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| | name = John Horton Conway | | {{Person |
| | image = John H Conway 2005 (cropped).jpg | | |name = John Conway |
| | image_size = 250px | | |image = true |
| | birth_date = {{birth date and age|1937|12|26|df=y}}
| | |born = December 26, 1937 |
| | birth_place = Liverpool , Merseyside , England
| | |res = United States |
| | residence = United States | | |nat = British |
| | nationality = UK|British | | |inst = Princeton University |
| | death_date =
| | |alma = University of Cambridge |
| | death_place =
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| | field = Mathematician | |
| | work_institutions = Princeton University
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| | alma_mater = University of Cambridge | |
| | doctoral_advisor = Harold Davenport
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| | doctoral_students = Richard Borcherds <br> Simon P. Norton|Simon Norton <br> Robert Arnott Wilson|Robert Wilson <!-- Robert Curtis , Charles Ferenbaugh , Timothy Hsu , Richard Margolin , Adrian Mathias , William Schneeburger , Christopher Simons , Derek smith mathematician|Derek Smith , Johnathan smith mathematician|Jonathan Smith , Warren smith mathematician|Warren Smith , Leonard Soicher , Frank Swenton , Robert Arnott Wilson|Robert Wilson -->
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| | thesis_title = Homogeneous ordered sets
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| | thesis_year = 1964
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| | known_for = Conway's Game of Life|Game of life ,<!-- group (mathematics)|groups , knot theory , number theory , combinatorial game theory , Doomsday rule and coding theory --> Look-and-say sequence
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| | prizes = Berwick Prize (1971), <br> Pólya Prize (LMS)|Polya Prize (1987), <br> Nemmers Prize in Mathematics (1998), <br> Leroy P. Steele Prize for Mathematical Exposition (2000)
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| | religion = Atheist
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| | Erdős number = 1
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| | footnotes =
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| }} | | }} |
| | '''John Horton Conway''' (born December 26, 1937, Liverpool, England) is a prolific mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He has also contributed to many branches of recreational mathematics, notably the invention of [[Conway's Game of Life|the Game of Life]], and was the leader of the [[JHC group]]. |
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| '''John Horton Conway''' (born 26 December 1937) is a British mathematician active in the theory of finite group s, knot theory , number theory , combinatorial game theory and coding theory . He has also contributed to many branches of recreational mathematics , notably the invention of the cellular automaton called the Conway's Game of Life|Game of Life .
| | Conway is currently professor of mathematics at Princeton University. He studied at Cambridge, where he started research under Harold Davenport. He has an Erdős number of one. He received the Berwick Prize (1971), was elected a Fellow of the Royal Society (1981), and was the first recipient of the Pólya Prize (LMS) (1987). |
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| Conway is currently Professor of Mathematics and John Von Neumann Professor in Applied and Computational Mathematics at Princeton University . He has also begun lecturing at City University of New York|CUNY 's Queens College, City University of New York|Queens College . He studied at University of Cambridge|Cambridge , where he started research under Harold Davenport . He received the Berwick Prizes|Berwick Prize (1971),<ref name="LMS Prizewinners">[http://www.lms.ac.uk/activities/prizes_com/pastwinners.html#berwick LMS Prizewinners]</ref> was elected a Fellow of the Royal Society (1981),<ref>[http://www.royalsoc.ac.uk/page.asp?id=1727 List of Royal Society Fellows]</ref> was the first recipient of the Pólya Prize (LMS) (1987),<ref name="LMS Prizewinners"/> won the Nemmers Prize in Mathematics (1998) and received the Leroy P. Steele Prize for Mathematical Exposition (2000) of the American Mathematical Society. He has an Erdős number of one.<ref>Conway, J. H., Croft, H. T., Erdos, P., & Guy, M. J. T. (1979). On the distribution of values of angles determined by coplanar points. J. London Math. Soc.(2), 19(1), 137–143.</ref>
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| ==Biography== | | ==Biography== |
| Conway's parents were Agnes Boyce and Cyril Horton Conway. He was born in Liverpool .<ref>{{cite web |url=http://www.nndb.com/people/680/000082434/ |title=John Conway |publisher=www.nndb.com |accessdate=2010-08-10 }}</ref> He became interested in mathematics at a very early age and his mother recalled that he could recite the powers of two when he was four years old. At the age of eleven his ambition was to become a mathematician. | | Conway's parents were Agnes Boyce and Cyril Horton Conway. John had two older sisters, Sylvia and Joan. Cyril Conway was a chemistry laboratory assistant. John became interested in mathematics at a very early age and his mother Agnes recalled that he could recite the powers of two when aged four years. John's young years were difficult for he grew up in Britain at a time of wartime shortages. At primary school John was outstanding and he topped almost every class. At the age of eleven his ambition was to become a mathematician. |
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| After leaving secondary school, Conway entered Gonville and Caius College, Cambridge to study mathematics. He was awarded his BA in 1959 and began to undertake research in number theory supervised by Harold Davenport . Having solved the open problem posed by Davenport on Waring's problem|writing numbers as the sums of fifth powers , Conway began to become interested in infinite ordinals. It appears that his interest in games began during his years studying at Cambridge, where he became an avid backgammon player, spending hours playing the game in the common room. He was awarded his doctorate in 1964 and was appointed as College Fellow and Lecturer in Mathematics at the University of Cambridge . | | After leaving secondary school, Conway entered Gonville and Caius College, Cambridge to study mathematics. He was awarded his BA in 1959 and began to undertake research in number theory supervised by Harold Davenport. Having solved the open problem posed by Davenport on writing numbers as the sums of fifth powers, Conway began to become interested in infinite ordinals. It appears that his interest in games began during his years studying at Cambridge, where he became an avid backgammon player spending hours playing the game in the common room. He was awarded his doctorate in 1964 and was appointed as Lecturer in Study at the University of Cambridge. He left Cambridge in 1986 to take up the appointment to the John von Neumann Chair of Mathematics at Princeton University. |
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| He left Cambridge in 1986 to take up the appointment to the John von Neumann Chair of Mathematics at Princeton University .
| | Conway resides in Princeton, New Jersey, United States with his wife and youngest son. He has six other children from his two previous marriages, three grandchildren, and two great-grandchildren. |
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| Conway resides in Princeton, New Jersey . He has seven children by various marriages, three grandchildren and four great-grand children. He has been married three times; his first wife was Eileen, and his second wife was Larissa. He has been married to his third wife, Diana, since 2001.<ref>{{cite web |url=http://www-history.mcs.st-andrews.ac.uk/Biographies/Conway.html |title=John Horton Conway Biography}}</ref> | | ==Contributions to Life== |
| | Conway is the inventor of [[Conway's Game of Life]], one of the earliest-studied and most well-known examples of a [[cellular automaton]]. He discovered many of its most fundamental and important patterns, including [[blinker]], [[block]], [[lightweight spaceship]], [[pulsar]], and [[R-pentomino]]. He was the first person to enumerate all [[still life]]s with 7 or fewer [[cell]]s. |
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| ==Achievements== | | ==Books== |
| | | He has (co-)written several books, including ''[[Winning Ways for Your Mathematical Plays]]'' with [[Richard K. Guy]] and [[Elwyn Berlekamp]]. |
| ===Combinatorial game theory===
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| File:Gospers glider gun.gif|thumb|right|A single Bill Gosper|Gosper 's Gun (cellular automaton)|Glider Gun creating " Glider (Conway's Life)|gliders " in Conway's Game of Life
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| Among amateur mathematicians, he is perhaps most widely known for his contributions to combinatorial game theory (CGT), a theory of partisan game s. This he developed with Elwyn Berlekamp and Richard K. Guy|Richard Guy , and with them also co-authored the book '' Winning Ways for your Mathematical Plays ''. He also wrote the book '' On Numbers and Games '' (''ONAG'') which lays out the mathematical foundations of CGT.
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| He is also one of the inventors of Sprouts (game)|sprouts , as well as phutball|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.
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| 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 novel by Donald Knuth . He also invented a nomenclature for exceedingly large number s, the Conway chained arrow notation . Much of this is discussed in the 0th part of ''ONAG''.
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| He is also known for the invention of Conway's Game of Life , one of the early and still celebrated examples of a cellular automaton . His early experiments in that field were done with pen and paper, long before personal computers existed.
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| ===Geometry===
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| In the mid-1960s with Michael Guy (computer scientist)|Michael Guy , son of Richard K. Guy|Richard Guy , he established that there are sixty-four uniform polychoron|convex uniform polychora excluding two infinite sets of prismatic forms. They discovered the grand antiprism in the process, the only non-Wythoffian uniform polychoron . Conway has also suggested a system of notation dedicated to describing polyhedra called Conway polyhedron notation .
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| He extensively investigated lattices in higher dimensions, and determined the symmetry group of the Leech lattice .
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| ===Geometric topology===
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| Conway's approach to computing the Alexander polynomial of knot theory involved skein relation s, by a variant now called the Alexander-Conway polynomial. After lying dormant for more than a decade, this concept became central to work in the 1980s on the novel knot polynomial s. Conway further developed tangle theory and invented a system of notation for tabulating knots, nowadays known as Conway notation (knot theory)|Conway notation , while completing the knot tables up to 10 crossings.
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| ===Group theory===
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| He worked on the classification of finite simple groups and discovered the Conway group s. He was the primary author of the '' ATLAS of Finite Groups '' giving properties of many finite simple group s. He, along with collaborators, constructed the first concrete representations of some of the sporadic group s. More specifically, he discovered three sporadic groups based on the symmetry of the Leech lattice , which have been designated the Conway groups.
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| With Simon P. Norton he formulated the complex of conjectures relating the monster group with modular function s, which was named monstrous moonshine by them.
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| He introduced the Mathieu groupoid , an extension of the Mathieu group M<sub>12</sub> to 13 points.
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| ===Number theory===
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| As a graduate student, he proved the Waring's problem|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 the work could be published.<ref>[http://www.ems-ph.org/journals/newsletter/pdf/2005-09-57.pdf#page=34 Breakfast with John Horton Conway]</ref>
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| ===Algebra===
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| He has also done work in algebra, particularly with quaternion s. Together with Neil Sloane|Neil James Alexander Sloane , he invented the system of icosians|icosian .<ref>[http://math.ucr.edu/home/baez/week20.html This Week's Finds in Mathematical Physics (Week 20)]</ref>
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| ===Algorithmics=== | | {{PatternsFoundBy|name=John Conway}} |
| 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 can usually give the correct answer in under two seconds. To improve his speed, he practices his calendrical calculations on his computer, which is programmed to quiz him with random dates every time he logs on. One of his early books was on finite state machine s.
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| ===Theoretical physics=== | | ==References== |
| In 2004, Conway and Simon B. Kochen , another Princeton mathematician, proved the Free will theorem , a startling version of the Hidden variable theory|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 in order to make the measurements consistent with physical law. In Conway's provocative wording: "if experimenters have free will , then so do elementary particles."
| | *{{cite web|url=http://codercontest.com/mniemiec/lifecred.htm#conway|publisher=Mark D. Niemiec |title=Life Credits |accessdate=May 5, 2009}} |
| | *[http://www.royalsoc.ac.uk/page.asp?id=1727 List of Royal Society Fellows] |
| | *[http://www.lms.ac.uk/activities/prizes_com/pastwinners.html#berwick LMS Prizewinners] |
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| ==Books== | | ==External links== |
| He has (co-)written several books including the '' ATLAS of Finite Groups '', ''Regular Algebra and Finite Machines'', ''Sphere Packings, Lattices and Groups'', ''The Sensual (Quadratic) Form'', '' On Numbers and Games '', '' Winning Ways for your Mathematical Plays '', ''The Book of Numbers'', ''On Quaternions and Octonions'', ''The Triangle Book'' (written with Steve Sigur)<ref>http://www.goodreads.com/book/show/1391661.The_Triangle_Book</ref> and in summer 2008 published ''The Symmetries of Things'' with Chaim Goodman-Strauss and Heidi Burgiel.
| | * Charles Seife, [http://www.users.cloud9.net/~cgseife/conway.html "Impressions of Conway"], The Sciences |
| | * Mark Alpert, "Not Just Fun and Games", ''Scientific American'' April 1999. ([http://www.sciam.com/article.cfm?articleID=0000FFD8-61FF-1C70-84A9809EC588EF21&catID=2 official online version]; [http://www.cpdee.ufmg.br/~seixas/PaginaATR/Download/DownloadFiles/NotJustFunAndGames.PDF registration-free online version]) |
| | {{LinkWikipedia|John_Horton_Conway|name=John Horton Conway}} |
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| | | {{DEFAULTSORT:Conway, John}} |
| ==Contributions to Life==
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| Conway is the inventor of [[Conway's Game of Life]], one of the earliest-studied and most well-known examples of a [[cellular automaton]]. He discovered many of its most fundamental and important patterns, including [[blinker]], [[block]], [[lightweight spaceship]], [[pulsar]], and [[R-pentomino]]. He was the first person to enumerate all [[still life]]s with 7 or fewer [[cell]]s. | |
John Conway
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Born
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December 26, 1937
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Residence
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United States
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Nationality
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British
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Institutions
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Princeton University
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Alma mater
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University of Cambridge
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John Horton Conway (born December 26, 1937, Liverpool, England) is a prolific mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He has also contributed to many branches of recreational mathematics, notably the invention of the Game of Life, and was the leader of the JHC group.
Conway is currently professor of mathematics at Princeton University. He studied at Cambridge, where he started research under Harold Davenport. He has an Erdős number of one. He received the Berwick Prize (1971), was elected a Fellow of the Royal Society (1981), and was the first recipient of the Pólya Prize (LMS) (1987).
Biography
Conway's parents were Agnes Boyce and Cyril Horton Conway. John had two older sisters, Sylvia and Joan. Cyril Conway was a chemistry laboratory assistant. John became interested in mathematics at a very early age and his mother Agnes recalled that he could recite the powers of two when aged four years. John's young years were difficult for he grew up in Britain at a time of wartime shortages. At primary school John was outstanding and he topped almost every class. At the age of eleven his ambition was to become a mathematician.
After leaving secondary school, Conway entered Gonville and Caius College, Cambridge to study mathematics. He was awarded his BA in 1959 and began to undertake research in number theory supervised by Harold Davenport. Having solved the open problem posed by Davenport on writing numbers as the sums of fifth powers, Conway began to become interested in infinite ordinals. It appears that his interest in games began during his years studying at Cambridge, where he became an avid backgammon player spending hours playing the game in the common room. He was awarded his doctorate in 1964 and was appointed as Lecturer in Study at the University of Cambridge. He left Cambridge in 1986 to take up the appointment to the John von Neumann Chair of Mathematics at Princeton University.
Conway resides in Princeton, New Jersey, United States with his wife and youngest son. He has six other children from his two previous marriages, three grandchildren, and two great-grandchildren.
Contributions to Life
Conway is the inventor of Conway's Game of Life, one of the earliest-studied and most well-known examples of a cellular automaton. He discovered many of its most fundamental and important patterns, including blinker, block, lightweight spaceship, pulsar, and R-pentomino. He was the first person to enumerate all still lifes with 7 or fewer cells.
Books
He has (co-)written several books, including Winning Ways for Your Mathematical Plays with Richard K. Guy and Elwyn Berlekamp.
Patterns found by John Conway
References
External links