1,526
个编辑
更改
跳到导航
跳到搜索
第325行：
第325行： − == 相关链接 == − 第341行：
第339行： + + + + + − − ==Major areas of research== − − ===Combinatorial game theory=== − Conway is 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 novelette by [[Donald Knuth]].<ref>[http://discovermagazine.com/1995/dec/infinityplusonea599 Infinity Plus One, and Other Surreal Numbers] by Polly Shulman, [[Discover Magazine]], 1 December 1995</ref> 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''. − − ===Geometry=== − In the mid-1960s with [[Michael Guy (computer scientist)|Michael Guy]], Conway 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]]. − − In the theory of tessellations, he devised the [[Conway criterion]] which describes rules for deciding if a prototile will tile the plane.<ref name=rhoads>{{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 }}</ref> − − He investigated lattices in higher dimensions, and was the first to determine the symmetry group of the [[Leech lattice]]. − − ===Geometric topology=== − In knot theory, Conway formulated a new variation of the [[Alexander polynomial]] and produced a new invariant now called the Conway polynomial.<ref>[http://mathworld.wolfram.com/ConwayPolynomial.html Conway Polynomial] [[Wolfram MathWorld]]</ref> After lying dormant for more than a decade, this concept became central to work in the 1980s on the novel [[knot polynomial]]s.<ref>Livingston, Charles, Knot Theory (MAA Textbooks), 1993, {{ISBN|0883850273}}</ref> Conway further developed [[tangle theory]] and invented a system of notation for tabulating knots, nowadays known as [[Conway notation (knot theory)|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. See Topology Proceedings 7 (1982) 118. − − ===Group theory=== − He was the primary author of the ''[[ATLAS of Finite Groups]]'' giving properties of many [[finite simple group]]s. Working with his colleagues Robert Curtis and [[Simon P. Norton]] he 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]].<ref name=harris>Harris (2015)</ref> 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 (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 function]]s, thus bridging two previously distinct areas of mathematics–[[finite group]]s and [[complex function theory]]. Monstrous moonshine theory has now been revealed to also have deep connections to [[string theory]].<ref>[http://www.daviddarling.info/encyclopedia/M/Monstrous_Moonshine_conjecture.html Monstrous Moonshine conjecture] David Darling: Encyclopedia of Science</ref> − − Conway introduced the [[Mathieu groupoid]], an extension of the [[Mathieu group M12|Mathieu group M<sub>12</sub>]] to 13 points. − − ===Number theory=== − As a graduate student, he proved one case of a [[Waring's problem|conjecture]] by [[Edward Waring]], that in which 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.<ref>[http://www.ems-ph.org/journals/newsletter/pdf/2005-09-57.pdf#page=34 Breakfast with John Horton Conway]</ref> − − ===Algebra=== − Conway has written textbooks and done original work in algebra, focusing particularly on [[quaternion]]s and [[octonion]]s.<ref>Conway and Smith (2003): "Conway and Smith's book is a wonderful introduction to the normed division algebras: the real numbers, the complex numbers, the quaternions, and the octonions."</ref> Together with [[Neil Sloane]], he invented the [[icosians]].<ref>{{cite web| url=http://math.ucr.edu/home/baez/week20.html| title=This Week's Finds in Mathematical Physics (Week 20)| author=John Baez| date=2 October 1993}}</ref> − − ===Analysis=== − He invented a [[Conway base 13 function|base 13 function]] as a counterexample to the [[converse (logic)|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 function|continuous]]. − − ===Algorithmics=== − 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=== − 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 to make the measurements consistent with physical law. In Conway's provocative wording: "if experimenters have [[free will]], then so do elementary particles."<ref>''[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/20100516002546/http://www.cs.auckland.ac.nz/~jas/one/freewill-theorem.html |date=16 May 2010 }}'' by Jasvir Nagra</ref> − − ==Awards and honours== − Conway received the [[Berwick Prizes|Berwick Prize]] (1971),<ref name="LMS Prizewinners"> − [https://www.lms.ac.uk/prizes/list-lms-prize-winners London Mathematical Society Prizewinners]</ref> was elected a [[Fellow of the Royal Society]] (1981),<ref name=royal/> 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]]. − His nomination, in 1981, reads: {{quote|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).<ref name=royal/>}} − − In 2017 Conway was given honorary membership of the British [[Mathematical Association]].<ref>{{Cite web|url=https://www.m-a.org.uk/honorary-members|title=Honorary Members|last=|first=|date=|website=The Mathematical Association|url-status=live|archive-url=|archive-date=|access-date=April 11, 2020}}</ref> − − ==Publications== − * 2008 ''The Symmetries of Things'' (with Heidi Burgiel and [[Chaim Goodman-Strauss]]). [[A. K. Peters]], Wellesley, MA, 2008, {{ISBN|1568812205}}. − * 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}}. − * 1996 ''The Book of Numbers'' (with [[Richard K. Guy]]). [[Copernicus Publications|Copernicus]], New York, 1996, {{isbn|0614971667}}. − * 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. − * 1988 ''Sphere Packings, Lattices, and Groups''<ref>{{cite journal |last=Guy |first=Richard K.|authorlink=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 (N.S.) |year=1989 |volume=21|issue=1|pages=142–147|url=http://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 }}</ref> (with [[Neil Sloane]]). [[Springer-Verlag]], New York, Series: Grundlehren der mathematischen Wissenschaften, 290, {{isbn|9780387966175}}. − * 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}}. − * 1982 ''[[Winning Ways for your Mathematical Plays]]'' (with [[Richard K. Guy]] and [[Elwyn Berlekamp]]). [[Academic Press]], {{isbn|0120911507}}. − * 1979 ''Monstrous Moonshine'' (with [[Simon P. Norton]]).<ref>http://blms.oxfordjournals.org/content/11/3/308</ref> [[Bulletin of the London Mathematical Society]], vol. 11, issue 2, pp. 308–339. − * 1979 ''On the Distribution of Values of Angles Determined by Coplanar Points'' (with [[Paul Erdős]], [[Michael Guy]], and H. T. Croft). [[London Mathematical Society|Journal of the London Mathematical Society]], vol. II, series 19, pp. 137–143. − * 1976 ''[[On numbers and games]]''. [[Academic Press]], New York, 1976, Series: L.M.S. monographs, 6, {{isbn|0121863506}}. − * 1971 ''Regular algebra and finite machines''. [[Chapman and Hall]], London, 1971, Series: Chapman and Hall mathematics series, {{isbn|0412106205}}. − − ==See also== − * [[List of things named after John Horton Conway]] − − ==References== − {{reflist|30em}} − − ==Sources== − * 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 − * Conway, John and Smith, Derek A. (2003). ''[http://math.ucr.edu/home/baez/octonions/conway_smith/ On quaternions and Octonions : their Geometry, Arithmetic, and Symmetry]'' Bull. Amer. Math. Soc. 2005, vol=42, issue=2, pp. 229–243, {{ISBN|1568811349}} − * [[Margaret Boden|Boden, Margaret]] (2006). ''Mind As Machine'', Oxford University Press, 2006, p. 1271 − * Case, James (2014). ''[https://sinews.siam.org/Details-Page/martin-gardners-mathematical-grapevine Martin Gardner’s Mathematical Grapevine]'' Book Reviews of ''Undiluted Hocus-Pocus: The Autobiography of Martin Gardner'' and ''Martin Gardner in the Twenty-First Century'', By James Case, [[Society for Industrial and Applied Mathematics|SIAM]] News, April 01, 2014 − * Conway, John and Sigur, Steve (2005). ''[https://openlibrary.org/books/OL12190669M/The_Triangle_Book The Triangle Book]'' AK Peters, Ltd, 15 June 2005, {{isbn|1568811659}} − * [[Marcus du Sautoy|du Sautoy, Marcus]] (2008). ''Symmetry'', HarperCollins, p. 308 − * [[Richard K. Guy|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 − * [[Michael Harris (mathematician)|Harris, Michael]] (2015). [http://www.nature.com/nature/journal/v523/n7561/full/523406a.html Review of ''Genius At Play: The Curious Mind of John Horton Conway''] ''[[Nature (journal)|Nature]]'', 23 July 2015 − * Mulcahy, Colm (2014). ''[https://blogs.scientificamerican.com/guest-blog/the-top-10-martin-gardner-scientific-american-articles/?redirect=1 The Top 10 Martin Gardner Scientific American Articles]'' Scientific American, October 21, 2014 − * {{cite book |last=Roberts |first=Siobhan |date=2015 |title=Genius at play: The curious mind of John Horton Conway |url= |location= |publisher= Bloomsbury |page= |isbn=978-1620405932 |author-link= }} − * {{MacTutor Biography|id=Conway}} − * {{MathGenealogy|id=18849}} − * Princeton University (2009). [http://www.math.princeton.edu/WebCV/ConwayBIB.pdf Bibliography of John H. Conway] Mathematics Department − * Rendell, Paul (2015). ''[https://www.springer.com/gp/book/9783319198415 Turing Machine Universality of the Game of Life]'' Springer, July 2015, {{isbn|3319198416}} − * [[Charles Seife|Seife, Charles]] (1994). ''[http://www.users.cloud9.net/~cgseife/conway.html Impressions of Conway]'' [[The Sciences]] − * [Dierk Schleicher (2011) ''https://www.ams.org/notices/201305/rnoti-p567.pdf'' Interview with John Conway, Notices of the AMS] − − − ==External links== − {{Sister project links| wikt=no | commons=Category:John Horton Conway | b=no | n=no | q=John Horton Conway | s=no | v=no | voy=no | species=no | d=no}} − * [http://www.adeptis.ru/vinci/m_part3_3.html Photos of John Horton Conway] − * {{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 − − {{Conway's Game of Life}} − − {{FRS 1981}} − {{Authority control}} − − {{DEFAULTSORT:Conway, John Horton}} − [[Category:1937 births]] − [[Category:Living people]] − [[Category:20th-century British mathematicians]] − [[Category:21st-century mathematicians]] − [[Category:Algebraists]] − [[Category:Group theorists]] − [[Category:Combinatorial game theorists]] − [[Category:Cellular automatists]] − [[Category:Mathematics popularizers]] − [[Category:Recreational mathematicians]] − [[Category:English mathematicians]] − [[Category:Alumni of Gonville and Caius College, Cambridge]] − [[Category:Fellows of Sidney Sussex College, Cambridge]] − [[Category:Fellows of the Royal Society]] − [[Category:Princeton University faculty]] − [[Category:Scientists from Liverpool]] − [[Category:British expatriate academics in the United States]] − [[Category:English atheists]] − [[Category:John Horton Conway]] − [[Category:Researchers of artificial life]]
无编辑摘要
* [https://dof.princeton.edu/about/clerk-faculty/emeritus/john-horton-conway John Horton Conway] Dean of the Faculty, Princeton University
* [https://dof.princeton.edu/about/clerk-faculty/emeritus/john-horton-conway John Horton Conway] Dean of the Faculty, Princeton University
=== 视频 ===
=== 视频 ===
[https://www.math.princeton.edu/people/john-conway 普林斯顿大学数学系个人主页]
[https://www.math.princeton.edu/people/john-conway 普林斯顿大学数学系个人主页]
----
本中文词条由[[用户:费米子|费米子]]编辑，欢迎在讨论页面留言。
'''本词条内容源自wikipedia及公开资料，遵守 CC3.0协议。'''
[[Category:元胞自动机]]
[[Category:元胞自动机]]
[[Category:人物]]
[[Category:人物]]