Difference between revisions of "John Conway"

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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 =
| field = Mathematician 
| work_institutions = Princeton University
| alma_mater = University of Cambridge
| doctoral_advisor =  Harold Davenport 
| 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 -->
| thesis_title = Homogeneous ordered sets
| thesis_year = 1964
| 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
| 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)
| religion =  Atheist
|  Erdős number  = 1
| footnotes =
}}
}}
'''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]].


'''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).
 
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>


==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.


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.


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.


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.


==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===
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 
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.
 
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.
 
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''.
 
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.
 
===Geometry===
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 .
 
He extensively investigated lattices in higher dimensions, and determined the symmetry group of the  Leech lattice .
 
===Geometric topology===
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.
 
===Group theory===
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.
 
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.
 
He introduced the  Mathieu groupoid , an extension of the  Mathieu group  M<sub>12</sub> to 13 points.
 
===Number theory===
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>
 
===Algebra===
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>


===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.


===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]


==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&amp;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}}


 
{{DEFAULTSORT:Conway, John}}
==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.

Revision as of 18:26, 14 March 2018

John Conway
John Conway
Born December 26, 1937
Residence United States
Nationality British
Institutions Princeton University
Alma mater University of Cambridge

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