John Horton Conway

Conway was born on 26 December 1937 in Liverpool, the son of Cyril Horton Conway and Agnes Boyce.{{cite web |url=http://www.ukwhoswho.com/view/article/oupww/whoswho/U11688 |title=CONWAY, Prof. John Horton |work=Who's Who 2014, A & C Black, an imprint of Bloomsbury Publishing plc, 2014; online edn, Oxford University Press }}{{subscription required}} He became interested in mathematics at a very early age. By the time he was 11, his ambition was to become a mathematician.{{cite web|title=John Horton Conway|website=Dean of the Faculty, Princeton University|url=https://dof.princeton.edu/about/clerk-faculty/emeritus/john-horton-conway|access-date=3 November 2020|archive-date=16 March 2019|archive-url=https://web.archive.org/web/20190316023012/https://dof.princeton.edu/about/clerk-faculty/emeritus/john-horton-conway|url-status=dead}}{{cite book|title=Mathematical Frontiers|url=https://books.google.com/books?id=gmCSpNhXMooC&pg=PA38 | page=38 | publisher=Infobase Publishing | year = 2006 | isbn=978-0-7910-9719-9}} After leaving sixth form, he studied mathematics at Gonville and Caius College, Cambridge. A "terribly introverted adolescent" in school, he took his admission to Cambridge as an opportunity to transform himself into an extrovert, a change which would later earn him the nickname of "the world's most charismatic mathematician".{{cite news|last1=Roberts|first1=Siobhan|author-link=Siobhan Roberts|title=John Horton Conway: the world's most charismatic mathematician|url=https://www.theguardian.com/science/2015/jul/23/john-horton-conway-the-most-charismatic-mathematician-in-the-world|newspaper=The Guardian|date=23 July 2015}}{{cite book|author=Mark Ronan|title=Symmetry and the Monster: One of the greatest quests of mathematics|url=https://archive.org/details/symmetrymonstero0000rona|url-access=registration|date=18 May 2006|publisher=Oxford University Press, UK|isbn=978-0-19-157938-7|pages=[https://archive.org/details/symmetrymonstero0000rona/page/163 163]|author-link=Mark Ronan}}

Conway was awarded a BA in 1959 and, supervised by Harold Davenport, began to undertake research in number theory. Having solved the open problem posed by Davenport on writing numbers as the sums of fifth powers, Conway became interested in infinite ordinals. It appears that his interest in games began during his years studying the Cambridge Mathematical Tripos, where he became an avid backgammon player, spending hours playing the game in the common room.

In 1964, Conway was awarded his doctorate and was appointed as College Fellow and Lecturer in Mathematics at Sidney Sussex College, Cambridge.{{cite book|author=Sooyoung Chang|year=2011|title = Academic Genealogy of Mathematicians | publisher = World Scientific | page=205 | isbn=978-981-4282-29-1}}

After leaving Cambridge in 1986, he took up the appointment to the John von Neumann Chair of Mathematics at Princeton University. There, he won the Princeton University Pi Day pie-eating contest.{{Cite magazine |title=This Is How the Number 3.14 Got the Name 'Pi' |url=https://time.com/4699479/pi-day-history-origins/ |access-date=2022-09-21 |magazine=Time |language=en}}

Conway's career was intertwined with that of Martin Gardner. When Gardner featured Conway's Game of Life in his Mathematical Games column in October 1970, it became the most widely read of all his columns and made Conway an instant celebrity.Mulcahy, Colm (21 October 2014) [https://www.bbc.com/news/magazine-29688355 Martin Gardner, puzzle master extraordinaire], BBC News Magazine: "The Game of Life appeared in Scientific American in 1970, and was by far the most successful of Gardner's columns, in terms of reader response." Gardner and Conway had first corresponded in the late 1950s, and over the years Gardner had frequently written about recreational aspects of Conway's work.[http://mathfactor.uark.edu/2010/06/ha-conway-on-gardner/ The Math Factor Podcast Website] John H. Conway reminisces on his long friendship and collaboration with Martin Gardner. For instance, he discussed Conway's game of Sprouts (July 1967), Hackenbush (January 1972), and his angel and devil problem (February 1974). In the September 1976 column, he reviewed Conway's book On Numbers and Games and even managed to explain Conway's surreal numbers.Gardner, Martin (1989) Penrose Tiles to Trapdoor Ciphers, W. H. Freeman & Co., {{ISBN|0-7167-1987-8}}, Chapter 4. A non-technical overview; reprint of the 1976 Scientific American article.

Conway was a prominent member of Martin Gardner's Mathematical Grapevine. He regularly visited Gardner and often wrote him long letters summarizing his recreational research. In a 1976 visit, Gardner kept him for a week, pumping him for information on the Penrose tilings which had just been announced. Conway had discovered many (if not most) of the major properties of the tilings.{{cite journal|url=https://www.ams.org/notices/200506/fea-gardner.pdf |title=Interview with Martin Gardner|journal=Notices of the AMS|volume=52|issue=6|date=2005|pages=602–611|author=Jackson, Allyn }} Gardner used these results when he introduced the world to Penrose tiles in his January 1977 column.{{cite journal|url=https://www.quantamagazine.org/john-conways-life-in-games-20150828/ |title=A Life In Games: The Playful Genius of John Conway|author=Roberts, Siobhan |journal=Quanta Magazine|date=28 August 2015}} The cover of that issue of Scientific American features the Penrose tiles and is based on a sketch by Conway.

{{Main|Conway's Game of Life}}

File:Gospers glider gun.gif's Glider Gun creating "gliders" in Conway's Game of Life]]

Conway invented the Game of Life, one of the early examples of a cellular automaton. His initial experiments in that field were done with pen and paper, long before personal computers existed. Since Conway's game was popularized by Martin Gardner in Scientific American in 1970,{{Cite magazine|title=Mathematical Games: The fantastic combinations of John Conway's new solitaire game "Life"|first=Martin|last=Gardner|magazine=Scientific American|volume=223|date=October 1970|pages=120–123|jstor=24927642|url=https://web.stanford.edu/class/sts145/Library/life.pdf}} it has spawned hundreds of computer programs, web sites, and articles.{{Cite web |url=https://www.dmoz.org/Computers/Artificial_Life/Cellular_Automata/Conway%27s_Game_of_Life |title=DMOZ: Conway's Game of Life: Sites |access-date=11 January 2017 |archive-url=https://web.archive.org/web/20170317103511/http://www.dmoz.org/Computers/Artificial_Life/Cellular_Automata/Conway%27s_Game_of_Life/ |archive-date=17 March 2017 |url-status=dead }} It is a staple of recreational mathematics. The LifeWiki is devoted to curating and cataloging the various aspects of the game.{{Cite web|url=https://www.conwaylife.com/wiki/Main_Page|title=LifeWiki|website=www.conwaylife.com}} From the earliest days, it has been a favorite in computer labs, both for its theoretical interest and as a practical exercise in programming and data display. Conway came to dislike how discussions of him heavily focused on his Game of Life, feeling that it overshadowed deeper and more important things he had done, although he remained proud of his work on it.{{Cite AV media |url=https://www.youtube.com/watch?v=E8kUJL04ELA |title=Does John Conway hate his Game of Life? |date=2014-03-03 |last=Numberphile |access-date=2024-11-05 |via=YouTube}} The game helped to launch a new branch of mathematics, the field of cellular automata.MacTutor History: The game made Conway instantly famous, but it also opened up a whole new field of mathematical research, the field of cellular automata.

The Game of Life is known to be Turing complete.{{cite book |last=Rendell |first=Paul |date=July 2015 |title=Turing Machine Universality of the Game of Life |series=Emergence, Complexity and Computation |volume=18 |publisher=Springer |isbn=978-3319198415 |doi=10.1007/978-3-319-19842-2 |url=https://books.google.com/books?id=w92moAEACAAJ}}{{cite news |last=Case |first=James |date=1 April 2014 |title=Martin Gardner's Mathematical Grapevine |website=SIAM NEWS |url=https://sinews.siam.org/Details-Page/martin-gardners-mathematical-grapevine |at=Book reviews of Gardner, Martin, 2013 Undiluted Hocus-Pocus: The Autobiography of Martin Gardner. Princeton University Press and Henle, Michael; Hopkins, Brian (edts.) 2012 Martin Gardner in the Twenty-First Century. MAA Publications }}

Conway contributed to combinatorial game theory (CGT), a theory of partisan games. He developed the theory with Elwyn Berlekamp and Richard Guy, and also co-authored the book Winning Ways for your Mathematical Plays with them. He also wrote On Numbers and Games (ONAG) which lays out the mathematical foundations of CGT.

He was also one of the inventors of the game sprouts, as well as philosopher's football. He developed detailed analyses of many other games and puzzles, such as the Soma cube, peg solitaire, and Conway's soldiers. He came up with the angel problem, which was solved in 2006.

He invented a new system of numbers, the surreal numbers, which are closely related to certain games and have been the subject of a mathematical novelette by Donald Knuth.[http://discovermagazine.com/1995/dec/infinityplusonea599 Infinity Plus One, and Other Surreal Numbers] by Polly Shulman, Discover Magazine, 1 December 1995 He also invented a nomenclature for exceedingly large numbers, the Conway chained arrow notation. Much of this is discussed in the 0th part of ONAG.

In the mid-1960s with Michael Guy, Conway established that there are sixty-four convex uniform polychora excluding two infinite sets of prismatic forms. They discovered the grand antiprism in the process, the only non-Wythoffian uniform polychoron.{{cite journal|author=Conway, J. H. |title=Four-dimensional Archimedean polytopes|journal=Proc. Colloquium on Convexity, Copenhagen |year=1967|publisher= Kobenhavns Univ. Mat. Institut|pages= 38–39}} Conway also suggested a system of notation dedicated to describing polyhedra called Conway polyhedron notation.

In the theory of tessellations, he devised the Conway criterion which is a fast way to identify many prototiles that tile the plane.{{cite journal| doi=10.1016/j.cam.2004.05.002 | volume=174 | issue=2 | title=Planar tilings by polyominoes, polyhexes, and polyiamonds | year=2005 | journal=Journal of Computational and Applied Mathematics | pages=329–353 | last1 = Rhoads | first1 = Glenn C.| bibcode=2005JCoAM.174..329R | doi-access=free }}

He investigated lattices in higher dimensions and was the first to determine the symmetry group of the Leech lattice.

In knot theory, Conway formulated a new variation of the Alexander polynomial and produced a new invariant now called the Conway polynomial.{{Cite web |last=Weisstein |first=Eric W. |title=Conway Polynomial |url=https://mathworld.wolfram.com/ConwayPolynomial.html |access-date=2024-11-05 |website=mathworld.wolfram.com |language=en}} After lying dormant for more than a decade, this concept became central to work in the 1980s on the novel knot polynomials.Livingston, Charles (1993) Knot Theory. MAA Textbooks. {{ISBN|0883850273}} Conway further developed tangle theory and invented a system of notation for tabulating knots, now known as Conway notation, while correcting a number of errors in the 19th-century knot tables and extending them to include all but four of the non-alternating primes with 11 crossings.{{cite journal|journal=Topology Proceedings |volume=7 |year=1982|pages= 109–118|author=Perko, Ken |url=http://topology.nipissingu.ca/tp/reprints/v07/tp07110.pdf|title=Primality of certain knots}} The Conway knot is named after him.

Conway's conjecture that, in any thrackle, the number of edges is at most equal to the number of vertices, is still open.

He was the primary author of the ATLAS of Finite Groups giving properties of many finite simple groups. Working with his colleagues Robert Curtis and Simon P. Norton he constructed the first concrete representations of some of the sporadic groups. More specifically, he discovered three sporadic groups based on the symmetry of the Leech lattice, which have been designated the Conway groups.{{cite journal |last=Harris |first=Michael |author-link=Michael Harris (mathematician) |date=2015 |title=Mathematics: The mercurial mathematician |journal=Nature |volume=523 |pages=406–7 |doi=10.1038/523406a |others=Review of Genius At Play: The Curious Mind of John Horton Conway

|issue=7561 |bibcode=2015Natur.523..406H |doi-access=free }} This work made him a key player in the successful classification of the finite simple groups.

Based on a 1978 observation by mathematician John McKay, Conway and Norton formulated the complex of conjectures known as monstrous moonshine. This subject, named by Conway, relates the monster group with elliptic modular functions, thus bridging two previously distinct areas of mathematics—finite groups and complex function theory. Monstrous moonshine theory has now been revealed to also have deep connections to string theory.{{Cite web |last=Darling |first=David |title=Monstrous Moonshine conjecture |url=https://www.daviddarling.info/encyclopedia/M/Monstrous_Moonshine_conjecture.html |access-date=2024-11-05 |website=www.daviddarling.info}}

Conway introduced the Mathieu groupoid, an extension of the Mathieu group M₁₂ to 13 points.

As a graduate student, he proved one case of a conjecture by Edward Waring, that every integer could be written as the sum of 37 numbers each raised to the fifth power, though Chen Jingrun solved the problem independently before Conway's work could be published.{{cite journal|url=http://www.ems-ph.org/journals/newsletter/pdf/2005-09-57.pdf#page=34 |title=Breakfast with John Horton Conway|pages=32–34|journal=EMS Newsletter |date=September 2005|author=Jorge Nuno Silva|volume=57}} In 1972, Conway proved that a natural generalization of the Collatz problem is algorithmically undecidable. Related to that, he developed the esoteric programming language FRACTRAN. While lecturing on the Collatz conjecture, Terence Tao (who was taught by him in graduate school) mentioned Conway's result and said that he was "always very good at making extremely weird connections in mathematics".{{Citation |title=Day 2 - The notorious Collatz conjecture - Terence Tao | date=30 October 2021 |url=https://www.youtube.com/watch?v=X2p5eMWyaFs |access-date=2023-03-23 |language=en}}

Conway wrote a textbook on Stephen Kleene's theory of state machines, and published original work on algebraic structures, focusing particularly on quaternions and octonions.{{cite journal |last=Baez |first=John C. |date=2005 |title=Book Review: On quaternions and octonions: Their geometry, arithmetic, and symmetry |journal=Bulletin of the American Mathematical Society |volume=42 |issue=2 |pages=229–243 |doi=10.1090/S0273-0979-05-01043-8 |doi-access=free }} Together with Neil Sloane, he invented the icosians.{{cite web| url=http://math.ucr.edu/home/baez/week20.html| title=This Week's Finds in Mathematical Physics (Week 20)| author=Baez, John | date=2 October 1993}}

He invented a base 13 function as a counterexample to the converse of the intermediate value theorem: the function takes on every real value in each interval on the real line, so it has a Darboux property but is not continuous.

For calculating the day of the week, he invented the Doomsday algorithm. The algorithm is simple enough for anyone with basic arithmetic ability to do the calculations mentally. Conway could usually give the correct answer in under two seconds. To improve his speed, he practised his calendrical calculations on his computer, which was programmed to quiz him with random dates every time he logged on. One of his early books was on finite-state machines.

In 2004, Conway and Simon B. Kochen, another Princeton mathematician, proved the free will theorem, a version of the "no hidden variables" principle of quantum mechanics. It states that given certain conditions, if an experimenter can freely decide what quantities to measure in a particular experiment, then elementary particles must be free to choose their spins to make the measurements consistent with physical law. Conway said that "if experimenters have free will, then so do elementary particles."[http://www.cs.auckland.ac.nz/~jas/one/freewill-theorem.html Conway's Proof Of The Free Will Theorem] {{Webarchive|url=https://web.archive.org/web/20171125154530/https://www.cs.auckland.ac.nz/~jas/one/freewill-theorem.html |date=25 November 2017 }} by Jasvir Nagra

Conway was married three times. With his first two wives he had two sons and four daughters. He married Diana in 2001 and had another son with her.{{cite web

|url=https://www.princeton.edu/news/2020/04/14/mathematician-john-horton-conway-magical-genius-known-inventing-game-life-dies-age

|last1=Zandonella

|first1=Catherine

|title=Mathematician John Horton Conway, a 'magical genius' known for inventing the 'Game of Life,' dies at age 82

}} He had three grandchildren and two great-grandchildren.

On 8 April 2020, Conway developed symptoms of COVID-19.{{cite web |last1=Levine |first1=Cecilia |title=COVID-19 Kills Renowned Princeton Mathematician, 'Game Of Life' Inventor John Conway In 3 Days |url=https://dailyvoice.com/new-jersey/mercer/obituaries/covid-19-kills-renowned-princeton-mathematician-game-of-life-inventor-john-conway-in-3-days/786461/ |website=Mercer Daily Voice |date=12 April 2020}} On 11 April, he died in New Brunswick, New Jersey, at the age of 82.{{Cite news |last=Zandonella |first=Catherine |url=https://www.princeton.edu/news/2020/04/14/mathematician-john-horton-conway-magical-genius-known-inventing-game-life-dies-age |title=Mathematician John Horton Conway, a 'magical genius' known for inventing the 'Game of Life,' dies at age 82 |date=14 April 2020 |access-date=2020-04-15 |publisher=Princeton University }}{{Cite news |last=Van den Brandhof |first=Alex |url=https://www.nrc.nl/nieuws/2020/04/12/wiskundige-conway-was-een-speels-genie-en-kenner-van-symmetrie-a3996590 |title=Mathematician Conway was a playful genius and expert on symmetry |date=12 April 2020 |work=NRC Handelsblad |access-date=12 April 2020 |language=nl}}{{cite web|url=https://www.nytimes.com/2020/04/15/technology/john-horton-conway-dead-coronavirus.html|title=John Horton Conway, a 'Magical Genius' in Math, Dies at 82|work=The New York Times|date=15 April 2020|last=Roberts|first=Siobhan|access-date=17 April 2020|url-access=limited}}{{Cite news|last=Mulcahy|first=Colm|date=2020-04-23|title=John Horton Conway obituary|work=The Guardian|url=https://www.theguardian.com/science/2020/apr/23/john-horton-conway-obituary|access-date=2020-05-30|issn=0261-3077}}

Conway received the Berwick Prize (1971),{{Cite web|url=https://www.lms.ac.uk/prizes/list-lms-prize-winners|title=List of LMS prize winners | London Mathematical Society|website=www.lms.ac.uk}} was elected a Fellow of the Royal Society (1981),{{Cite web|url=https://royalsociety.org/people/john-conway-11257/|title=John Conway|website=The Royal Society|access-date=11 April 2020}}{{Cite journal|last=Curtis|first=Robert Turner|title=John Horton Conway. 26 December 1937—11 April 2020|journal=Biographical Memoirs of Fellows of the Royal Society|year=2022 |volume=72|pages=117–138 |doi=10.1098/rsbm.2021.0034 |s2cid=245355088 |doi-access=free}} became a fellow of the American Academy of Arts and Sciences in 1992, was the first recipient of the Pólya Prize (LMS) (1987), won the Nemmers Prize in Mathematics (1998) and received the Leroy P. Steele Prize for Mathematical Exposition (2000) of the American Mathematical Society. In 2001 he was awarded an honorary degree from the University of Liverpool,{{Cite web|url=https://www.cnn.com/2020/04/14/us/john-conway-death-obit-trnd/index.html|title=John H. Conway, a renowned mathematician who created one of the first computer games, dies of coronavirus complications|first=Anna |last=Sturla|website=CNN|date=14 April 2020 |access-date=2020-04-16}} and in 2014 one from Alexandru Ioan Cuza University.{{Cite web|url=https://www.uaic.ro/en/doctor-honoris-causa-john-horton-conway-mathematics-chair-princeton-university/ |title=Doctor Honoris Causa for John Horton Conway |website=Alexandru Ioan Cuza University |date=19 June 2014 |access-date=2020-07-07 }}

His Fellow of the Royal Society nomination in 1981 reads: {{Blockquote|A versatile mathematician who combines a deep combinatorial insight with algebraic virtuosity, particularly in the construction and manipulation of "off-beat" algebraic structures which illuminate a wide variety of problems in completely unexpected ways. He has made distinguished contributions to the theory of finite groups, to the theory of knots, to mathematical logic (both set theory and automata theory) and to the theory of games (as also to its practice).}}

In 2017 Conway was given honorary membership of the British Mathematical Association.{{Cite web|url=https://www.m-a.org.uk/honorary-members|title=Honorary Members|website=The Mathematical Association|access-date=11 April 2020}}

Conferences called Gathering 4 Gardner are held every two years to celebrate the legacy of Martin Gardner, and Conway himself was often a featured speaker at these events, discussing various aspects of recreational mathematics.[http://gathering4gardner.org/VIDEOS.html Presentation Videos] {{webarchive|url=https://web.archive.org/web/20160809042801/http://gathering4gardner.org/VIDEOS.html |date=9 August 2016 }} from 2014 Gathering 4 GardnerBellos, Alex (2008). [https://www.theguardian.com/science/2008/may/31/maths.science The science of fun]. The Guardian, 30 May 2008

{{Scholia}}

• 1971 – Regular algebra and finite machines. Chapman and Hall, London, 1971, Series: Chapman and Hall mathematics series, {{isbn|0412106205}}.
• 1976 – On numbers and games. Academic Press, New York, 1976, Series: L.M.S. monographs, 6, {{isbn|0121863506}}.
• 1979 – On the Distribution of Values of Angles Determined by Coplanar Points (with Paul Erdős, Michael Guy, and H. T. Croft). Journal of the London Mathematical Society, vol. II, series 19, pp. 137–143.
• 1979 – Monstrous Moonshine (with Simon P. Norton).{{Cite journal|url=https://academic.oup.com/blms/article/11/3/308/339059|title=Monstrous Moonshine|first1=J. H.|last1=Conway|first2=S. P.|last2=Norton|date=1 October 1979|journal=Bulletin of the London Mathematical Society|volume=11|issue=3|pages=308–339|via=academic.oup.com|doi=10.1112/blms/11.3.308}} Bulletin of the London Mathematical Society, vol. 11, issue 2, pp. 308–339.
• 1982 – Winning Ways for your Mathematical Plays (with Richard K. Guy and Elwyn Berlekamp). Academic Press, {{isbn|0120911507}}.
• 1985 – Atlas of finite groups (with Robert Turner Curtis, Simon Phillips Norton, Richard A. Parker, and Robert Arnott Wilson). Clarendon Press, New York, Oxford University Press, 1985, {{isbn|0198531990}}.
• 1988 – Sphere Packings, Lattices, and Groups{{cite journal |last=Guy |first=Richard K.|author-link=Richard K. Guy|title=Review: Sphere packings, lattices and groups, by J. H. Conway and N. J. A. Sloane |journal=Bulletin of the American Mathematical Society |series=New Series |year=1989 |volume=21|issue=1|pages=142–147|url=https://www.ams.org/journals/bull/1989-21-01/S0273-0979-1989-15795-9/S0273-0979-1989-15795-9.pdf |doi= 10.1090/s0273-0979-1989-15795-9 |doi-access=free }} (with Neil Sloane). Springer-Verlag, New York, Series: Grundlehren der mathematischen Wissenschaften, 290, {{isbn|9780387966175}}.
• 1995 – Minimal-Energy Clusters of Hard Spheres (with Neil Sloane, R. H. Hardin, and Tom Duff). Discrete & Computational Geometry, vol. 14, no. 3, pp. 237–259.
• 1996 – The Book of Numbers (with Richard K. Guy). Copernicus, New York, 1996, {{isbn|0614971667}}.
• 1997 – The Sensual (quadratic) Form (with Francis Yein Chei Fung). Mathematical Association of America, Washington, DC, 1997, Series: Carus mathematical monographs, no. 26, {{isbn|1614440255}}.
• 2002 – On Quaternions and Octonions (with Derek A. Smith). A. K. Peters, Natick, MA, 2002, {{ISBN|1568811349}}.
• 2008 – The Symmetries of Things (with Heidi Burgiel and Chaim Goodman-Strauss). A. K. Peters, Wellesley, MA, 2008, {{ISBN|1568812205}}.

• List of things named after John Horton Conway

{{reflist|refs=

{{cite web |last=Mulcahy |first=Colm |date=21 October 2014 |title=The Top 10 Martin Gardner Scientific American Articles |url=https://blogs.scientificamerican.com/guest-blog/the-top-10-martin-gardner-scientific-american-articles/?redirect=1 |website=Scientific American

}}

}}

• Alpert, Mark (1999). [https://web.archive.org/web/20030427214911/http://www.cpdee.ufmg.br/~seixas/PaginaATR/Download/DownloadFiles/NotJustFunAndGames.PDF Not Just Fun and Games] Scientific American, April 1999
• Boden, Margaret (2006). Mind As Machine, Oxford University Press, 2006, p. 1271
• du Sautoy, Marcus (2008). Symmetry, HarperCollins, p. 308
• Guy, Richard K (1983). [https://www.jstor.org/pss/2690263 Conway's Prime Producing Machine] Mathematics Magazine, Vol. 56, No. 1 (Jan. 1983), pp. 26–33
• {{cite book |last=Roberts |first=Siobhan |date=2015 |title=Genius at play: The curious mind of John Horton Conway |publisher= Bloomsbury |isbn=978-1620405932 }}
• {{MacTutor Biography|id=Conway}}
• {{MathGenealogy|id=18849}}
• Princeton University (2009). [http://www.math.princeton.edu/WebCV/ConwayBIB.pdf Bibliography of John H. Conway] {{Webarchive|url=https://web.archive.org/web/20110927013037/http://www.math.princeton.edu/WebCV/ConwayBIB.pdf |date=27 September 2011 }} Mathematics Department
• Seife, Charles (1994). [http://www.users.cloud9.net/~cgseife/conway.html Impressions of Conway] The Sciences
• Schleicher, Dierk (2011), [https://www.ams.org/notices/201305/rnoti-p567.pdf Interview with John Conway], Notices of the AMS

{{Sister project links| wikt=no | commons=Category:John Horton Conway | b=no | n=English mathematician John Horton Conway dies after contracting COVID-19 | q=John Horton Conway | s=no | v=no | voy=no | species=no | d=no}}

• {{Scopus|id=55322875100}}
• {{cite web |url= https://mediacentral.princeton.edu/media/Proof+of+the+Free+Will+Theorem/1_pvviswj5 |format= Video |title= Proof of the Free Will Theorem |series= Archived Lectures |date= 20 April 2009 |first= John |last= Conway }}
• {{YouTube|p= PLt5AfwLFPxWIL8XA1npoNAHseS-j1y-7V |John Conway. Videos. Numberphile. }}
• {{YouTube|ea7lJkEhytA|Look-and-Say Numbers. Feat John Conway (2014) }}
• {{YouTube|R9Plq-D1gEk|Inventing the Game of Life (2014) }}
• {{YouTube|dVpydmTqfNw|The Princeton Brick (2014) }} Conway leading a tour of brickwork patterns in Princeton, lecturing on the ordinals and on sums of powers and the Bernoulli numbers
• [https://www.quantamagazine.org/john-conway-solved-mathematical-problems-with-his-bare-hands-20200420/ necrology by Keith Hartnett in Quanta Magazine, April 20, 2020]

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