John Horton Conway (26 December 1937 – 11 April 2020) was an English mathematician. He was active in the theory of

finite group In abstract algebra, a finite group is a group whose underlying set is finite. Finite groups often arise when considering symmetry of mathematical or physical objects, when those objects admit just a finite number of structure-preserving tra ...

knot theory In topology, knot theory is the study of knot (mathematics), mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are joined so it cannot be und ...

number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

combinatorial game theory Combinatorial game theory is a branch of mathematics and theoretical computer science that typically studies sequential games with perfect information. Research in this field has primarily focused on two-player games in which a ''position'' ev ...

and

coding theory Coding theory is the study of the properties of codes and their respective fitness for specific applications. Codes are used for data compression, cryptography, error detection and correction, data transmission and computer data storage, data sto ...

. He also made contributions to many branches of

recreational mathematics Recreational mathematics is mathematics carried out for recreation (entertainment) rather than as a strictly research-and-application-based professional activity or as a part of a student's formal education. Although it is not necessarily limited ...

, most notably the invention of the

cellular automaton A cellular automaton (pl. cellular automata, abbrev. CA) is a discrete model of computation studied in automata theory. Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tessel ...

called the Game of Life. Born and raised in

Liverpool Liverpool is a port City status in the United Kingdom, city and metropolitan borough in Merseyside, England. It is situated on the eastern side of the River Mersey, Mersey Estuary, near the Irish Sea, north-west of London. With a population ...

, Conway spent the first half of his career at the

University of Cambridge The University of Cambridge is a Public university, public collegiate university, collegiate research university in Cambridge, England. Founded in 1209, the University of Cambridge is the List of oldest universities in continuous operation, wo ...

before moving to the United States, where he held the

John von Neumann John von Neumann ( ; ; December 28, 1903 – February 8, 1957) was a Hungarian and American mathematician, physicist, computer scientist and engineer. Von Neumann had perhaps the widest coverage of any mathematician of his time, in ...

Professorship at

Princeton University Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial ...

for the rest of his career. On 11 April 2020, at age 82, he died of complications from

COVID-19 Coronavirus disease 2019 (COVID-19) is a contagious disease caused by the coronavirus SARS-CoV-2. In January 2020, the disease spread worldwide, resulting in the COVID-19 pandemic. The symptoms of COVID‑19 can vary but often include fever ...

Early life and education

Conway was born on 26 December 1937 in

, the son of Cyril Horton Conway and Agnes Boyce. He became interested in mathematics at a very early age. By the time he was 11, his ambition was to become a mathematician. After leaving

sixth form In the education systems of Barbados, England, Jamaica, Northern Ireland, Trinidad and Tobago, Wales, and some other Commonwealth countries, sixth form represents the final two years of secondary education, ages 16 to 18. Pupils typically prepa ...

, he studied mathematics at

Gonville and Caius College, Cambridge Gonville and Caius College, commonly known as Caius ( ), is a constituent college of the University of Cambridge in Cambridge, England. Founded in 1348 by Edmund Gonville, it is the fourth-oldest of the University of Cambridge's 31 colleges and ...

. 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". Conway was awarded a BA in 1959 and, supervised by

Harold Davenport Harold Davenport FRS (30 October 1907 – 9 June 1969) was an English mathematician, known for his extensive work in number theory. Early life and education Born on 30 October 1907 in Huncoat, Lancashire, Davenport was educated at Accringto ...

, began to undertake research in number theory. Having solved the open problem posed by Davenport on writing numbers as the sums of fifth powers, Conway became interested in infinite ordinals. It appears that his interest in games began during his years studying the

Cambridge Mathematical Tripos The Mathematical Tripos is the mathematics course that is taught in the Faculty of Mathematics at the University of Cambridge. Origin In its classical nineteenth-century form, the tripos was a distinctive written examination of undergraduate s ...

, where he became an avid

backgammon Backgammon is a two-player board game played with counters and dice on tables boards. It is the most widespread Western member of the large family of tables games, whose ancestors date back at least 1,600 years. The earliest record of backgammo ...

player, spending hours playing the game in the common room. In 1964, Conway was awarded his doctorate and was appointed as College Fellow and Lecturer in Mathematics at

Sidney Sussex College, Cambridge Sidney Sussex College (historically known as "Sussex College" and today referred to informally as "Sidney") is a Colleges of the University of Cambridge, constituent college of the University of Cambridge in England. The College was founded in 1 ...

. After leaving Cambridge in 1986, he took up the appointment to the

Chair of Mathematics at Princeton University. There, he won the Princeton University

Pi Day Pi Day is an annual celebration of the mathematical constant (pi). Pi Day is observed on March 14 (the 3rd month) since 3, 1, and 4 are the first three significant figures of , and was first celebrated in the United States. It was founded i ...

pie-eating contest.

Conway and Martin Gardner

Conway's career was intertwined with that of

Martin Gardner Martin Gardner (October 21, 1914May 22, 2010) was an American popular mathematics and popular science writer with interests also encompassing magic, scientific skepticism, micromagic, philosophy, religion, and literatureespecially the writin ...

. When Gardner featured

Conway's Game of Life The Game of Life, also known as Conway's Game of Life or simply Life, is a cellular automaton devised by the British mathematician John Horton Conway in 1970. It is a zero-player game, meaning that its evolution is determined by its initial ...

in his

Mathematical Games column Over a period of 24 years (January 1957 – December 1980), Martin Gardner wrote 288 consecutive monthly "Mathematical Games" columns for ''Scientific American'' magazine. During the next years, until June 1986, Gardner wrote 9 more columns, br ...

in October 1970, it became the most widely read of all his columns and made Conway an instant celebrity. 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. For instance, he discussed Conway's game of Sprouts (July 1967),

Hackenbush Hackenbush is a two-player game invented by mathematician John Horton Conway. It may be played on any configuration of line segments connected to one another by their endpoints and to a "ground" line. Other versions of the game use differently co ...

(January 1972), and his angel and devil problem (February 1974). In the September 1976 column, he reviewed Conway's book ''

On Numbers and Games ''On Numbers and Games'' is a mathematics book by John Horton Conway first published in 1976. The book is written by a pre-eminent mathematician, and is directed at other mathematicians. The material is, however, developed in a playful and unpr ...

'' and even managed to explain Conway's

surreal numbers In mathematics, the surreal number system is a totally ordered proper class containing not only the real numbers but also infinite and infinitesimal numbers, respectively larger or smaller in absolute value than any positive real number. Researc ...

. Conway was a prominent member of Martin 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 the

Penrose tiling A Penrose tiling is an example of an aperiodic tiling. Here, a ''tiling'' is a covering of two-dimensional space, the plane by non-overlapping polygons or other shapes, and a tiling is ''aperiodic'' if it does not contain arbitrarily large Perio ...

s which had just been announced. Conway had discovered many (if not most) of the major properties of the tilings. Gardner used these results when he introduced the world to Penrose tiles in his January 1977 column. The cover of that issue of ''Scientific American'' features the Penrose tiles and is based on a sketch by Conway.

Major areas of research

Recreational mathematics

Conway invented the Game of Life, one of the early examples of a

. 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 in ''

Scientific American ''Scientific American'', informally abbreviated ''SciAm'' or sometimes ''SA'', is an American popular science magazine. Many scientists, including Albert Einstein and Nikola Tesla, have contributed articles to it, with more than 150 Nobel Pri ...

'' in 1970, it has spawned hundreds of computer programs, web sites, and articles. It is a staple of recreational mathematics. The LifeWiki is devoted to curating and cataloging the various aspects of the game. 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. The game helped to launch a new branch of mathematics, the field of

cellular automata A cellular automaton (pl. cellular automata, abbrev. CA) is a discrete model of computation studied in automata theory. Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tessel ...

. The Game of Life is known to be

Turing complete Alan Mathison Turing (; 23 June 1912 – 7 June 1954) was an English mathematician, computer scientist, logician, cryptanalyst, philosopher and theoretical biologist. He was highly influential in the development of theoretical comput ...

Combinatorial game theory

Conway contributed to

(CGT), a theory of

partisan game In combinatorial game theory, a game is partisan (sometimes partizan) if it is not impartial. That is, some moves are available to one player and not to the other, or the payoffs are not symmetric. Most games are partisan. For example, in chess, on ...

s. He developed the theory with

Elwyn Berlekamp Elwyn Ralph Berlekamp (September 6, 1940 – April 9, 2019) was a professor of mathematics and computer science at the University of California, Berkeley.Richard Guy, and also co-authored the book '' Winning Ways for your Mathematical Plays'' with them. He also wrote ''

'' (''ONAG'') which lays out the mathematical foundations of CGT. He was also one of the inventors of the game sprouts, as well as

philosopher's football Phutball (short for Philosopher's Football) is a two-player abstract strategy board game described in Elwyn Berlekamp, John Horton Conway, and Richard K. Guy's '' Winning Ways for your Mathematical Plays''. Rules Phutball is played on the in ...

. He developed detailed analyses of many other games and puzzles, such as the

Soma cube The Soma cube is a mechanical puzzle#Assembly, solid dissection puzzle invented by Danish polymath Piet Hein (scientist), Piet Hein in 1933 during a lecture on quantum mechanics conducted by Werner Heisenberg. Seven different Polycube, pieces ...

peg solitaire Peg Solitaire, Solo Noble, Solo Goli, Marble Solitaire or simply Solitaire is a board game for one player involving movement of pegs on a board with holes. Some sets use marbles in a board with indentations. The game is known as solitaire in Bri ...

, and Conway's soldiers. He came up with the

angel problem The angel problem is a question in combinatorial game theory proposed by John Horton Conway. The game is commonly referred to as the angels and devils game.John H. Conway, The angel problem', in: Richard Nowakowski (editor) ''Games of No Chance'' ...

, which was solved in 2006. He invented a new system of numbers, the

, which are closely related to certain games and have been the subject of a mathematical novelette by

Donald Knuth Donald Ervin Knuth ( ; born January 10, 1938) is an American computer scientist and mathematician. He is a professor emeritus at Stanford University. He is the 1974 recipient of the ACM Turing Award, informally considered the Nobel Prize of comp ...

. He also invented a nomenclature for exceedingly

large number Large numbers, far beyond those encountered in everyday life—such as simple counting or financial transactions—play a crucial role in various domains. These expansive quantities appear prominently in mathematics, cosmology, cryptography, and s ...

s, the

Conway chained arrow notation Conway chained arrow notation, created by mathematician John Horton Conway, is a means of expressing certain extremely large numbers. It is simply a finite sequence of positive integers separated by rightward arrows, e.g. 2\to3\to4\to5\to6. As wi ...

. Much of this is discussed in the 0th part of ''ONAG''.

Geometry

In the mid-1960s with

Michael Guy Michael J. T. Guy (born 1 April 1943) is a British computer scientist and mathematician. He is known for early work on computer systems, such as the Phoenix system at the University of Cambridge, and for contributions to number theory, computer ...

, Conway established that there are sixty-four convex uniform polychora excluding two infinite sets of prismatic forms. They discovered the

grand antiprism In geometry, the grand antiprism or pentagonal double antiprismoid is a uniform 4-polytope (4-dimensional uniform polytope) bounded by 320 cells: 20 pentagonal antiprisms, and 300 tetrahedra. It is an anomalous, non-Wythoffian uniform 4-polyto ...

in the process, the only

non-Wythoffian In geometry, a Wythoff construction, named after mathematician Willem Abraham Wythoff, is a method for constructing a uniform polyhedron or plane tiling. It is often referred to as Wythoff's kaleidoscopic construction. Construction process ...

uniform

polychoron In geometry, a 4-polytope (sometimes also called a polychoron, polycell, or polyhedroid) is a four-dimensional polytope. It is a connected and closed figure, composed of lower-dimensional polytopal elements: vertices, edges, faces (polygons), a ...

. Conway also suggested a system of notation dedicated to describing

polyhedra In geometry, a polyhedron (: polyhedra or polyhedrons; ) is a three-dimensional figure with flat polygonal faces, straight edges and sharp corners or vertices. The term "polyhedron" may refer either to a solid figure or to its boundary su ...

called

Conway polyhedron notation In geometry and topology, Conway polyhedron notation, invented by John Horton Conway and promoted by George W. Hart, is used to describe polyhedra based on a seed polyhedron modified by various prefix operations. Conway and Hart extended the i ...

. In the theory of tessellations, he devised the

Conway criterion In the mathematical theory of tessellations, the Conway criterion, named for the English mathematician John Horton Conway, is a Necessity and sufficiency, sufficient rule for when a prototile will tile the plane. It consists of the following req ...

which is a fast way to identify many prototiles that tile the plane. He investigated lattices in higher dimensions and was the first to determine the symmetry group of the

Leech lattice In mathematics, the Leech lattice is an even unimodular lattice Λ24 in 24-dimensional Euclidean space which is one of the best models for the kissing number problem. It was discovered by . It may also have been discovered (but not published) by Er ...

Geometric topology

In knot theory, Conway formulated a new variation of the

Alexander polynomial In mathematics, the Alexander polynomial is a knot invariant which assigns a polynomial with integer coefficients to each knot type. James Waddell Alexander II discovered this, the first knot polynomial, in 1923. In 1969, John Conway showed a ...

and produced a new invariant now called the Conway polynomial. After lying dormant for more than a decade, this concept became central to work in the 1980s on the novel

knot polynomial In the mathematical field of knot theory, a knot polynomial is a knot invariant in the form of a polynomial whose coefficients encode some of the properties of a given knot. History The first knot polynomial, the Alexander polynomial, was introdu ...

s. Conway further developed tangle theory and invented a system of notation for tabulating knots, now known as 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. The

Conway knot In mathematics, specifically in knot theory, the Conway knot (or Conway's knot) is a particular knot (mathematics), knot with 11 crossings, named after John Horton Conway. It is related by mutation (knot theory), mutation to the Kinoshita–Te ...

is named after him. Conway's conjecture that, in any

thrackle A thrackle is an embedding of a graph in the plane in which each edge is a Jordan arc and every pair of edges meet exactly once. Edges may either meet at a common endpoint, or, if they have no endpoints in common, at a point in their interiors. I ...

, the number of edges is at most equal to the number of vertices, is still open.

Group theory

He was the primary author of the ''

ATLAS of Finite Groups The ''ATLAS of Finite Groups'', often simply known as the ''ATLAS'', is a group theory book by John Horton Conway, Robert Turner Curtis, Simon Phillips Norton, Richard Alan Parker and Robert Arnott Wilson (with computational assistance from ...

'' giving properties of many

finite simple group In mathematics, the classification of finite simple groups states that every finite simple group is cyclic, or alternating, or in one of 16 families of groups of Lie type, or one of 26 sporadic groups. The list below gives all finite simple g ...

s. Working with his colleagues Robert Curtis and Simon P. Norton he constructed the first concrete representations of some of the

sporadic group In the mathematical classification of finite simple groups, there are a number of groups which do not fit into any infinite family. These are called the sporadic simple groups, or the sporadic finite groups, or just the sporadic groups. A simpl ...

s. More specifically, he discovered three sporadic groups based on the symmetry of the

, which have been designated the Conway groups. This work made him a key player in the successful

classification of the finite simple groups In mathematics, the classification of finite simple groups (popularly called the enormous theorem) is a result of group theory stating that every finite simple group is either cyclic, or alternating, or belongs to a broad infinite class called ...

. Based on a 1978 observation by mathematician John McKay, Conway and Norton formulated the complex of conjectures known as

monstrous moonshine In mathematics, monstrous moonshine, or moonshine theory, is the unexpected connection between the monster group ''M'' and modular functions, in particular the ''j'' function. The initial numerical observation was made by John McKay in 1978, ...

. This subject, named by Conway, relates the

monster group In the area of abstract algebra known as group theory, the monster group M (also known as the Fischer–Griess monster, or the friendly giant) is the largest sporadic simple group; it has order : : = 2463205976112133171923293 ...

with

elliptic modular function In mathematics, Felix Klein's -invariant or function is a modular function of weight zero for the special linear group \operatorname(2,\Z) defined on the upper half-plane of complex numbers. It is the unique such function that is holomorphic aw ...

s, thus bridging two previously distinct areas of mathematics—

s and

complex function theory Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebraic g ...

. Monstrous moonshine theory has now been revealed to also have deep connections to

string theory In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and intera ...

. Conway introduced the

Mathieu groupoid In mathematics, the Mathieu groupoid M13 is a groupoid acting on 13 points such that the stabilizer of each point is the Mathieu group M12. It was introduced by and studied in detail by . Construction The projective plane of order 3 has 13 point ...

, an extension of the Mathieu group M₁₂ to 13 points.

Number theory

As a graduate student, he proved one case of a

conjecture In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. Some conjectures, such as the Riemann hypothesis or Fermat's conjecture (now a theorem, proven in 1995 by Andrew Wiles), ha ...

Edward Waring Edward Waring (15 August 1798) was a British mathematician. He entered Magdalene College, Cambridge as a sizar and became Senior wrangler in 1757. He was elected a Fellow of Magdalene and in 1760 Lucasian Professor of Mathematics, holding the ...

, that every integer could be written as the sum of 37 numbers each raised to the fifth power, though

Chen Jingrun Chen Jingrun (; 22 May 1933 – 19 March 1996), also known as Jing-Run Chen, was a Chinese mathematician who made significant contributions to number theory, including Chen's theorem and the Chen prime. Life and career Chen was the third son i ...

solved the problem independently before Conway's work could be published. In 1972, Conway proved that a natural generalization of the Collatz problem is algorithmically undecidable. Related to that, he developed the esoteric programming language

FRACTRAN FRACTRAN is a Turing-complete esoteric programming language invented by the mathematician John Conway. A FRACTRAN program is an ordered list of positive fractions together with an initial positive integer input ''n''. The program is run by updat ...

. While lecturing on the Collatz conjecture,

Terence Tao Terence Chi-Shen Tao (; born 17 July 1975) is an Australian-American mathematician, Fields medalist, and professor of mathematics at the University of California, Los Angeles (UCLA), where he holds the James and Carol Collins Chair in the Co ...

(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".

Algebra

Conway wrote a textbook on

Stephen Kleene Stephen Cole Kleene ( ; January 5, 1909 – January 25, 1994) was an American mathematician. One of the students of Alonzo Church, Kleene, along with Rózsa Péter, Alan Turing, Emil Post, and others, is best known as a founder of the branch of ...

's theory of state machines, and published original work on

algebraic structure In mathematics, an algebraic structure or algebraic system consists of a nonempty set ''A'' (called the underlying set, carrier set or domain), a collection of operations on ''A'' (typically binary operations such as addition and multiplicatio ...

s, focusing particularly on

quaternion In mathematics, the quaternion number system extends the complex numbers. Quaternions were first described by the Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. The algebra of quater ...

s and

octonion In mathematics, the octonions are a normed division algebra over the real numbers, a kind of Hypercomplex number, hypercomplex Number#Classification, number system. The octonions are usually represented by the capital letter O, using boldface or ...

s. Together with

Neil Sloane __NOTOC__ Neil James Alexander Sloane FLSW (born October 10, 1939) is a British-American mathematician. His major contributions are in the fields of combinatorics, error-correcting codes, and sphere packing. Sloane is best known for being the cre ...

, he invented the

icosian In mathematics, the icosians are a specific set of Hamiltonian quaternions with the same symmetry as the 600-cell. The term can be used to refer to two related, but distinct, concepts: * The icosian Group (mathematics), group: a multiplicative g ...

Analysis

He invented a base 13 function as a counterexample to the converse of the

intermediate value theorem In mathematical analysis, the intermediate value theorem states that if f is a continuous function whose domain contains the interval , then it takes on any given value between f(a) and f(b) at some point within the interval. This has two imp ...

: the function takes on every real value in each interval on the real line, so it has a Darboux property but is ''not''

continuous Continuity or continuous may refer to: Mathematics * Continuity (mathematics), the opposing concept to discreteness; common examples include ** Continuous probability distribution or random variable in probability and statistics ** Continuous ...

Algorithmics

For calculating the day of the week, he invented the

Doomsday algorithm The Doomsday rule, Doomsday algorithm or Doomsday method is an algorithm of determination of the day of the week for a given date. It provides a perpetual calendar because the Gregorian calendar moves in cycles of 400 years. The algorithm for ...

. 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 on

finite-state machine A finite-state machine (FSM) or finite-state automaton (FSA, plural: ''automata''), finite automaton, or simply a state machine, is a mathematical model of computation. It is an abstract machine that can be in exactly one of a finite number o ...

Theoretical physics

In 2004, Conway and

Simon B. Kochen Simon Bernhard Kochen (; born 14 August 1934) is a Canadian mathematician, working in the fields of model theory, number theory and quantum mechanics. Education and career Kochen was born in Antwerp, Belgium, and escaped the Nazis with his family ...

, another Princeton mathematician, proved the

free will theorem The free will theorem of John H. Conway and Simon B. Kochen states that if we have a free will in the sense that our choices are not a function of the past, then, under specific assumptions drawn from quantum mechanics and relativity, so must som ...

, a version of the " no hidden variables" principle of

quantum mechanics Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is ...

. 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 have

free will Free will is generally understood as the capacity or ability of people to (a) choice, choose between different possible courses of Action (philosophy), action, (b) exercise control over their actions in a way that is necessary for moral respon ...

, then so do elementary particles."

Personal life and death

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. He had three grandchildren and two great-grandchildren. On 8 April 2020, Conway developed symptoms of

. On 11 April, he died in

New Brunswick New Brunswick is a Provinces and Territories of Canada, province of Canada, bordering Quebec to the north, Nova Scotia to the east, the Gulf of Saint Lawrence to the northeast, the Bay of Fundy to the southeast, and the U.S. state of Maine to ...

New Jersey New Jersey is a U.S. state, state located in both the Mid-Atlantic States, Mid-Atlantic and Northeastern United States, Northeastern regions of the United States. Located at the geographic hub of the urban area, heavily urbanized Northeas ...

, at the age of 82.

Awards and honours

Conway received the

Berwick Prize The Berwick Prize and Senior Berwick Prize are two prizes of the London Mathematical Society awarded in alternating years in memory of William Edward Hodgson Berwick, a previous Vice-President of the LMS. Berwick left some money to be given to the ...

(1971), was elected a

Fellow of the Royal Society Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the Fellows of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural science, natural knowledge, incl ...

(1981), became a fellow of the American Academy of Arts and Sciences in 1992, was the first recipient of the

Pólya Prize (LMS) The Pólya Prize is a prize in mathematics, awarded by the London Mathematical Society. Second only to the triennial De Morgan Medal in prestige among the society's awards, it is awarded in the years that are not divisible by three – those in wh ...

(1987), won the

Nemmers Prize in Mathematics Larry Nemmers (born July 12, 1943) is a retired educator and better known as a former American football official in the National Football League (NFL). Nemmers made his debut as an NFL official in the 1985 season and continued in this role unt ...

(1998) and received the

Leroy P. Steele Prize The Leroy P. Steele Prizes are awarded every year by the American Mathematical Society, for distinguished research work and writing in the field of mathematics. Since 1993, there has been a formal division into three categories. The prizes have b ...

for Mathematical Exposition (2000) of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

. In 2001 he was awarded an honorary degree from the

University of Liverpool The University of Liverpool (abbreviated UOL) is a Public university, public research university in Liverpool, England. Founded in 1881 as University College Liverpool, Victoria University (United Kingdom), Victoria University, it received Ro ...

, and in 2014 one from

Alexandru Ioan Cuza University The Alexandru Ioan Cuza University (; acronym: UAIC) is a public university located in , Romania. Founded by an 1860 decree of Prince Alexandru Ioan Cuza, under whom the former was converted to a university, the University of , as it was named ...

. His Fellow of the Royal Society nomination in 1981 reads: In 2017 Conway was given honorary membership of the British

Mathematical Association The Mathematical Association is a professional society concerned with mathematics education in the UK. History It was founded in 1871 as the Association for the Improvement of Geometrical Teaching and renamed to the Mathematical Association in ...

. Conferences called

Gathering 4 Gardner Gathering 4 Gardner (G4G) is an educational foundation and non-profit corporation (Gathering 4 Gardner, Inc.) devoted to preserving the legacy and spirit of prolific writer Martin Gardner. G4G organizes conferences where people who have been ins ...

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.Bellos, Alex (2008)
The science of fun
''The Guardian'', 30 May 2008

Select publications

* 1971 – ''Regular algebra and finite machines''.

Chapman and Hall Chapman & Hall is an imprint owned by CRC Press, originally founded as a British publishing house in London in the first half of the 19th century by Edward Chapman and William Hall. Chapman & Hall were publishers for Charles Dickens (from 1840 ...

, London, 1971, Series: Chapman and Hall mathematics series, . * 1976 – ''

On numbers and games ''On Numbers and Games'' is a mathematics book by John Horton Conway first published in 1976. The book is written by a pre-eminent mathematician, and is directed at other mathematicians. The material is, however, developed in a playful and unpr ...

''.

Academic Press Academic Press (AP) is an academic book publisher founded in 1941. It launched a British division in the 1950s. Academic Press was acquired by Harcourt, Brace & World in 1969. Reed Elsevier said in 2000 it would buy Harcourt, a deal complete ...

, New York, 1976, Series: L.M.S. monographs, 6, . * 1979 – ''On the Distribution of Values of Angles Determined by Coplanar Points'' (with

Paul Erdős Paul Erdős ( ; 26March 191320September 1996) was a Hungarian mathematician. He was one of the most prolific mathematicians and producers of mathematical conjectures of the 20th century. pursued and proposed problems in discrete mathematics, g ...

, and H. T. Croft).

Journal of the London Mathematical Society The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh Mathematical S ...

, vol. II, series 19, pp. 137–143. * 1979 – ''Monstrous Moonshine'' (with Simon P. Norton).

Bulletin of the London Mathematical Society The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh Mathematical Soc ...

, vol. 11, issue 2, pp. 308–339. * 1982 – '' Winning Ways for your Mathematical Plays'' (with Richard K. Guy and

Elwyn Berlekamp Elwyn Ralph Berlekamp (September 6, 1940 – April 9, 2019) was a professor of mathematics and computer science at the University of California, Berkeley.Academic Press Academic Press (AP) is an academic book publisher founded in 1941. It launched a British division in the 1950s. Academic Press was acquired by Harcourt, Brace & World in 1969. Reed Elsevier said in 2000 it would buy Harcourt, a deal complete ...

, . * 1985 – ''

Atlas of finite groups The ''ATLAS of Finite Groups'', often simply known as the ''ATLAS'', is a group theory book by John Horton Conway, Robert Turner Curtis, Simon Phillips Norton, Richard Alan Parker and Robert Arnott Wilson (with computational assistance from ...

'' (with Robert Turner Curtis, Simon Phillips Norton, Richard A. Parker, and

Robert Arnott Wilson Robert Arnott Wilson (born 1958) is a retired mathematician in London, England, who is best known for his work on classifying the maximal subgroups of finite simple groups and for the work in the Monster group In the area of abstract algebr ...

Clarendon Press Oxford University Press (OUP) is the publishing house of the University of Oxford. It is the largest university press in the world. Its first book was printed in Oxford in 1478, with the Press officially granted the legal right to print books ...

, New York,

Oxford University Press Oxford University Press (OUP) is the publishing house of the University of Oxford. It is the largest university press in the world. Its first book was printed in Oxford in 1478, with the Press officially granted the legal right to print books ...

, 1985, . * 1988 – ''Sphere Packings, Lattices, and Groups'' (with

Springer-Verlag Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in ...

, New York, Series: Grundlehren der mathematischen Wissenschaften, 290, . * 1995 – ''Minimal-Energy Clusters of Hard Spheres'' (with

, R. H. Hardin, and

Tom Duff Thomas Douglas Selkirk Duff (born December 8, 1952) is a Canadian computer programmer. Life and career Early life Duff was born in Toronto, Ontario, Canada, and was named for his putative ancestor, the fifth Earl of Selkirk. He grew up in Tor ...

Discrete & Computational Geometry '' Discrete & Computational Geometry'' is a peer-reviewed mathematics journal published quarterly by Springer. Founded in 1986 by Jacob E. Goodman and Richard M. Pollack, the journal publishes articles on discrete geometry and computational ...

, vol. 14, no. 3, pp. 237–259. * 1996 – ''The Book of Numbers'' (with Richard K. Guy).

Copernicus Nicolaus Copernicus (19 February 1473 – 24 May 1543) was a Renaissance polymath who formulated a mathematical model, model of Celestial spheres#Renaissance, the universe that placed heliocentrism, the Sun rather than Earth at its cen ...

, New York, 1996, . * 1997 – ''The Sensual (quadratic) Form'' (with Francis Yein Chei Fung).

Mathematical Association of America The Mathematical Association of America (MAA) is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university A university () is an educational institution, institution of tertiary edu ...

, Washington, DC, 1997, Series: Carus mathematical monographs, no. 26, . * 2002 – ''On Quaternions and Octonions'' (with Derek A. Smith). A. K. Peters, Natick, MA, 2002, . * 2008 – '' The Symmetries of Things'' (with Heidi Burgiel and

Chaim Goodman-Strauss Chaim Goodman-Strauss (born June 22, 1967 in Austin, Texas) is an American mathematician who works in convex geometry, especially aperiodic tiling. He retired from the faculty of the University of Arkansas and currently serves as outreach mathem ...

). A. K. Peters, Wellesley, MA, 2008, .

References

Sources

* Alpert, Mark (1999).
Not Just Fun and Games
' ''Scientific American'', April 1999 * Boden, Margaret (2006). ''Mind As Machine'', Oxford University Press, 2006, p. 1271 * du Sautoy, Marcus (2008). ''Symmetry'', HarperCollins, p. 308 * Guy, Richard K (1983).
Conway's Prime Producing Machine
'

Mathematics Magazine ''Mathematics Magazine'' is a refereed bimonthly publication of the Mathematical Association of America. Its intended audience is teachers of collegiate mathematics, especially at the junior/senior level, and their students. It is explicitly a j ...

, Vol. 56, No. 1 (Jan. 1983), pp. 26–33 * * * * Princeton University (2009)
Bibliography of John H. Conway
Mathematics Department * Seife, Charles (1994).
Impressions of Conway
'

The Sciences ''The Sciences'' was a magazine published from 1961 to 2001 by the New York Academy of Sciences. Each issue contained articles that discussed science issues with cultural relevance, illustrated with fine art and an occasional cartoon. The perio ...

* Schleicher, Dierk (2011)
Interview with John Conway
Notices of the AMS

External links

* * * ** ** * Conway leading a tour of brickwork patterns in Princeton, lecturing on the ordinals and on sums of powers and the Bernoulli numbers
necrology by Keith Hartnett in Quanta Magazine, April 20, 2020
{{DEFAULTSORT:Conway, John Horton 1937 births 2020 deaths 20th-century English mathematicians 21st-century English mathematicians Algebraists Group theorists Combinatorial game theorists Cellular automatists Mathematics popularizers Recreational mathematicians Alumni of Gonville and Caius College, Cambridge Fellows of Sidney Sussex College, Cambridge Fellows of the Royal Society Princeton University faculty Scientists from Liverpool British expatriate academics in the United States Researchers of artificial life Deaths from the COVID-19 pandemic in New Jersey Historical treatment of octonions