue= 4|pages=1041–1045 |doi=10.1103/PhysRev.116.1041 |volume=116 |bibcode = 1959PhRv..116.1041T }}</ref><ref>{{Cite journal |doi=10.1017/S0305004100033776 |first=Roger |last=Penrose |date=1959 |title=The Apparent Shape of a Relativistically Moving Sphere |journal=Proceedings of the Cambridge Philosophical Society |volume=55 |issue= 1|pages=137–139 |bibcode = 1959PCPS...55..137P |s2cid=123023118 }}</ref>

[[File:Penrose Tiling (Rhombi).svg|thumb|A [[Penrose tiling]]|alt=]]
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).<ref>{{Cite web|title=New Horizons in Twistor Theory {{!}} Mathematical Institute|url=http://www.maths.ox.ac.uk/groups/mathematical-physics/events/twistors50|access-date=7 October 2020|website=www.maths.ox.ac.uk|archive-date=8 October 2020|archive-url=https://web.archive.org/web/20201008153713/http://www.maths.ox.ac.uk/groups/mathematical-physics/events/twistors50|url-status=live}}</ref><ref>{{Cite book |last1=Huggett |first1=S. A. |url=http://dx.doi.org/10.1017/cbo9780511624018 |title=An Introduction to Twistor Theory |last2=Tod |first2=K. P. |date=1994-07-21 |publisher=Cambridge University Press |isbn=978-0-521-45157-4 |edition=2nd |pages=1|doi=10.1017/cbo9780511624018 }}</ref>

Penrose is well known for his 1974 discovery of [[Penrose tiling]]s, which are formed from two tiles that can only [[tessellation|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 [[quasicrystal]]s.<ref>{{Cite journal |doi=10.1073/pnas.93.25.14267 |first=Paul |last=Steinhardt |title=New perspectives on forbidden symmetries, quasicrystals, and Penrose tilings |journal=[[Proceedings of the National Academy of Sciences|PNAS]] |volume=93 |issue= 25|pages=14267–14270 |date=1996 |pmid=8962037 |pmc=34472 |bibcode = 1996PNAS...9314267S |doi-access=free }}</ref> Another noteworthy contribution is his 1971 invention of [[spin network]]s, which later came to form the geometry of [[spacetime]] in [[loop quantum gravity]].<ref>{{Cite web|title=Penrose on Spin Networks|url=https://math.ucr.edu/home/baez/penrose/|access-date=7 October 2020|website=math.ucr.edu|archive-date=12 October 2020|archive-url=https://web.archive.org/web/20201012031549/https://math.ucr.edu/home/baez/penrose/|url-status=live}}</ref> He was influential in popularising what are commonly known as [[Penrose diagram]]s (causal diagrams).<ref>{{Cite web|title=Penrose diagrams|url=https://jila.colorado.edu/~ajsh/insidebh/penrose.html|access-date=7 October 2020|website=jila.colorado.edu|language=en|archive-date=11 November 2020|archive-url=https://web.archive.org/web/20201111203436/https://jila.colorado.edu/~ajsh/insidebh/penrose.html|url-status=live}}</ref>

In 1983, Penrose was invited to teach at [[Rice University]] in Houston, by the then provost Bill Gordon. He worked there from 1983 to 1987.<ref>{{cite web|url=http://ricehistorycorner.com/2013/05/22/roger-penrose-at-rice-1983-87/|title=Roger Penrose at Rice, 1983–87|work=Rice History Corner|date=22 May 2013|access-date=29 January 2014|archive-date=17 June 2016|archive-url=https://web.archive.org/web/20160617233239/https://ricehistorycorner.com/2013/05/22/roger-penrose-at-rice-1983-87/|url-status=live}}</ref> His doctoral students have included, among others, [[Andrew Hodges]],<ref name=aphd>{{cite thesis|degree=PhD|publisher=Birkbeck, University of London|url=http://catalogue.libraries.london.ac.uk/record=b3004898|doi=|title=The Description of Mass within the Theory of Twistors|first= Andrew Philip|last=Hodges|date=1975|id={{EThOS|uk.bl.ethos.459296}}|website=london.ac.uk|oclc=500473477}}</ref> [[Lane P. Hughston|Lane Hughston]], [[Richard Jozsa]], [[Claude LeBrun]], [[John McNamara (mathematical biologist)|John McNamara]], [[Tristan Needham]], [[Tim Poston]],<ref name=mathgene>{{MathGenealogy}}</ref> [[Asghar Qadir]], and [[Richard S. Ward]].

In 2004 Penrose released ''[[The Road to Reality: A Complete Guide to the Laws of the Universe]]'', a 1,099-page comprehensive guide to the [[physical law|Laws of Physics]] that includes an explanation of his own theory. The [[Penrose interpretation|Penrose Interpretation]] predicts the relationship between [[quantum mechanics]] and [[general relativity]], and proposes that a [[quantum state]] remains in [[Quantum superposition|superposition]] until the difference of [[space-time curvature]] attains a significant level.<ref>{{cite web |url=https://www.nytimes.com/2005/02/27/books/review/the-road-to-reality-a-really-long-history-of-time.html?_r=0 |title='The Road to Reality': A Really Long History of Time |first1=George |last1=Johnson |author-link=George Johnson (writer)| date=27 February 2005 |work=[[The New York Times]] |access-date=3 April 2017 |archive-date=3 January 2021 |archive-url=https://web.archive.org/web/20210103115129/https://www.nytimes.com/2005/02/27/books/review/the-road-to-reality-a-really-long-history-of-time.html?_r=0 |url-status=live }}</ref><ref>{{cite web  | title=If an Electron Can Be in Two Places at Once, Why Can't You? | last=Folger| first=Tim| author-link=Tim Folger| work=[[Discover (magazine)|Discover]]| url=http://discovermagazine.com/2005/jun/cover/article_view?b_start:int=0&-C= | access-date = 27 October 2008 | archive-url=https://web.archive.org/web/20121101130211/http://discovermagazine.com/2005/jun/cover/article_view?b_start:int=0&-C= | archive-date=1 November 2012}}</ref>

Penrose is the Francis and Helen Pentz Distinguished Visiting professor of Physics and Mathematics at [[Pennsylvania State University]].<ref>{{cite web| title =Dr. Roger Penrose at Penn State University| url =http://www.phys.psu.edu/people/display/index.html?person_id=233&mode=contact.| access-date =9 July 2007| url-status =dead| archive-url =https://web.archive.org/web/20080416131322/http://www.phys.psu.edu/people/display/index.html?person_id=233&mode=contact.| archive-date =16 April 2008| df =dmy-all}}</ref>

=== An earlier universe ===
[[File:WMAP 2010.png|thumb|300px|[[Wilkinson Microwave Anisotropy Probe|WMAP]] image of the (extremely tiny) anisotropies in the [[cosmic background radiation]]]]

In 2010 Penrose reported possible evidence, based on concentric circles found in [[WMAP|Wilkinson Microwave Anisotropy Probe]] data of the [[CMB|cosmic microwave background]] sky, of an earlier universe existing before the [[Big Bang]] of the present universe.<ref name="Gurzadyan">{{cite arXiv |eprint=1011.3706 |class=astro-ph.CO |first1=V. G. |last1=Gurzadyan |first2=R. |last2=Penrose |title=Concentric circles in WMAP data may provide evidence of violent pre-Big-Bang activity". volume "v1 |date=2010}}</ref> He mentions this evidence in the epilogue of his 2010 book ''[[Cycles of Time]]'',<ref>Roger Penrose, ''Cycles of Time'', Vintage; Reprint edition (1 May 2012)</ref> a book in which he presents his reasons, to do with [[Einstein's field equations]], the [[Weyl curvature]] C, and the [[Weyl curvature hypothesis]] (WCH), that the transition at the Big Bang could have been smooth enough for a previous universe to survive it.<ref>{{Cite journal|last=Stoica|first=Ovidiu-Cristinel|date=November 2013|title=On the Weyl Curvature Hypothesis|journal=Annals of Physics|volume=338|pages=186–194|doi=10.1016/j.aop.2013.08.002|arxiv=1203.3382|bibcode=2013AnPhy.338..186S|s2cid=119329306}}</ref><ref>{{cite conference |author=Penrose |first=Roger |date=1979 |editor-last=Hawking |editor-first=S. W. |editor2=Israel |editor2-first=W. |title=Singularities and Time-Asymmetry |conference= |publisher=[[Cambridge University Press]] |pages=581–638 |book-title=General Relativity: An Einstein Centenary Survey}}</ref> He made several conjectures about C and the WCH, some of which were subsequently proved by others, and he also popularized his [[conformal cyclic cosmology]] (CCC) theory.<ref>{{Cite web|date=21 August 2018|title=New evidence for cyclic universe claimed by Roger Penrose and colleagues|url=https://physicsworld.com/a/new-evidence-for-cyclic-universe-claimed-by-roger-penrose-and-colleagues/|access-date=7 October 2020|website=Physics World|language=en-GB|archive-date=1 November 2020|archive-url=https://web.archive.org/web/20201101015848/https://physicsworld.com/a/new-evidence-for-cyclic-universe-claimed-by-roger-penrose-and-colleagues/|url-status=live}}</ref> In this theory, Penrose postulates that at the end of the universe all matter is eventually contained within black holes, which subsequently evaporate via [[Hawking radiation]]. At this point, everything contained within the universe consists of [[photons]], which "experience" neither time nor space. There is essentially no difference between an infinitely large universe consisting only of photons and an infinitely small universe consisting only of photons. Therefore, a singularity for a Big Bang and an infinitely expanded universe are equivalent.<ref>{{Cite web|url = https://physicsworld.com/a/new-evidence-for-cyclic-universe-claimed-by-roger-penrose-and-colleagues/|title = New evidence for cyclic universe claimed by Roger Penrose and colleagues|date = 21 August 2018|access-date = 7 October 2020|archive-date = 1 November 2020|archive-url = https://web.archive.org/web/20201101015848/https://physicsworld.com/a/new-evidence-for-cyclic-universe-claimed-by-roger-penrose-and-colleagues/|url-status = live}}</ref>

In simple terms, Penrose believes that the singularity in [[Einstein's field equation]] at the Big Bang is only an apparent singularity, similar to the well-known apparent singularity at the [[event horizon]] of a [[black hole]].<ref name="Curiel 2020"/> The latter singularity can be removed by a change of [[coordinate system]], and Penrose proposes a different change of coordinate system that will remove the singularity at the big bang.<ref>{{Cite book|last=Penrose|first=Roger|url=https://books.google.com/books?id=9XKYDwAAQBAJ&q=roger+penrose+%22change+of+coordinate%22&pg=PA55|title=Fashion, Faith, and Fantasy in the New Physics of the Universe|date=5 September 2017|publisher=Princeton University Press|isbn=978-0-691-17853-0|language=en|access-date=12 October 2020|archive-date=7 December 2021|archive-url=https://web.archive.org/web/20211207185551/https://books.google.com/books?id=9XKYDwAAQBAJ&q=roger+penrose+%22change+of+coordinate%22&pg=PA55|url-status=live}}</ref> One implication of this is that the major events at the Big Bang can be understood without unifying general relativity and quantum mechanics, and therefore we are not necessarily constrained by the [[Wheeler–DeWitt equation]], which disrupts time.<ref>{{Cite journal|last=Kiefer|first=Claus|date=13 August 2013|title=Conceptual Problems in Quantum Gravity and Quantum Cosmology|journal=ISRN Mathematical Physics|volume=2013|pages=1–17|doi=10.1155/2013/509316|language=en|doi-access=free|arxiv=1401.3578}}</ref><ref>{{Cite arXiv |last=Vaas |first=Rüdiger |title=The Inverted Big-Bang <!-- unsupported parameter |url=https://arxiv.org/pdf/physics/0407071.pdf --> |year=2004 |eprint=physics/0407071 }}</ref> Alternatively, one can use the Einstein–Maxwell–Dirac equations.<ref>{{Cite web |last1=Finster |first1=F. |last2=Smoller |first2=J. A. |last3=Yau |first3=S. -T. |title=The Einstein–Dirac–Maxwell Equations – Black Hole Solutions |url=https://cds.cern.ch/record/403056/files/9910030.pdf |url-status=live |archive-url=https://web.archive.org/web/20201007132312/https://cds.cern.ch/record/403056/files/9910030.pdf |archive-date=7 October 2020 |access-date=7 October 2020}}</ref>

=== Consciousness ===
[[File:Roger Penrose 9671.JPG|thumb|Penrose at a conference {{Circa|2011}}]]
Penrose has written 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.<ref>{{Cite news|last=Ferris|first=Timothy|date=19 November 1989|title=HOW THE BRAIN WORKS, MAYBE (Published 1989)|language=en-US|work=[[The New York Times]]| author-link=Timothy Ferris| url=https://www.nytimes.com/1989/11/19/books/how-the-brain-works-maybe.html|access-date=7 October 2020|issn=0362-4331|archive-date=19 November 2021|archive-url=https://web.archive.org/web/20211119091901/https://www.nytimes.com/1989/11/19/books/how-the-brain-works-maybe.html|url-status=live}}</ref> 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'').<ref>{{Cite web|last=Stork|first=David G.|date=29 October 1989|title=The Physicist Against the Hackers : THE EMPEROR'S NEW MIND: On Computers, Minds, and the Laws of Physics by Roger Penrose (Oxford University Press: $24.95; 428 pp.)|url=https://www.latimes.com/archives/la-xpm-1989-10-29-bk-90-story.html|access-date=7 October 2020|website=Los Angeles Times|language=en-US|archive-date=7 December 2021|archive-url=https://web.archive.org/web/20211207185551/https://www.latimes.com/archives/la-xpm-1989-10-29-bk-90-story.html|url-status=live}}</ref> Penrose uses a variant of [[Turing's halting theorem]] to demonstrate that a system can be [[deterministic]] without being [[algorithm]]ic. (For example, imagine a system with only two states, ON and OFF. If the system's state is ON when a given [[Turing machine]] halts and OFF when the Turing machine does not halt, then the system's state is completely determined by the machine; nevertheless, there is no algorithmic way to determine whether the Turing machine stops.)<ref>{{Cite book|last=Penrose|first=Roger|url=https://books.google.com/books?id=JF4vDwAAQBAJ&q=turing+halting|title=The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics|date=28 April 2016|publisher=Oxford University Press|isbn=978-0-19-255007-1|language=en|access-date=12 October 2020|archive-date=7 December 2021|archive-url=https://web.archive.org/web/20211207185551/https://books.google.com/books?id=JF4vDwAAQBAJ&q=turing+halting|url-status=live}}</ref><ref>{{Cite web|title=20th WCP: Computational Complexity and Philosophical Dualism|url=https://www.bu.edu/wcp/Papers/Cogn/CognTeix.htm|access-date=7 October 2020|website=www.bu.edu|archive-date=13 October 2020|archive-url=https://web.archive.org/web/20201013092220/https://www.bu.edu/wcp/Papers/Cogn/CognTeix.htm|url-status=live}}</ref>

Penrose believes that such deterministic yet non-algorithmic processes may come into play in the quantum mechanical [[Wave function collapse|wave function reduction]], and may be harnessed by the brain. He argues that computers today are unable to have intelligence because they are algorithmically deterministic systems. 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.<ref name="Penrose-2016">{{Cite book|last=Penrose|first=Roger|url=https://books.google.com/books?id=X28sDwAAQBAJ&q=G%C3%B6del's+incompleteness+theorem|title=The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics|date=2016|publisher=Oxford University Press|isbn=978-0-19-878492-0|language=en|access-date=7 December 2021|archive-date=19 November 2021|archive-url=https://web.archive.org/web/20211119091917/https://books.google.com/books?id=X28sDwAAQBAJ&q=G%C3%B6del%27s+incompleteness+theorem|url-status=live}}</ref> This contrasts with supporters of [[computational theory of mind|strong artificial intelligence]], who contend that thought can be simulated algorithmically. He bases this on claims that consciousness transcends [[formal logic]] because factors 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.<ref name="Penrose-2016" /> These claims were originally espoused by the philosopher [[John Lucas (philosopher)|John Lucas]] of [[Merton College, Oxford|Merton College]], [[University of Oxford|Oxford]].<ref>{{Cite web|title=In Memoriam: John Lucas|url=https://www.philosophy.ox.ac.uk/article/in-memoriam-john-lucas|access-date=7 October 2020|website=www.philosophy.ox.ac.uk|language=en|archive-date=9 October 2020|archive-url=https://web.archive.org/web/20201009111739/https://www.philosophy.ox.ac.uk/article/in-memoriam-john-lucas|url-status=live}}</ref>

The [[Penrose–Lucas argument]] about the implications of Gödel's incompleteness theorem for computational theories of human intelligence has been criticised by mathematicians, computer scientists and philosophers. Many experts in these fields assert that Penrose's argument fails, though different authors choose different aspects of the argument to attack.<ref>Criticism of the Lucas/Penrose argument that intelligence can not be entirely algorithmic:

* [http://consc.net/mindpapers/6.1b MindPapers: 6.1b. Godelian arguments]. {{Webarchive|url=https://web.archive.org/web/20110611213335/http://consc.net/mindpapers/6.1b|date=11 June 2011}}.
* [http://users.ox.ac.uk/~jrlucas/Godel/referenc.html References for Criticisms of the Gödelian Argument]. {{Webarchive|url=https://web.archive.org/web/20200703180031/http://users.ox.ac.uk/~jrlucas/Godel/referenc.html|date=3 July 2020}}.
* [[George Boolos|Boolos, George]], et al. 1990. ''An Open Peer Commentary on The Emperor's New Mind.'' Behavioral and Brain Sciences 13 (4), p. 655.
* [[Martin Davis (mathematician)|Davis, Martin]] 1993. ''How subtle is Gödel's theorem? More on Roger Penrose.'' Behavioral and Brain Sciences, 16, pp. 611–612. Online version at Davis' faculty page at http://cs.nyu.edu/cs/faculty/davism/. {{Webarchive|url=https://web.archive.org/web/19981203160909/http://www.cs.nyu.edu/cs/faculty/davism/|date=3 December 1998}}.
* {{cite journal |last=Feferman |first=Solomon |author-link=Solomon Feferman |date=1996 |title=Penrose's Gödelian argument |journal=[[Psyche (consciousness journal)|Psyche]] |volume=2 |pages=21–32 |citeseerx=10.1.1.130.7027}}
* Krajewski, Stanislaw 2007. ''On Gödel's Theorem and Mechanism: Inconsistency or Unsoundness is Unavoidable in any Attempt to 'Out-Gödel' the Mechanist.'' Fundamenta Informaticae 81, pp. 173–181. Reprinted in [https://books.google.com/books?id=0jSS-3Bl06cC&pg=PA173 Topics in Logic, Philosophy and Foundations of Mathematics and Computer Science:In Recognition of Professor Andrzej Grzegorczyk (2008), p. 173]. {{Webarchive|url=https://web.archive.org/web/20161226205008/https://books.google.com/books?id=0jSS-3Bl06cC&lpg=PP1&pg=PA173|date=26 December 2016}}.
* {{cite journal |last1=LaForte |first1=Geoffrey |last2=Hayes |first2=Patrick J. |last3=Ford |first3=Kenneth M. |year=1998 |title=Why Gödel's Theorem Cannot Refute Computationalism |journal=Artificial Intelligence |volume=104 |issue=1–2 |pages=265–286 |doi=10.1016/s0004-3702(98)00052-6 |doi-access=free}}
* [[David Kellogg Lewis|Lewis, David K.]] 1969. ''[http://www2.units.it/etica/2003_1/7_monographica.doc Lucas against mechanism]. {{Webarchive|url=https://web.archive.org/web/20210225215326/http://www2.units.it/etica/2003_1/7_monographica.doc|date=25 February 2021}}''. Philosophy 44, pp. 231–233.
* [[Hilary Putnam|Putnam, Hilary]] 1995. ''Review of Shadows of the Mind.'' In Bulletin of the American Mathematical Society 32, pp. 370–373 (also see Putnam's less technical criticisms in his [https://www.nytimes.com/books/97/04/27/nnp/17540.html ''The New York Times'' review]. {{Webarchive|url=https://web.archive.org/web/20210309045619/https://archive.nytimes.com/www.nytimes.com/books/97/04/27/nnp/17540.html|date=9 March 2021}}).
Sources that indicate Penrose's argument is generally rejected:

* Bringsford, S. and Xiao, H. 2000. ''[http://kryten.mm.rpi.edu/refute.penrose.pdf A Refutation of Penrose's Gödelian Case Against Artificial Intelligence]. {{Webarchive|url=https://web.archive.org/web/20210224130103/http://kryten.mm.rpi.edu/refute.penrose.pdf|date=24 February 2021}}.'' [[Journal of Experimental and Theoretical Artificial Intelligence]] 12: 307–329. The authors write that it is "generally agreed" that Penrose "failed to destroy the computational conception of mind."
* In an article at {{cite web |title=King's College London – Department of Mathematics |url=http://www.mth.kcl.ac.uk/~llandau/Homepage/Math/penrose.html |url-status=dead |archive-url=https://web.archive.org/web/20010125011300/http://www.mth.kcl.ac.uk/~llandau/Homepage/Math/penrose.html |archive-date=25 January 2001 |access-date=22 October 2010}} L. J. Landau at the Mathematics Department of King's College London writes that "Penrose's argument, its basis and implications, is rejected by experts in the fields which it touches."
Sources that also note that different sources attack different points of the argument:

* Princeton Philosophy professor John Burgess writes in ''[http://www.princeton.edu/~jburgess/Montreal.doc On the Outside Looking In: A Caution about Conservativeness]. {{Webarchive|url=https://web.archive.org/web/20121019093317/http://www.princeton.edu/~jburgess/Montreal.doc|date=19 October 2012}}'', (published in Kurt Gödel: Essays for his Centennial, with the following comments found on [https://books.google.com/books?id=83Attf6BsJ4C&pg=PA131 pp. 131–132]. {{Webarchive|url=https://web.archive.org/web/20161227005431/https://books.google.com/books?id=83Attf6BsJ4C&lpg=PP1&pg=PA131|date=27 December 2016}}) that "the consensus view of logicians today seems to be that the Lucas–Penrose argument is fallacious, though as I have said elsewhere, there is at least this much to be said for Lucas and Penrose, that logicians are not unanimously agreed as to where precisely the fallacy in their argument lies. There are at least three points at which the argument may be attacked."
* [[Nachum Dershowitz]] 2005. ''[http://www.cs.tau.ac.il/~nachumd/papers/FourSonsOfPenrose.pdf The Four Sons of Penrose]. {{Webarchive|url=https://web.archive.org/web/20170809142617/http://www.cs.tau.ac.il/%7Enachumd/papers/FourSonsOfPenrose.pdf|date=9 August 2017}}'', in ''Proceedings of the Eleventh Conference on [[Logic for Programming, Artificial Intelligence and Reasoning]] (LPAR; Jamaica)'', G. Sutcliffe and [[Andrei Voronkov]], eds., Lecture Notes in Computer Science, vol. 3835, Springer-Verlag, Berlin, Germany, pp. 125–138.</ref> [[Marvin Minsky]], a leading proponent of artificial intelligence, was particularly critical, writing that Penrose "tries to show, in chapter after chapter, that human thought cannot be based on any known scientific principle." Minsky's position is exactly the opposite – he believed that humans are, in fact, machines, whose functioning, although complex, is fully explainable by current physics. Minsky maintained 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."<ref>Marvin Minsky. "Conscious Machines." Machinery of Consciousness, Proceedings, [[National Research Council of Canada]], 75th Anniversary Symposium on Science in Society, June 1991.</ref>

Penrose responded to criticism of ''The Emperor's New Mind'' with his follow-up 1994 book ''[[Shadows of the Mind]]'', and in 1997 with ''[[The Large, the Small and the Human Mind]]''. In those works, he also combined his observations with those of anesthesiologist [[Stuart Hameroff]].<ref>{{Cite web|title=Can Quantum Physics Explain Consciousness? One Scientist Thinks It Might|url=https://www.discovermagazine.com/the-sciences/can-quantum-physics-explain-consciousness-one-scientist-thinks-it-might|access-date=7 October 2020|website=Discover Magazine|language=en|archive-date=3 October 2020|archive-url=https://web.archive.org/web/20201003024544/https://www.discovermagazine.com/the-sciences/can-quantum-physics-explain-consciousness-one-scientist-thinks-it-might|url-status=live}}</ref>

Penrose and Hameroff have argued that consciousness is the result of quantum gravity effects in [[microtubule]]s, which they dubbed [[Orch-OR]] (orchestrated objective reduction). [[Max Tegmark]], in a paper in ''Physical Review E'',<ref>{{cite journal | last1 = Tegmark | first1 = Max | date = 2000 | title = The importance of quantum decoherence in brain processes | journal = [[Physical Review E]] | volume = 61 | issue = 4| pages = 4194–4206 | doi=10.1103/physreve.61.4194| pmid = 11088215 |arxiv = quant-ph/9907009 |bibcode = 2000PhRvE..61.4194T | s2cid = 17140058 }}</ref> calculated that the time scale of neuron firing and excitations in microtubules is slower than the [[quantum decoherence|decoherence]] time by a factor of at least 10 billion. The paper's reception 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'".<ref name="Tetlow 2007 166">
{{cite book
|url=https://books.google.com/books?id=3mPI9rUuhJ8C&q=penrose%20
|last=Tetlow
|first=Philip
|title=The Web's Awake: An Introduction to the Field of Web Science and the Concept of Web Life
|publisher=John Wiley & Sons
|location=Hoboken, New Jersey
|date=2007
|isbn=978-0-470-13794-9
|page=166
|access-date=5 October 2020
|archive-date=7 December 2021
|archive-url=https://web.archive.org/web/20211207185552/https://books.google.com/books?id=3mPI9rUuhJ8C&q=penrose+
|url-status=live
}}</ref> Tegmark's paper has been widely cited by critics of the Penrose–Hameroff position.

Phillip Tetlow, although himself supportive of Penrose's views, acknowledges that Penrose's ideas about the human thought process are a minority view in scientific circles, citing Minsky's criticisms and quoting the 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.<ref name="Tetlow 2007 166"/>

In January 2014 Hameroff and Penrose ventured that a discovery of quantum vibrations in microtubules by [[Anirban Bandyopadhyay]] of the National Institute for Materials Science in Japan<ref>{{cite web |url=https://www.researchgate.net/profile/Anirban_Bandyopadhyay |title=Anirban Bandyopadhyay |access-date=22 February 2014 |archive-date=10 March 2014 |archive-url=https://web.archive.org/web/20140310053951/http://www.researchgate.net/profile/Anirban_Bandyopadhyay/ |url-status=live }}</ref> supports the hypothesis of [[Orchestrated objective reduction|Orch-OR theory]]. A reviewed and updated version of the theory was published along with critical commentary and debate in the March 2014 issue of ''[[Physics of Life Reviews]]''.<ref name="Hameroff2014">{{cite journal |last1=Hameroff |first1=S. |last2=Penrose |first2=R. |date=2014 |title=Consciousness in the universe: A review of the 'Orch OR' theory |journal=Physics of Life Reviews |volume=11 |issue=1 |pages=39–78 |bibcode=2014PhLRv..11...39H |doi=10.1016/j.plrev.2013.08.002 |pmid=24070914 |doi-access=free}}</ref>

=== Publications ===
His popular publications include:
* ''[[The Emperor's New Mind|The Emperor's New Mind: Concerning Computers, Minds, and The Laws of Physics]]'' (1989)<ref>{{Cite book|last=Penrose|first=Roger|url=https://books.google.com/books?id=_ibtvQEACAAJ|title=The Emperor's New Mind|date=1989|language=en|access-date=7 October 2020|archive-date=7 December 2021|archive-url=https://web.archive.org/web/20211207185554/https://books.google.com/books?id=_ibtvQEACAAJ|url-status=live}}</ref>
* ''[[Shadows of the Mind|Shadows of the Mind: A Search for the Missing Science of Consciousness]]'' (1994)<ref>{{Cite book|last=Penrose|first=Roger|url=https://books.google.com/books?id=gDbOAK89tmcC&q=Shadows+of+the+Mind:+A+Search+for+the+Missing+Science+of+Consciousness|title=Shadows of the Mind: A Search for the Missing Science of Consciousness|date=1994|publisher=Oxford University Press|isbn=978-0-19-510646-6|language=en|access-date=12 October 2020|archive-date=7 December 2021|archive-url=https://web.archive.org/web/20211207185555/https://books.google.com/books?id=gDbOAK89tmcC&q=Shadows+of+the+Mind%3A+A+Search+for+the+Missing+Science+of+Consciousness|url-status=live}}</ref>
* ''[[The Road to Reality: A Complete Guide to the Laws of the Universe]]'' (2004)<ref>{{Cite book|last=Penrose|first=Roger|url=https://books.google.com/books?id=VWTNCwAAQBAJ|title=The Road to Reality: A Complete Guide to the Laws of the Universe|date=31 March 2016|publisher=Random House|isbn=978-1-4464-1820-8|language=en|access-date=7 October 2020|archive-date=7 December 2021|archive-url=https://web.archive.org/web/20211207185554/https://books.google.com/books?id=VWTNCwAAQBAJ|url-status=live}}</ref>
* ''[[Cycles of Time|Cycles of Time: An Extraordinary New View of the Universe]]'' (2010)<ref>{{Cite book|last=Penrose|first=Roger|url=https://books.google.com/books?id=gv8o1XydoCQC&q=Cycles+of+Time:+An+Extraordinary+New+View+of+the+Universe|title=Cycles of Time: An Extraordinary New View of the Universe|date=6 September 2011|publisher=Knopf Doubleday Publishing Group|isbn=978-0-307-59674-1|language=en}}</ref>
* ''[[Fashion, Faith, and Fantasy in the New Physics of the Universe]]'' (2016)<ref>{{Cite book|last=Penrose|first=Roger|url=https://books.google.com/books?id=9XKYDwAAQBAJ&q=Fashion,+Faith,+and+Fantasy+in+the+New+Physics+of+the+Universe|title=Fashion, Faith, and Fantasy in the New Physics of the Universe|date=5 September 2017|publisher=Princeton University Press|isbn=978-0-691-17853-0|language=en}}</ref>

His co-authored publications include:
* ''[[The Nature of Space and Time]]'' (with [[Stephen Hawking]]) (1996)<ref>{{Cite book|last1=Hawking|first1=Stephen W.|url=https://books.google.com/books?id=8RatQgAACAAJ|title=The Nature of Space and Time|last2=Penrose|first2=Roger|date=1996|publisher=Princeton University Press|isbn=978-0-691-03791-2|language=en|access-date=7 October 2020|archive-date=7 December 2021|archive-url=https://web.archive.org/web/20211207185837/https://books.google.com/books?id=8RatQgAACAAJ|url-status=live}}</ref>
* ''[[The Large, the Small and the Human Mind]]'' (with [[Abner Shimony]], [[Nancy Cartwright (philosopher)|Nancy Cartwright]], and Stephen Hawking) (1997)<ref>{{Cite book|last1=Penrose|first1=Roger|url=https://books.google.com/books?id=jWHqlijAjyMC&q=The+Large,+the+Small+and+the+Human+Mind|title=The Large, the Small and the Human Mind|last2=Shimony|first2=Abner|last3=Cartwright|first3=Nancy|last4=Hawking|first4=Stephen|date=28 April 2000|publisher=Cambridge University Press|isbn=978-0-521-78572-3|language=en}}</ref>
* ''White Mars: The Mind Set Free'' (with [[Brian Aldiss]]) (1999)<ref>{{Cite book|last1=Aldiss|first1=Brian W.|url=https://books.google.com/books?id=K_-jBwAAQBAJ&q=White+Mars:+The+Mind+Set+Free(1999)|title=White Mars; or, The Mind Set Free: A 21st-Century Utopia|last2=Penrose|first2=Roger|date=19 May 2015|publisher=Open Road Media|isbn=978-1-5040-1028-3|language=en}}</ref>

His academic books include:
* ''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)

His forewords to other books include:
* Foreword to [https://www.springer.com/book/9783319724775 "The Map and the Territory: Exploring the foundations of science, thought and reality"] by Shyam Wuppuluri and Francisco Antonio Doria. Published by Springer in "The Frontiers Collection", 2018.<ref>{{Cite book|last1=Wuppuluri|first1=Shyam|url=https://books.google.com/books?id=mRBMDwAAQBAJ&q=%E2%80%9CThe+Map+and+the+Territory:+Exploring+the+foundations+of+science,+thought+and+reality+roger+penrose|title=The Map and the Territory: Exploring the Foundations of Science, Thought and Reality|last2=Doria|first2=Francisco Antonio|date=13 February 2018|publisher=Springer|isbn=978-3-319-72478-2|language=en}}</ref>
* Foreword to [http://www.worldscientific.com/worldscibooks/10.1142/p856 ''Beating the Odds: The Life and Times of E. A. Milne''], written by Meg Weston Smith. Published by World Scientific Publishing Co in June 2013.<ref>{{Cite book|last=Weston-smith|first=Meg|url=https://books.google.com/books?id=P826CgAAQBAJ&q=Beating+the+Odds:+The+Life+and+Times+of+E.+A.+Milne+roger+penrose&pg=PR3|title=Beating The Odds: The Life And Times Of E A Milne|date=16 April 2013|publisher=World Scientific|isbn=978-1-84816-943-2|language=en|access-date=12 October 2020|archive-date=26 January 2021|archive-url=https://web.archive.org/web/20210126000706/https://books.google.com/books?id=P826CgAAQBAJ&q=Beating+the+Odds:+The+Life+and+Times+of+E.+A.+Milne+roger+penrose&pg=PR3|url-status=live}}</ref>
* Foreword to [http://www.worldscientific.com/worldscibooks/10.1142/8306 "A Computable Universe"] by Hector Zenil. Published by World Scientific Publishing Co in December 2012.<ref>{{Cite book|last=Zenil|first=Hector|url=https://books.google.com/books?id=SGG6CgAAQBAJ&q=%22A+Computable+Universe%22+roger+penrose|title=A Computable Universe: Understanding and Exploring Nature as Computation|date=2013|publisher=World Scientific|isbn=978-981-4374-30-9|language=en}}</ref>
* Foreword to ''[[Quantum Aspects of Life]]'' by Derek Abbott, Paul C. W. Davies, and Arun K. Pati. Published by Imperial College Press in 2008.<ref>{{Cite book|last1=Abbott|first1=Derek|url=https://books.google.com/books?id=C1y7CgAAQBAJ&q=Quantum+Aspects+of+Life+roger+penrose|title=Quantum Aspects Of Life|last2=Davies|first2=Paul C. W.|last3=Pati|first3=Arun Kumar|date=12 September 2008|publisher=World Scientific|isbn=978-1-908978-73-8|language=en|access-date=12 October 2020|archive-date=26 January 2021|archive-url=https://web.archive.org/web/20210126162257/https://books.google.com/books?id=C1y7CgAAQBAJ&q=Quantum+Aspects+of+Life+roger+penrose|url-status=live}}</ref>
* Foreword to [http://press.princeton.edu/chapters/p8509.pdf ''Fearful Symmetry''] by [[Anthony Zee]]. Published by Princeton University Press in 2007.<ref>{{Cite book|last=Zee|first=A.|url=https://books.google.com/books?id=Xq1mCgAAQBAJ&q=fearful+symmetry+roger+penrose|title=Fearful Symmetry: The Search for Beauty in Modern Physics|date=1 October 2015|publisher=Princeton University Press|isbn=978-1-4008-7450-7|language=en|access-date=12 October 2020|archive-date=26 January 2021|archive-url=https://web.archive.org/web/20210126162300/https://books.google.com/books?id=Xq1mCgAAQBAJ&q=fearful+symmetry+roger+penrose|url-status=live}}</ref>

=== Awards and honours ===
[[File:RogerPenrose CapturingInfinity cropped.jpg|thumb|Penrose during a lecture]]
Penrose has been awarded many prizes for his contributions to science. In 1971 he was awarded the [[Dannie Heineman Prize for Astrophysics]] by the [[American Astronomical Society]] and [[American Institute of Physics]]. He was elected a [[List of Fellows of the Royal Society elected in 1972|Fellow of the Royal Society (FRS) in 1972]]. In 1975 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 Hawking, he was awarded the prestigious [[Wolf Prize in Physics]] by the [[Wolf Foundation]] (Israel) in 1988.

In 1989 Penrose was awarded the [[Dirac Medal (IOP)|Dirac Medal and Prize]] of the British [[Institute of Physics]]. He was also made an [[Honorary Fellow of the Institute of Physics]] (HonFInstP).<ref>{{cite web |title=Our Honorary Fellows |url=https://www.iop.org/about/awards/honorary-fellowship/our-honorary-fellows |publisher=[[Institute of Physics]] |access-date=26 December 2022}}</ref> In 1990 Penrose was awarded the [[Albert Einstein Medal]] for outstanding work related to the work of [[Albert Einstein]] by the [[Albert Einstein Society]] (Switzerland). In 1991, he was awarded the [[Naylor Prize]] of the [[London Mathematical Society]]. Penrose was awarded an honorary [[Doctor of Science]] degree (DSc) from the [[University of New Brunswick]] (Canada) in 1992,<ref>[https://graduations.lib.unb.ca/award/17499 1992 Fredericton Convocation: Penrose, Roger], website of the [[University of New Brunswick]].</ref> and an honorary degree from the [[University of Surrey]] in 1993.<ref>[https://www.surrey.ac.uk/about/people/honorary-graduates Honorary graduates], website of the [[University of Surrey]].</ref> From 1992 to 1995 he served as President of the [http://www.isgrg.org/ International Society on General Relativity and Gravitation].

In 1994 Penrose was [[Knight Bachelor|knighted]] for services to science.<ref>{{cite web|title=Supplement 53696,10 June 1994, London Gazette|url=https://www.thegazette.co.uk/London/issue/53696/supplement/2|website=The Gazette|access-date=16 August 2015|archive-date=29 April 2016|archive-url=https://web.archive.org/web/20160429222205/https://www.thegazette.co.uk/London/issue/53696/supplement/2|url-status=live}}</ref> In the same year, he was also awarded an honorary degree of [[Doctor of Science]] (DSc) by the [[University of Bath]],<ref>{{cite web |url= http://www.bath.ac.uk/ceremonies/hongrads/ |title= Honorary Graduates 1989 to present |publisher= [[University of Bath]] |access-date= 18 February 2012 |archive-date= 19 December 2015 |archive-url= https://web.archive.org/web/20151219000643/http://www.bath.ac.uk/ceremonies/hongrads/ |url-status= dead }}</ref> and became a member of [[Polish Academy of Sciences]]. Penrose was awarded honorary degrees from the [[University of London]] in 1995,<ref name="ae">[https://www.ae-info.org/ae/Member/Penrose_Roger Professor Sir Roger Penrose OM FRS], website of the [[Academia Europaea]].</ref> the [[University of Glasgow]] ([[Doctor of Science]], DSc)<ref>[https://www.gla.ac.uk/media/Media_61834_smxx.pdf Who, Where and When: The History & Constitution of the University of Glasgow], website of [[The University of Glasgow]].</ref> and [[University of Essex]], both in 1996,<ref>[https://www.essex.ac.uk/alumni/honorary/honorary-graduates Honorary graduates over the years], website of the [[University of Essex]].</ref> from the [[University of St Andrews]] in 1997,<ref name="ae" /> and the [[Visva-Bharati University|Visva-Bharati University of Santiniketan]] (India)<ref name="ae" /> and [[Open University]] ([[Doctor of the University]], DUniv),<ref>[https://www5.open.ac.uk/students/ceremonies/sites/www.open.ac.uk.students.ceremonies/files/Honorary%20graduate%20cumulative%20list(1).pdf Honorary graduate cumulative] website of [[Open University]]</ref> both in 1998. In 1998 he was elected Foreign Associate of the [[United States National Academy of Sciences]].<ref>{{Cite web|title=Sir Roger Penrose {{!}} Person|url=https://www.fetzer-franklin-fund.org/media/sir-roger-penrose/|access-date=7 October 2020|website=Fetzer Franklin Fund|language=de-DE|archive-date=24 September 2020|archive-url=https://web.archive.org/web/20200924081714/https://www.fetzer-franklin-fund.org/media/sir-roger-penrose/|url-status=live}}</ref> In 2000 he was appointed a [[Member of the Order of Merit]] (OM).<ref>{{Cite news|title=Appointments to the Order of Merit|newspaper=The Royal Family |date=January 2012|url=https://www.royal.uk/appointments-order-merit|access-date=25 October 2020|language=en|archive-date=29 September 2020|archive-url=https://web.archive.org/web/20200929015241/https://www.royal.uk/appointments-order-merit|url-status=live|last1=Fisher |first1=Connie }}</ref> He was awarded an [[honorary doctorate]] from the [[University of Southampton]] in 2002.<ref>[https://www.southampton.ac.uk/news/2020/11/roger-penrose-nobel-prize.page Nobel Prize winner Sir Roger Penrose congratulated by Southampton academics], website of the [[University of Southampton]].</ref>

In 2004 Penrose was awarded an honorary [[Doctor of Science]] (DSc) degree from the [[University of Waterloo]] ([[Ontario, Canada]])<ref>[https://bulletin.uwaterloo.ca/2004/sep/21tu.html DAily bulletin September 21, 2004], website of the [[University of Waterloo]].</ref><ref>[https://uwaterloo.ca/secretariat/honorary-degrees-granted Honorary degrees granted], website of the [[University of Waterloo]].</ref> and was awarded the [[De Morgan Medal]] by the [[London Mathematical Society]] for his wide and original contributions to mathematical physics.<ref>{{Cite journal|date=8 August 2018|title=Roger Penrose|language=EN|doi=10.1063/PT.6.6.20180808a|journal=Physics Today|issue=8 |article-number=4433 |doi-access=free|bibcode=2018PhT..2018h4433. }}</ref> To quote the citation from the society:
{{blockquote|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.<ref>{{Cite web|url=http://www.lms.ac.uk/activities/prizes_com/citations04.html|archive-url=https://web.archive.org/web/20041231232542/http://www.lms.ac.uk/activities/prizes_com/citations04.html|title=London Mathematical Society|archive-date=31 December 2004}}</ref>}}

In 2005 Penrose received a [[Doctorate Honoris Causa]] (Dr.h.c.) from each the [[Warsaw University]] (Poland)<ref>[https://www.fuw.edu.pl/~amt/laudatioe.pdf Laudatio by Andrzej Trautman to Roger_Penrose], website of the Faculty of Physics of [[Warsaw University]].</ref> and the [[Katholieke Universiteit Leuven]] (Belgium),<ref>[https://nieuws.kuleuven.be/nl/2012_en_vroeger/0405/07/eredoctor-sir-roger-penrose Eredoctor Sir Roger Penrose], website of [[KU Leuven]].</ref> and an honorary [[Doctor of Philosophy]] (PhD) degree from the [[Athens University of Economics and Business]] (Greece).<ref>[https://www.aueb.gr/en/content/honorary-doctors-philosophy-aueb Honorary Doctors of Philosophy at AUEB], website from [[Athens University of Economics and Business]].</ref>  In 2005 he was also awarded the [[Manchester Literary and Philosophical Society]] Dalton Medal.<ref>Memoirs And Proceedings Of The Manchester Literary And Philosophical Society Volume 152 2013-14</ref>  In 2006 he was conferred the honorary degree of [[Doctor of the University]] (DUniv) by the [[University of York]]<ref>[https://www.york.ac.uk/media/mathematics/honorarydrpresentations/Professor%20Sir%20Roger%20Penrose%20Presentation.pdf Presentation address] by Dr Bernard Kay to Professor Sir Roger Penrose</ref> and also won the [[Dirac Medal (UNSW)|Dirac Medal]] given by the [[University of New South Wales]] (Australia). In 2008 Penrose was awarded the [[Copley Medal]] of the Royal Society. He is also a Distinguished Supporter of [[Humanists UK]] and one of the patrons of the [[Oxford University Scientific Society]].

He was elected to the [[American Philosophical Society]] in 2011.<ref>{{Cite web|title=APS Member History|url=https://search.amphilsoc.org/memhist/search?creator=Roger+Penrose&title=&subject=&subdiv=&mem=&year=&year-max=&dead=&keyword=&smode=advanced|access-date=2021-04-02|website=search.amphilsoc.org|archive-date=7 December 2021|archive-url=https://web.archive.org/web/20211207185556/https://search.amphilsoc.org/memhist/search?creator=Roger+Penrose&title=&subject=&subdiv=&mem=&year=&year-max=&dead=&keyword=&smode=advanced|url-status=live}}</ref> The same year, he was also awarded the [[Fonseca Prize]] by the [[University of Santiago de Compostela]] (Spain).

In 2012 Penrose was awarded the Richard R. Ernst Medal by [[ETH Zürich]] (Switzerland) for his contributions to science and strengthening the connection between science and society. In that year he was also awarded the honorary degree of [[Doctor of Science]] (DSc) by the [[Trinity College Dublin]] (Ireland)<ref>[https://www.tcd.ie/registrar/honorary-degrees/2011-12/ Registrar: Honorary Degrees 2011-2012], website by the [[Trinity College Dublin]].</ref> as well an honorary doctorate degree by the [[Igor Sikorsky Kyiv Polytechnic Institute]] (Ukraine).<ref>[https://kpi.ua/en/penrose-photo Sir Roger Penrose, one of the greatest scientists of our times, visited NTUU "KPI"], website of [[Kyiv Polytechnic Institute]].</ref>

In 2015 Penrose was awarded a [[Doctorate Honoris Causa]] (Dr.h.c.) by [[CINVESTAV]] (Mexico).<ref>{{Cite web|title=Roger Penrose Doctor Honoris Causa por el Cinvestav|url=http://micrositios.cinvestav.mx/avance/Publicaciones/ArtMID/4126/ArticleID/36/Roger-Penrose-Doctor-Honoris-Causa-por-el-Cinvestav|access-date=6 October 2020|website=cinvestav.mx|language=es-MX|archive-date=7 December 2021|archive-url=https://web.archive.org/web/20211207185555/http://micrositios.cinvestav.mx/avance/Publicaciones/ArtMID/4126/ArticleID/36/Roger-Penrose-Doctor-Honoris-Causa-por-el-Cinvestav|url-status=live}}</ref> In 2017 he was awarded the Commandino Medal at the [[Urbino University]] (Italy) for his contributions to the history of science. In that year as well, he was awarded an [[honorary Doctor of Science]] degree (DSc) by the [[University of Edinburgh]].<ref>[https://www.maths.ed.ac.uk/school-of-mathematics/news?nid=712 Sir Roger Penrose : Honorary Degree, Whittaker Colloquium and seminar], website of the [[University of Edinburgh]].</ref> In 2018 Penrose received an honorary degree from [[King's College London]].<ref>[https://www.kcl.ac.uk/news/professor-sir-roger-penrose-recognised-at-kings-honorary-degree-ceremony-1 Professor Sir Roger Penrose recognised at King's Honorary Degree Ceremony], website of [[King's College London]].</ref>

In 2020 Penrose was awarded one half of the [[Nobel Prize in Physics]] by the [[Royal Swedish Academy of Sciences]] for the discovery that black hole formation is a robust prediction of the general theory of relativity, a half-share also going to [[Reinhard Genzel]] and [[Andrea Ghez]] for the discovery of a [[Galactic Center#Supermassive black hole|supermassive compact object]] at the [[centre of our galaxy]].<ref name="Nobel Prize 2020"/> In the same year, he was also awarded the honorary degree of [[Doctor of Science]] (DSc) by the [[University of Cambridge]].<ref>[https://www.staff.admin.cam.ac.uk/features/nominations-for-honorary-degrees-2020 Nominations for honorary degrees 2020], website of the [[University of Cambridge]].</ref><ref>[https://www.cam.ac.uk/news/cambridge-confers-honorary-degrees Cambridge confers honorary degrees], website of the [[University of Cambridge]].</ref>

In 2025 Penrose received the Golden Plate Award of the [[Academy of Achievement|American Academy of Achievement]].<ref>{{cite web|title= Golden Plate Awardees of the American Academy of Achievement |website=www.achievement.org|publisher=American Academy of Achievement|url= https://achievement.org/our-history/golden-plate-awards/#science-exploration}}</ref>

== Personal life ==
Penrose's first marriage was to Joan Isabel Penrose (born Wedge), an American he married in 1959. They had three sons.<ref>{{Cite web|date=27 October 2019|title=7+ Out of This World Facts About Physicist Sir Roger Penrose|url=https://interestingengineering.com/who-is-sir-roger-penrose-and-why-is-he-famous|access-date=7 October 2020|website=interestingengineering.com|language=en-US|archive-date=8 October 2020|archive-url=https://web.archive.org/web/20201008211346/https://interestingengineering.com/who-is-sir-roger-penrose-and-why-is-he-famous|url-status=live}}</ref><ref>{{Cite web|date=18 August 2014|title=Roger Penrose|url=https://www.giffordlectures.org/lecturers/roger-penrose|access-date=7 October 2020|website=The Gifford Lectures|language=en|archive-date=11 October 2020|archive-url=https://web.archive.org/web/20201011220956/https://www.giffordlectures.org/lecturers/roger-penrose|url-status=live}}</ref> Penrose is now married to Vanessa Thomas, director of Academic Development at [[Cokethorpe School]] in [[Witney]], [[Oxfordshire]], and former head of mathematics at [[Abingdon School]].<ref name="gruberprizes.org">{{cite web |url=http://www.gruberprizes.org/SelectingRecipients/SelectionAdvisoryBoard_Bio.php?id=4 |title=The Peter & Patricia Gruber Foundation, St. Thomas US Virgin Islands – Grants and International Awards |publisher=Gruberprizes.org |date=8 August 1931 |access-date=13 August 2012 |archive-date=30 October 2012 |archive-url=https://web.archive.org/web/20121030084628/http://www.gruberprizes.org/SelectingRecipients/SelectionAdvisoryBoard_Bio.php?id=4 |url-status=live }}</ref><ref>{{cite web |url=http://www.abingdon.org.uk/vanessa_penrose/ |title=Vanessa Penrose |publisher=Abingdon School |date=6 July 2012 |access-date=13 August 2012 |archive-url=https://web.archive.org/web/20120327144417/http://www.abingdon.org.uk/vanessa_penrose/ |archive-date=27 March 2012 |url-status=dead }}</ref> They have one son.<ref>{{Cite web|title=Interview with Sir Roger Penrose|publisher=European Mathematical Society Newsletter March 2001|url=https://www.emis.de/newsletter/newsletter39.pdf#page=17|website=European Mathematical Information Service}}</ref><ref name="gruberprizes.org"/>

=== Religious views ===

During an interview with [[BBC Radio 4]] on 25 September 2010, Penrose stated, "I'm not a believer myself. I don't believe in established religions of any kind."<ref>{{cite news|url=https://news.bbc.co.uk/today/hi/today/newsid_9032000/9032626.stm|title=Big Bang follows Big Bang follows Big Bang|access-date=1 December 2010|publisher=BBC News|date=25 September 2010|archive-date=30 November 2010|archive-url=https://web.archive.org/web/20101130152519/http://news.bbc.co.uk/today/hi/today/newsid_9032000/9032626.stm|url-status=live}}</ref> He regards himself as an agnostic.<ref>{{cite web |author1=Thomas Fink |title=A singular mind: Roger Penrose on his Nobel Prize |url=https://www.spectator.co.uk/article/a-singular-mind-roger-penrose-on-his-nobel-prize |website=The Spectator |publisher= |access-date=18 May 2021 |date=December 19, 2020 |archive-date=18 May 2021 |archive-url=https://web.archive.org/web/20210518203446/https://www.spectator.co.uk/article/a-singular-mind-roger-penrose-on-his-nobel-prize |url-status=live }}</ref> In the 1991 film ''[[A Brief History of Time (film)|A Brief History of Time]]'', he also said, "I think I would say that the universe has a purpose, it's not somehow just there by chance ... some people, I think, take the view that the universe is just there and it runs along—it's a bit like it just sort of computes, and we happen somehow by accident to find ourselves in this thing. But 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."<ref>See [http://www.springfieldspringfield.co.uk/movie_script.php?movie=a-brief-history-of-time A Brief History of Time (1991) film script – springfieldspringfield.co.uk] {{Webarchive|url=https://web.archive.org/web/20150924105028/http://www.springfieldspringfield.co.uk/movie_script.php?movie=a-brief-history-of-time |date=24 September 2015 }}</ref>

Penrose is a patron of [[Humanists UK]].<ref>{{cite web |title=Patrons |url=https://humanism.org.uk/about/our-people/patrons/ |website=Humanists UK |access-date=6 October 2020 |archive-date=5 October 2020 |archive-url=https://web.archive.org/web/20201005083241/https://humanism.org.uk/about/our-people/patrons/ |url-status=live }}</ref>

== See also ==
* [[List of things named after Roger Penrose]]

== Notes ==
{{notelist}}

== References ==
{{reflist}}

==Further reading==
* {{cite book | last=Barss | first=Patchen | title=The Impossible Man: Roger Penrose and the Cost of Genius | publisher=Basic Books | publication-place=New York | date=2024 | isbn=978-1-5416-0366-0}}

== External links ==
{{Wikiquote}}
{{Commons category}}
{{Scholia}}
* [http://iai.tv/video/awake-in-the-universe-htlgi-2010 Awake in the Universe] – Penrose debates how creativity, the most elusive of faculties, has helped us unlock the country of the mind and the mysteries of the cosmos with [[Bonnie Greer]].
* {{Internet Archive author |sname= Roger Penrose}}
* {{YouTube|Cw-zNRNcF90|Dangerous Knowledge}} – Penrose was one of the principal interviewees in a BBC documentary about the mathematics of infinity directed by [[David Malone (independent filmmaker)|David Malone]]
* Penrose's new theory "Aeons Before the Big Bang?":
** Original 2005 lecture: [http://www.newton.ac.uk/webseminars/pg+ws/2005/gmr/gmrw04/1107/penrose/frames.html "Before the Big Bang? A new perspective on the Weyl curvature hypothesis"] {{Webarchive|url=https://web.archive.org/web/20090807022659/http://www.newton.ac.uk/webseminars/pg+ws/2005/gmr/gmrw04/1107/penrose/frames.html |date=7 August 2009 }} (Isaac Newton Institute for Mathematical Sciences, Cambridge, 11 November 2005).
** Original publication: [http://accelconf.web.cern.ch/AccelConf/e06/PAPERS/THESPA01.PDF "Before the Big Bang: an outrageous new perspective and its implications for particle physics".] ''Proceedings of EPAC 2006''. Edinburgh. 2759–2762 (cf. also Hill, C.D. & Nurowski, P. (2007) [https://arxiv.org/abs/0710.3879 "On Penrose's 'Before the Big Bang' ideas"]. Ithaca)
** Revised 2009 lecture: [http://smartech.gatech.edu/handle/1853/27632 "Aeons Before the Big Bang?"] ([[Georgia Institute of Technology]], Center for Relativistic Astrophysics)
** {{YouTube|pEIj9zcLzp0|BBC interview on the new theory}}
* [https://www.bbc.co.uk/programmes/p004kln9 Roger Penrose] on ''[[The Forum (BBC World Service)|The Forum]]''
* {{YouTube|xiYDc1LA0I4|Penrose on sidestepping reason}}
* [https://www.ams.org/bull/pre-1996-data/199507/199507015.pdf Hilary Putnam's review of Penrose's 'Shadows of the Mind' claiming that Penrose's use of Godel's Incompleteness Theorem is fallacious] {{Webarchive|url=https://web.archive.org/web/20071128081513/http://www.ams.org/bull/pre-1996-data/199507/199507015.pdf |date=28 November 2007 }}
** {{webarchive |url=https://web.archive.org/web/20080618195657/http://psyche.csse.monash.edu.au/v2/psyche-2-23-penrose.html |date=18 June 2008 |title=Beyond the Doubting of a Shadow: A Reply to Commentaries on Shadows of the Mind }}
* [https://www.sciencenews.org/article/ancient-islamic-penrose-tiles-0 Penrose Tiling found in Islamic Architecture]
* [https://web.archive.org/web/20040314072735/http://www.sciencenews.org/Sn_arch/10_12_96/Bob1.htm Two theories for the formation of quasicrystals resembling Penrose tilings]
* {{cite journal | last1 = Tegmark | first1 = Max | author-link=Max Tegmark | date = 2000 | title = The importance of quantum decoherence in brain processes | journal = Physical Review E | volume = 61 | issue = 4| pages = 4194–4206 | doi=10.1103/physreve.61.4194| pmid = 11088215 |arxiv = quant-ph/9907009 |bibcode = 2000PhRvE..61.4194T | s2cid = 17140058 }}
** "[https://web.archive.org/web/20051024022835/http://www.quantumconsciousness.org/pdfs/decoherence.pdf Biological feasibility of quantum states in the brain]" – (a disputation of Tegmark's result by Hagan, Hameroff, and Tuszyński)
*** [http://space.mit.edu/home/tegmark/brain.html Tegmarks's rejoinder to Hagan ''et al.'']
* {{webarchive |url=https://web.archive.org/web/20050312084035/http://www.parascope.com/articles/slips/fs_151.htm |date=12 March 2005 |title="Toilet Paper Plagiarism" }} – D. Trull about Penrose's lawsuit concerning the use of his Penrose tilings on toilet paper
* [https://web.archive.org/web/20070423214256/http://plus.maths.org/issue18/features/penrose/index.html Roger Penrose: A Knight on the tiles] (''[[Plus Magazine]]'')
* [https://web.archive.org/web/20080621162508/http://www.giffordlectures.org/Author.asp?AuthorID=254 Penrose's Gifford Lecture biography]
* [http://www.quantum-mind.co.uk Quantum-Mind]
* [https://www.bbc.co.uk/worldservice/documentaries/2009/04/090427_theforum_260409.shtml Audio: Roger Penrose in conversation on the BBC World Service discussion show]
* [https://web.archive.org/web/20130407184109/http://www.premierradio.org.uk/listen/ondemand.aspx?mediaid=%7B320D8898-A8F0-4433-8934-D64DDEB8A21C%7D Roger Penrose speaking about Hawking's new book on Premier Christian Radio]
* [https://web.archive.org/web/20140727062257/http://www.ideasroadshow.com/issues/sir-roger-penrose-2013-07-12 "The Cyclic Universe – A conversation with Roger Penrose"], ''[[Ideas Roadshow]]'', 2013
* [https://web.archive.org/web/20140327150655/http://richannel.org/forbidden-crystal-symmetry-in-mathematics-and-architecture Forbidden crystal symmetry in mathematics and architecture], filmed event at the [[Royal Institution]], October 2013
* [http://www.maths.ox.ac.uk/node/25923 ''Oxford Mathematics Interviews'': "Extra Time: Professor Sir Roger Penrose in conversation] with [[Andrew Hodges]]." These two films explore the development of Sir Roger Penrose's thought over more than 60 years, ending with his most recent theories and predictions. 51 min and 42 min. ([[Mathematical Institute, University of Oxford|Mathematical Institute]])
* [https://www.bbc.co.uk/programmes/b082ymnx BBC Radio 4 – The Life Scientific – Roger Penrose on Black Holes – 22 November 2016] Sir Roger Penrose talks to Jim Al-Khalili about his trailblazing work on how black holes form, the problems with quantum physics and his portrayal in films about Stephen Hawking.
* [https://web.archive.org/web/20171107025935/https://penroseinstitute.com/ The Penrose Institute] Website
* [https://web.archive.org/web/20190528065625/https://en.chessbase.com/post/a-chess-problem-holds-the-key-to-human-consciousness A chess problem holds the key to human consciousness?], Chessbase
* {{Nobelprize}}

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