John Horton Conway | |
|---|---|
.jpg) Conway in June 2005 | |
| Born | (1937-12-26)26 December 1937 Liverpool, England |
| Died | 11 April 2020(2020-04-11) (aged 82) |
| Education | Gonville and Caius College, Cambridge (BA,MA,PhD) |
| Known for |
|
| Awards |
|
| Scientific career | |
| Fields | Mathematics |
| Institutions | University of Cambridge Princeton University |
| Thesis | Homogeneous ordered sets (1964) |
| Doctoral advisor | Harold Davenport[1] |
| Doctoral students | |
| Website | Archived version @ web.archive.org |
John Horton ConwayFRS (26 December 1937 – 11 April 2020) was an English mathematician. He was active in the theory offinite groups,knot theory,number theory,combinatorial game theory andcoding theory. He also made contributions to many branches ofrecreational mathematics, most notably the invention of thecellular automaton called theGame of Life.
Born and raised inLiverpool, Conway spent the first half of his career at theUniversity of Cambridge before moving to the United States, where he held theJohn von Neumann Professorship atPrinceton University for the rest of his career.[2] On 11 April 2020, at age 82, he died of complications fromCOVID-19.[3]
Conway was born on 26 December 1937 inLiverpool, the son of Cyril Horton Conway and Agnes Boyce.[2][4] He became interested in mathematics at a very early age. By the time he was 11, his ambition was to become a mathematician.[5][6] After leavingsixth form, he studied mathematics atGonville and Caius College, Cambridge.[4] A "terribly introverted adolescent" in school, he took his admission to Cambridge as an opportunity to transform himself into an extrovert, a change which would later earn him the nickname of "the world's most charismatic mathematician".[7][8]
Conway was awarded aBA in 1959 and, supervised byHarold Davenport, began to undertake research in number theory. Having solved the open problem posed by Davenport onwriting numbers as the sums of fifth powers, Conway became interested in infinite ordinals.[6] It appears that his interest in games began during his years studying theCambridge Mathematical Tripos, where he became an avidbackgammon player, spending hours playing the game in the common room.[2]
In 1964, Conway was awarded his doctorate and was appointed as College Fellow and Lecturer in Mathematics atSidney Sussex College, Cambridge.[9]
After leaving Cambridge in 1986, he took up the appointment to theJohn von Neumann Chair of Mathematics at Princeton University.[9] There, he won the Princeton UniversityPi Day pie-eating contest.[10]
Conway's career was intertwined with that ofMartin Gardner. When Gardner featuredConway's Game of Life in hisMathematical Games column in October 1970, it became the most widely read of all his columns and made Conway an instant celebrity.[11][12] 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.[13] For instance, he discussed Conway's game ofSprouts (July 1967),Hackenbush (January 1972), and hisangel and devil problem (February 1974). In the September 1976 column, he reviewed Conway's bookOn Numbers and Games and even managed to explain Conway'ssurreal numbers.[14]
Conway was a prominent member ofMartin Gardner's Mathematical Grapevine. He regularly visited Gardner and often wrote him long letters summarizing his recreational research. In a 1976 visit, Gardner kept him for a week, pumping him for information on thePenrose tilings which had just been announced. Conway had discovered many (if not most) of the major properties of the tilings.[15] Gardner used these results when he introduced the world to Penrose tiles in his January 1977 column.[16] The cover of that issue ofScientific American features the Penrose tiles and is based on a sketch by Conway.[12]
Conway invented the Game of Life, one of the early examples of acellular automaton. His initial experiments in that field were done with pen and paper, long before personal computers existed. Since Conway's game was popularized by Martin Gardner inScientific American in 1970,[17] it has spawned hundreds of computer programs, web sites, and articles.[18] It is a staple of recreational mathematics. TheLifeWiki is devoted to curating and cataloging the various aspects of the game.[19] From the earliest days, it has been a favorite in computer labs, both for its theoretical interest and as a practical exercise in programming and data display. Conway came to dislike how discussions of him heavily focused on his Game of Life, feeling that it overshadowed deeper and more important things he had done, although he remained proud of his work on it.[20] The game helped to launch a new branch of mathematics, the field ofcellular automata.[21]The Game of Life is known to beTuring complete.[22][23]
Conway contributed tocombinatorial game theory (CGT), a theory ofpartisan games. He developed the theory withElwyn Berlekamp andRichard Guy, and also co-authored the bookWinning Ways for your Mathematical Plays with them. He also wroteOn Numbers and Games (ONAG) which lays out the mathematical foundations of CGT.
He was also one of the inventors of the gamesprouts, as well asphilosopher's football. He developed detailed analyses of many other games and puzzles, such as theSoma cube,peg solitaire, andConway's soldiers. He came up with theangel problem, which was solved in 2006.
He invented a new system of numbers, thesurreal numbers, which are closely related to certain games and have been the subject of a mathematical novelette byDonald Knuth.[24] He also invented a nomenclature for exceedinglylarge numbers, theConway chained arrow notation. Much of this is discussed in the 0th part ofONAG.
In the mid-1960s withMichael Guy, Conway established that there are sixty-fourconvex uniform polychora excluding two infinite sets of prismatic forms. They discovered thegrand antiprism in the process, the onlynon-Wythoffian uniformpolychoron.[25] Conway also suggested a system of notation dedicated to describingpolyhedra calledConway polyhedron notation.
In the theory of tessellations, he devised theConway criterion which is a fast way to identify many prototiles that tile the plane.[26]
He investigated lattices in higher dimensions and was the first to determine the symmetry group of theLeech lattice.
In knot theory, Conway formulated a new variation of theAlexander polynomial and produced a new invariant now called the Conway polynomial.[27] After lying dormant for more than a decade, this concept became central to work in the 1980s on the novelknot polynomials.[28] Conway further developedtangle theory and invented a system of notation for tabulating knots, now known asConway 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.[29] TheConway knot is named after him.
Conway's conjecture that, in anythrackle, the number of edges is at most equal to the number of vertices, is still open.
He was the primary author of theATLAS of Finite Groups giving properties of manyfinite simple groups. Working with his colleagues Robert Curtis andSimon P. Norton he constructed the first concrete representations of some of thesporadic groups. More specifically, he discovered three sporadic groups based on the symmetry of theLeech lattice, which have been designated theConway groups.[30] This work made him a key player in the successfulclassification of the finite simple groups.
Based on a 1978 observation by mathematicianJohn McKay, Conway and Norton formulated the complex of conjectures known asmonstrous moonshine. This subject, named by Conway, relates themonster group withelliptic modular functions, thus bridging two previously distinct areas of mathematics—finite groups andcomplex function theory. Monstrous moonshine theory has now been revealed to also have deep connections tostring theory.[31]
Conway introduced theMathieu groupoid, an extension of theMathieu group M12 to 13 points.
As a graduate student, he proved one case of aconjecture byEdward Waring, that every integer could be written as the sum of 37 numbers each raised to the fifth power, thoughChen Jingrun solved the problem independently before Conway's work could be published.[32] In 1972, Conway proved that a natural generalization of theCollatz problem is algorithmicallyundecidable. Related to that, he developed the esoteric programming languageFRACTRAN. While lecturing on the Collatz conjecture,Terence Tao (who was taught by him in graduate school) mentioned Conway's result and said that he was "always very good at making extremely weird connections in mathematics".[33]
Conway wrote a textbook onStephen Kleene's theory of state machines, and published original work onalgebraic structures, focusing particularly onquaternions andoctonions.[34] Together withNeil Sloane, he invented theicosians.[35]
He invented hisbase 13 function as a counterexample to theconverse of theintermediate value theorem: the function takes on every real value in each interval on the real line, so it has aDarboux property but isnotcontinuous.
For calculating the day of the week, he invented theDoomsday algorithm. The algorithm is simple enough for anyone with basic arithmetic ability to do the calculations mentally. Conway could usually give the correct answer in under two seconds. To improve his speed, he practised his calendrical calculations on his computer, which was programmed to quiz him with random dates every time he logged on. One of his early books was onfinite-state machines.
In 2004, Conway andSimon B. Kochen, another Princeton mathematician, proved thefree will theorem, a version of the "no hidden variables" principle ofquantum 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. Conway said that "if experimenters havefree will, then so do elementary particles."[36]
Conway was married three times. With his first two wives he had two sons and four daughters. He married Diana in 2001 and had another son with her.[37] He had three grandchildren and two great-grandchildren.[2]
On 8 April 2020, Conway developed symptoms ofCOVID-19.[38] On 11 April, he died inNew Brunswick,New Jersey, at the age of 82.[38][39][40][41][42]
Conway received theBerwick Prize (1971),[43] was elected aFellow of the Royal Society (1981),[44][45] became a fellow of the American Academy of Arts and Sciences in 1992, was the first recipient of thePólya Prize (LMS) (1987),[43] won theNemmers Prize in Mathematics (1998) and received theLeroy P. Steele Prize for Mathematical Exposition (2000) of theAmerican Mathematical Society. In 2001 he was awarded an honorary degree from theUniversity of Liverpool,[46] and in 2014 one fromAlexandru Ioan Cuza University.[47]
His Fellow of the Royal Society nomination in 1981 reads:
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).[44]
In 2017 Conway was given honorary membership of the BritishMathematical Association.[48]
Conferences calledGathering 4 Gardner are held every two years to celebrate the legacy of Martin Gardner, and Conway himself was often a featured speaker at these events, discussing various aspects of recreational mathematics.[49][50]
Media from Commons
News from Wikinews
Quotations from Wikiquote| International | |
|---|---|
| National | |
| Academics | |
| Artists | |
| People | |
| Other | |
