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约翰·何顿·康威 John Horton Conway (查看源代码)

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The Game of Life is now known to be [[Turing completeness|Turing complete]].<ref>Rendell (2015)</ref><ref name=case>Case (2014)</ref>
 
The Game of Life is now known to be [[Turing completeness|Turing complete]].<ref>Rendell (2015)</ref><ref name=case>Case (2014)</ref>
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==Conway and Martin Gardner==
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== 主要研究领域 ==
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Conway's career is intertwined with that of mathematics popularizer and ''[[Scientific American]]'' columnist [[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.<ref>''[https://www.bbc.com/news/magazine-29688355 Martin Gardner, puzzle master extraordinaire]'' by [[Colm Mulcahy]], [[BBC News Magazine]], 21 October 2014: "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."</ref><ref name=topten>Mulcahy (2014).</ref> 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.<ref>[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.</ref> For instance, he discussed Conway's game of [[Sprouts (game)|Sprouts]] (Jul 1967), [[Hackenbush]] (Jan 1972), and his [[Angel problem|angel and devil problem]] (Feb 1974). In the September 1976 column he reviewed Conway's book ''[[On Numbers and Games]]'' and even managed to explain Conway's [[surreal numbers]].<ref>Martin Gardner, ''Penrose Tiles to Trapdoor Ciphers'', W. H. Freeman & Co., 1989, {{ISBN|0-7167-1987-8}}, Chapter 4. A non-technical overview; reprint of the 1976 Scientific American article.</ref>
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=== 组合博弈论 ===
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康威因其对组合博弈论(CGT)的贡献而广为人知，这是一种党派博弈理论。他与 Elwyn Berlekamp 和 Richard Guy 共同发展了这一理论，并与他们合著了《数学游戏的制胜之道(Winning Ways for your Mathematical Plays)》一书。他还写了CGT 的数学奠基之作——《关于数字和游戏(On Numbers and Games)》(ONAG)。
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Conway was probably the most important member of[[Martin_Gardner#Martin_Gardner's_Mathematical_Grapevine| Martin Gardner's Mathematical Grapevine]]. He regularly visited Gardner and often wrote him long letters summarizing his recreational research.  In a 1976 visit Gardner pretty much held him prisoner for a week, pumping him for information on the [[Penrose tiling]]s which had just been announced.  Conway had discovered many (if not most) of the major properties of the tilings.<ref>''[http://www.ams.org/notices/200506/fea-gardner.pdf Interview with Martin Gardner]'' [[Notices of the AMS]], Vol. 52, No. 6, June/July 2005, pp. 602–611</ref> Gardner used these results when he introduced the world to Penrose tiles in his January 1977 column.<ref>[https://www.quantamagazine.org/john-conways-life-in-games-20150828/ A Life In Games: The Playful Genius of John Conway] by [[Siobhan Roberts]], [[Quanta Magazine]], August 28, 2015</ref> The cover of that issue of Scientific American features the Penrose tiles and is based on a sketch by Conway.<ref name=topten/>
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他还是豆芽游戏(sprouts)和哲球棋(Phutball)的发明者之一。他给出了索马立方(Soma cube)、孔明棋(Peg solitaire)、康威的士兵(Conway's Soldiers)等许多其他游戏和谜题的详细分析。他提出了天使问题(angel problem)，该问题在2006年已获解答。
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Conferences called [[Gathering 4 Gardner]] are held every two years to celebrate the legacy of Martin Gardner, and Conway himself has often been a featured speaker at these events, discussing various aspects of recreational mathematics.<ref>[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 Gardner</ref><ref name= bellos>Bellos, Alex (2008). ''[https://www.theguardian.com/science/2008/may/31/maths.science The science of fun]'' The Guardian, 30 May 2008</ref>
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他创立了一种新的数字系统——超现实数(surreal numbers)，这些数字与某些游戏密切相关，并成为唐纳德·克努斯(Donald Knuth)的数学中篇小说的主题。他还为大数发明了一种表示方法——康威链式箭号表示法(Conway chained arrow notation)，这个方法可以表示连高德纳箭号表示法都难以表示的数。
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=== 几何学 ===
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在20世纪60年代中期，康威与迈克尔·盖伊(Michael Guy)建立了64个[https://en.wikipedia.org/wiki/Uniform_polychoron 凸均匀多面体(convex uniform polychora)]，其中不包括两个棱形无穷集。 他们在这个过程中发现了巨大的[https://en.wikipedia.org/wiki/Grand_antiprism 反棱镜]，这是唯一的非维索菲安式均匀多面体([https://en.wikipedia.org/wiki/Non-Wythoffian non-Wythoffian] uniform polychoron)。此外，康威创立了一个用于描述多面体的符号系统，称为康威多面体表示法(Conway polyhedron notation)。
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康威提出了一种密铺数学理论——康威准则(Conway criterion)，描述多边形可用来做平面镶嵌的条件。
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他研究了更高维度的晶格，并首次确定了利奇格(Leech lattice，24维欧几里得空间的一种双幺模晶格)的对称群。
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=== 几何拓扑学 ===
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在纽结理论中，康威对亚历山大多项式(Alexander polynomial)的一个版本进行公式化，并产生了一个新的不变量——康威多项式(Conway polynomial)。在沉寂了十多年之后，这个概念在20世纪80年代成为新纽结多项式(knot polynomials)的核心。康威进一步发展了缠结理论(tangle theory)，并发明了一种描述纽结的符号系统——康威符号(Conway notation)。
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=== 群论 ===
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康威是给出许多有限简单群(finite simple groups)的性质的《有限群的阿特拉斯(ATLAS of Finite Groups)》的第一作者。他与同事罗伯特·柯蒂斯(Robert Curtis )和西蒙 · p·诺顿(Simon P. Norton)一起构建了一些散在群(sporadic groups)的第一个具体表述。具体来说，他根据利奇格(Leech lattice)的对称性发现了三个散在群，它们被命名为康威群(Conway groups)。这项工作使他成为有限单群分类的关键人物。
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1979年，康威和西蒙·诺顿(Simon P. Norton)提出怪兽月光理论(monstrous moonshine)，表达了怪兽群(monster group)和模函数(modular functions)间的惊人关系，这一理论沟通了原本分立的有限群理论和复函数理论。怪兽月光理论现已经被发现与弦理论有着深刻的联系。
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康威引入了Mathieu groupoid，它是马蒂厄群M<sub>12</sub>(Mathieu group M<sub>12</sub>)扩展到13点而来。
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=== 数论 ===
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康威研究生时证明了爱德华·华林(Edward Waring)的一个猜想，即每个整数都可以写成37个数字的的五次方之和。（陈景润在康威的著作出版之前独立地解决了这个问题。）
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=== 代数 ===
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代数方面，康威写过教科书，做过尤其是四元数(quaternions)和八元数(octonions)方面的原创性工作。他和尼尔·斯隆(Neil Sloane)一起发明了[https://en.wikipedia.org/wiki/Icosian icosian]。
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=== 分析 ===
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康威给出介值定理(intermediate value theorem)逆命题的一个反例——康威十三进制函数: 满足强达布性质(Darboux property)，但不是连续的。
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=== 算法 ===
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为了某天是星期几，康威发明了末日规则(Doomsday rule)。这个算法非常简单，任何一个有基本算术能力的人都可以心算得出答案。康威通常能在两秒钟内给出正确答案。
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=== 理论物理学 ===
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2004年，康威和另一位普林斯顿的数学家西蒙(Simon B. Kochen)证明了自由意志定理(free will theorem)，这是量子力学的无隐变量(no hidden variables)原理一个惊人版本。它指出，在某些条件下，如果实验者可以自由决定在特定实验中测量什么量，那么基本粒子必须能够自由选择其自旋，以使测量结果与物理定律一致。康威挑衅性的措辞是: “如果实验者有自由意志，那么基本粒子也有。”
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== 荣誉奖项 ==
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* 贝里克奖(Berwick Prize)，1971年
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* 皇家学会院士(FRS)，1981年
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* [https://en.wikipedia.org/wiki/P%C3%B3lya_Prize_(LMS) Pólya Prize(LMS]，伦敦数学学会)首位获奖者，1987年
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* 内默斯数学奖(Nemmers Prize in Mathematics)，1998年
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* 美国数学学会2000年数学博览会勒罗伊·P·斯蒂尔奖(Leroy P. Steele Prize)
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* 英国数学协会荣誉会员，2017年
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== 博士生导师 ==
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哈罗德·达文波特 Harold Davenport
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== 学生 ==
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理查德·博赫兹 Richard Borcherds
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罗伯特·威尔逊 Robert Wilson
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== 就职企业、机构或院校 ==
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应用与计算数学约翰·冯·诺伊曼教授(John von Neumann Professor)，荣誉退休
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== 著作 ==
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* Regular Algebra and Finite Machines, Chapman and Hall, Ltd. London, 1971.
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* All Numbers Great and Small, Research Paper No. 149, Calgary, Alberta, Canada: The University of Calgary, Dept. of Mathematics and Statistics, 1972.
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* All Games Bright and Beautiful, Research Paper No. 295, Calgary, Alberta, Canada: The University of Calgary, Dept. of Mathematics and Statistics, 1975.
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* On Numbers and Games, London Mathematical Society Monographs, No. 6, Academic Press, London-New-San Francisco, 1976.
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* (with E.R. Berlekamp and R.K. Guy), Winning Ways, for Your Mathematical Plays, Vol. 1: Games in General, Vol. 2: Games in Particular, New York-London: Academic Press, 1982, ISBN 0120911027, Paperback (August, 1982), Academic Press, ISBN 0120911027.
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* (with R.T. Curtis, S.P. Norton, R.A. Parker and R.A. Wilson), Atlas of Finite Groups: Maximal Subgroups and Ordinary Characters for Simple Groups, Oxford, Clarendon Press, New York, Oxford University Press, 1985.
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* (with N.J.A. Sloane), Sphere Packings, Lattices, and Groups, (with additional contributions by E. Bannai, J. Leech, S.P. Norton, A.M. Odlyzko, R.A. Parker, L. Queen and B.B. Venkov), Grundlehren der Mathematischen Wissenschaften, 209, Springer-Verlag, New York, 1988, ISBN 0-387-96617-X, Russian Translation: Mir, Moscow, 1990, 2nd edition 1993, ISBN 0-387-97912-3, 3rd edition 1998, ISBN 0-387-98585-9.
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* (with R.K. Guy), The Book of Numbers, Copernicus. An Imprint of SpringerVerlag, New York, 1996, ISBN 0-387-97993-X, Review by Ian Stewart. Review by Susan Stefney, Corrected 2nd printing, 1998.
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* (with Francis Y.C. Fung), The Sensual (Quadratic) Form, MAA (Series: Carus Mathematical Monographs), Printed in the U.S.A., 1997, ISBN 0-88385-030-3.
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* (with N.J.A. Sloane), The Geometry of Low-Dimensional Groups and Lattices, (in preparation).
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* (with D. Smith), “Quaternions, Octonions, and Geometry,” AK Peters, Publishers, January 2003. preparation).
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更多论文点击[https://www.math.princeton.edu/sites/default/files/2017-03/ConwayBIB1.pdf John H. Conway Bibliography]
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== 人物介绍和报道 ==
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* [https://www.quantamagazine.org/john-conways-life-in-games-20150828/ A Life in Games]：约翰·何顿·康威声称他一生中从未有一天是在工作。 此文根据传记《游戏中的天才(Genius at Play)》改编，展示了诸如超现实数(surreal numbers)之类的重大突破是如何从娱乐和游戏中产生的。《量子杂志(Quanta Magazine)》，西沃恩·罗伯茨(Siobhan Roberts)
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* [https://dof.princeton.edu/about/clerk-faculty/emeritus/john-horton-conway John Horton Conway] Dean of the Faculty, Princeton University
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== 相关链接 ==
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=== 视频 ===
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* [http://www.math.princeton.edu/facultypapers/Conway/ Lecture Videos]：讲座录像
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* [https://www.youtube.com/playlist?list=PLt5AfwLFPxWIL8XA1npoNAHseS-j1y-7V John Conway. Videos. Numberphile]：约翰·康威：数字狂
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=== 更多信息 ===
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[https://en.wikipedia.org/wiki/John_Horton_Conway wiki词条]
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[https://baike.baidu.com/item/%E7%BA%A6%E7%BF%B0%C2%B7%E4%BD%95%E9%A1%BF%C2%B7%E5%BA%B7%E5%A8%81/8748231?fr=aladdin 百度词条]
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[https://www.math.princeton.edu/sites/default/files/2017-03/ConwayCV.pdf CV]
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[https://www.math.princeton.edu/people/john-conway 普林斯顿大学数学系个人主页]
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[[Category:元胞自动机]] 
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[[Category:人物]]
    
==Major areas of research==
 
==Major areas of research==
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