Editing Roger Penrose (section)

== Early life and education ==
Born in [[Colchester]], Essex, Roger Penrose is a son of physician Margaret (née Leathes) and psychiatrist and geneticist [[Lionel Penrose]].{{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 artist, and The Hon. Elizabeth Josephine Peckover, daughter of [[Alexander Peckover, 1st Baron Peckover]]; his maternal grandparents were [[physiologist]] [[John Beresford Leathes]] and Sonia Marie Natanson, a [[History of the Jews in Russia|Russian Jew]].<ref>{{Cite book |last=Brookfield |first=Tarah |url=https://www.worldcat.org/oclc/1066070267 |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 artist Sir [[Roland Penrose]], whose son with 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 physicist [[Oliver Penrose]], of geneticist [[Shirley Hodgson]] and of [[Grandmaster (chess)|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 web|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=www.timesofisrael.com|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}}</ref> Their stepfather was the mathematician and computer scientist [[Max Newman]].

Penrose spent World War II 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, Sir [[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 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 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>}}