- John Horton Conway
name = John Horton Conway
image_width = 300px
birth_date = birth date and age|1937|12|26|mf=y
Liverpool, Merseyside, England
residence = U.S.
nationality = English
University of Cambridge
Richard BorcherdsRobert Wilson
known_for = Game of life ,
prizes = Polya Prize (1987),
Nemmers Prize in Mathematics(1998)
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 theoryand coding theory. He has also contributed to many branches of recreational mathematics, notably the invention of the Game of Life (the cellular automaton, not the board game).
Conway is currently professor of mathematics at
Princeton University. He studied at Cambridge, where he started research under Harold Davenport. He has an Erdős numberof one. He received the Berwick Prize (1971) [ [http://www.lms.ac.uk/activities/prizes_com/pastwinners.html#berwick LMS Prizewinners] ] , was elected a Fellow of the Royal Society(1981) [ [http://www.royalsoc.ac.uk/page.asp?id=1727 List of Royal Society Fellows] ] , and was the first recipient of the Pólya Prize (LMS)(1987). [ [http://www.lms.ac.uk/activities/prizes_com/pastwinners.html#berwick LMS Prizewinners] ]
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, Cambridgeto 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 NeumannChair of Mathematics at Princeton University. He is also a regular visitor at Mathcampand MathPath[http://www.mathpath.org] , summer math programs for high schoolers and middle schoolers, respectively.
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.Fact confirmed by wife.
Among amateur mathematicians, he is perhaps most widely known for his contributions to
combinatorial game theory, a theory of partisan games. This he developed with Elwyn Berlekampand Richard Guy.
He is also one of the inventors of 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 novel by Donald Knuth. He also invented a nomenclature for exceedingly large numbers, the Conway chained arrow notation.
He is also known for the invention of the Game of Life, one of the early and still celebrated examples of a
In the mid-1960s with Michael Guy, son of
Richard Guy, he established that there are sixty-four convex uniform polychora excluding two infinite sets of prismatic forms. Conway has also suggested a system of notation dedicated to describing polyhedracalled Conway polyhedron notation.
Conway's approach to computing the
Alexander polynomialof knot theory involved skein relations, 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 polynomials. Conway further developed tangle theoryand invented a system of notation for tabulating knots, while completing the knot tables up to 10 crossings.
He worked on the
classification of finite simple groupsand discovered the Conway groups. He was the primary author of the "Atlas of Finite Groups" giving properties of many finite simple groups. He with collaborators constructed the first concrete representations of some of the sporadic groups.
Simon Nortonhe formulated the complex of conjectures relating the monster groupwith modular functions, which was christened monstrous moonshineby them.
He proved the conjecture by
Edward Waringthat every integer could be written as the sum of 37 numbers, each raised to the fifth power.
He has also done work in algebra particularly with
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 machines.
In 2004, Conway and
Simon Kochen, another Princeton mathematician, proved the Free will theorem, a startling 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 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".
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", and "On Quaternions and Octonions". He is currently finishing "The Triangle Book" written with the late Steve Sigur, math teacher at Paideia School in Atlanta Georgia, and in summer 2008 published"The Symmetries of Things" with Chaim Goodman-Straussand Heidi Burgiel.
Conway polyhedron notation
Conway's LUX method for magic squares
Conway chained arrow notation
Conway's Game of Life
Conway's thrackle conjecture
Conway base 13 function
References and external links
* by O'Connor and Robertson
* 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] )
* Jasvir Nagra, "Conway's Proof Of The Free Will Theorem" [http://www.cs.auckland.ac.nz/~jas/one/freewill-theorem.html]
* Conway, J. H.; Curtis, R. T.; Norton, S. P.; Parker, R. A.; and Wilson, R. A.: "Atlas of Finite Groups: Maximal Subgroups and Ordinary Characters for Simple Groups." Oxford, England 1985.
* [http://www.math.dartmouth.edu/~doyle/docs/conway/conway Video] of Conway leading a tour of brickwork patterns in Princeton, lecturing on the ordinals, and lecturing on sums of powers and Bernoulli numbers.
* [http://www.adeptis.ru/vinci/m_part3_3.html Photos of John Horton Conway]
* "The Triangle Book", [http://www.amazon.com/dp/1568811659]
* John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, "The Symmetry of Things" 2008, ISBN 978-1-56881-220-5 [http://www.akpeters.com/product.asp?ProdCode=2205]
Margaret Boden, Mind As Machine, Oxford University Press, 2006, p. 1271
Marcus du Sautoy, Symmetry, HarperCollins, 2008, p.308
NAME= Conway, John Horton
DATE OF BIRTH= birth date|1937|12|26|mf=y
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