John Horton Conway
Encyclopedia
John Horton Conway is a prolific mathematician active in the theory of finite groups
, knot theory
, number theory
, combinatorial game theory
and coding theory
. He has also contributed to many branches of recreational mathematics
, notably the invention of the cellular automaton
called the Game of Life
.
Conway is currently Professor of Mathematics and John Von Neumann Professor in Applied and Computational Mathematics at Princeton University
. He studied at Cambridge
, where he started research under Harold Davenport
. He received the Berwick Prize
(1971), was elected a Fellow of the Royal Society (1981), was the first recipient of the Pólya Prize (LMS)
(1987), won the Nemmers Prize in Mathematics
(1998) and received the Leroy P. Steele Prize for Mathematical Exposition (2000) of the American Mathematical Society. He has an Erdős number
of one.
. He became interested in mathematics at a very early age and his mother recalled that he could recite the powers of two when aged four years. At the age of eleven his ambition was to become a mathematician.
After leaving secondary school, Conway entered Gonville and Caius College, Cambridge
to 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 College Fellow and Lecturer in Mathematics at the University of Cambridge
.
He left Cambridge in 1986 to take up the appointment to the John von Neumann
Chair of Mathematics at Princeton University
.
Conway resides in Princeton, New Jersey
. He has seven children by various marriages, three grandchildren and three great-grand children. He has been married three times; his first wife was Eileen, and his second wife was Larissa. He has been married to his third wife, Diana, since 2001.
(CGT), a theory of partisan game
s. This he developed with Elwyn Berlekamp
and 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
, 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
. Much of this is discussed in the 0th part of ONAG.
He is also known for the invention of the Game of Life
, one of the early and still celebrated examples of a cellular automaton
. His early experiments in that field were done with pen and paper, long before personal computers existed.
excluding two infinite sets of prismatic forms. They discovered the grand antiprism
in the process, the only non-Wythoffian uniform polyhedron. Conway has also suggested a system of notation dedicated to describing polyhedra called Conway polyhedron notation
.
He extensively investigated lattices in higher dimensions, and determined the symmetry group of the Leech lattice
.
of knot theory involved skein relation
s, 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 polynomial
s. Conway further developed tangle theory and invented a system of notation for tabulating knots, nowadays known as Conway notation
, while completing the knot tables up to 10 crossings.
and discovered the Conway group
s. He was the primary author of the ATLAS of Finite Groups
giving properties of many finite simple groups. He, along with collaborators, 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.
With Simon P. Norton
he formulated the complex of conjectures relating the monster group
with modular functions, which was named monstrous moonshine
by them.
by Edward Waring
that 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 the work could be published.
s. Together with Neil James Alexander Sloane
, he invented the system of icosians.
, 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.
, 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."
, 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-Strauss and Heidi Burgiel.
Group (mathematics)
In mathematics, a group is an algebraic structure consisting of a set together with an operation that combines any two of its elements to form a third element. To qualify as a group, the set and the operation must satisfy a few conditions called group axioms, namely closure, associativity, identity...
, knot theory
Knot theory
In topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life in shoelaces and rope, a mathematician's knot differs in that the ends are joined together so that it cannot be undone. In precise mathematical language, a knot is an embedding of a...
, number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
, combinatorial game theory
Combinatorial game theory
Combinatorial game theory is a branch of applied mathematics and theoretical computer science that studies sequential games with perfect information, that is, two-player games which have a position in which the players take turns changing in defined ways or moves to achieve a defined winning...
and coding theory
Coding theory
Coding theory is the study of the properties of codes and their fitness for a specific application. Codes are used for data compression, cryptography, error-correction and more recently also for network coding...
. He has also contributed to many branches of recreational mathematics
Recreational mathematics
Recreational mathematics is an umbrella term, referring to mathematical puzzles and mathematical games.Not all problems in this field require a knowledge of advanced mathematics, and thus, recreational mathematics often attracts the curiosity of non-mathematicians, and inspires their further study...
, notably the invention of the cellular automaton
Cellular automaton
A cellular automaton is a discrete model studied in computability theory, mathematics, physics, complexity science, theoretical biology and microstructure modeling. It consists of a regular grid of cells, each in one of a finite number of states, such as "On" and "Off"...
called the Game of Life
Conway's Game of Life
The Game of Life, also known simply as Life, is a cellular automaton devised by the British mathematician John Horton Conway in 1970....
.
Conway is currently Professor of Mathematics and John Von Neumann Professor in Applied and Computational Mathematics at Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
. He studied at Cambridge
University of Cambridge
The University of Cambridge is a public research university located in Cambridge, United Kingdom. It is the second-oldest university in both the United Kingdom and the English-speaking world , and the seventh-oldest globally...
, where he started research under Harold Davenport
Harold Davenport
Harold Davenport FRS was an English mathematician, known for his extensive work in number theory.-Early life:...
. He received the Berwick Prize
Berwick Prizes
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 society to establish two prizes...
(1971), was elected a Fellow of the Royal Society (1981), was the first recipient of the Pólya Prize (LMS)
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 which the De Morgan Medal is not awarded...
(1987), won the Nemmers Prize in Mathematics
Nemmers Prize in Mathematics
The Frederic Esser Nemmers Prize in Mathematics is awarded biennially from Northwestern University. It was initially endowed along with a companion prize, the Erwin Plein Nemmers Prize in Economics, as part of a $14 million donation from the Nemmers brothers. They envisioned creating an award that...
(1998) and received the Leroy P. Steele Prize for Mathematical Exposition (2000) of the American Mathematical Society. He has an Erdős number
Erdos number
The Erdős number describes the "collaborative distance" between a person and mathematician Paul Erdős, as measured by authorship of mathematical papers.The same principle has been proposed for other eminent persons in other fields.- Overview :...
of one.
Biography
Conway's parents were Agnes Boyce and Cyril Horton Conway. He was born in LiverpoolLiverpool
Liverpool is a city and metropolitan borough of Merseyside, England, along the eastern side of the Mersey Estuary. It was founded as a borough in 1207 and was granted city status in 1880...
. He became interested in mathematics at a very early age and his mother recalled that he could recite the powers of two when aged four years. At the age of eleven his ambition was to become a mathematician.
After leaving secondary school, Conway entered Gonville and Caius College, Cambridge
Gonville and Caius College, Cambridge
Gonville and Caius College is a constituent college of the University of Cambridge in Cambridge, England. The college is often referred to simply as "Caius" , after its second founder, John Keys, who fashionably latinised the spelling of his name after studying in Italy.- Outline :Gonville and...
to study mathematics. He was awarded his BA in 1959 and began to undertake research in number theory supervised by Harold Davenport
Harold Davenport
Harold Davenport FRS was an English mathematician, known for his extensive work in number theory.-Early life:...
. Having solved the open problem posed by Davenport on writing numbers as the sums of fifth powers
Waring's problem
In number theory, Waring's problem, proposed in 1770 by Edward Waring, asks whether for every natural number k there exists an associated positive integer s such that every natural number is the sum of at most s kth powers of natural numbers...
, 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
Backgammon
Backgammon is one of the oldest board games for two players. The playing pieces are moved according to the roll of dice, and players win by removing all of their pieces from the board. There are many variants of backgammon, most of which share common traits...
player, spending hours playing the game in the common room. He was awarded his doctorate in 1964 and was appointed as College Fellow and Lecturer in Mathematics at the University of Cambridge
University of Cambridge
The University of Cambridge is a public research university located in Cambridge, United Kingdom. It is the second-oldest university in both the United Kingdom and the English-speaking world , and the seventh-oldest globally...
.
He left Cambridge in 1986 to take up the appointment to the John von Neumann
John von Neumann
John von Neumann was a Hungarian-American mathematician and polymath who made major contributions to a vast number of fields, including set theory, functional analysis, quantum mechanics, ergodic theory, geometry, fluid dynamics, economics and game theory, computer science, numerical analysis,...
Chair of Mathematics at Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
.
Conway resides in Princeton, New Jersey
Princeton, New Jersey
Princeton is a community located in Mercer County, New Jersey, United States. It is best known as the location of Princeton University, which has been sited in the community since 1756...
. He has seven children by various marriages, three grandchildren and three great-grand children. He has been married three times; his first wife was Eileen, and his second wife was Larissa. He has been married to his third wife, Diana, since 2001.
Combinatorial game theory
Among amateur mathematicians, he is perhaps most widely known for his contributions to combinatorial game theoryCombinatorial game theory
Combinatorial game theory is a branch of applied mathematics and theoretical computer science that studies sequential games with perfect information, that is, two-player games which have a position in which the players take turns changing in defined ways or moves to achieve a defined winning...
(CGT), a theory of partisan game
Partisan game
In combinatorial game theory, a game is partisan or partizan if it is not impartial. That is, some moves are available to one player and not to the other.Most games are partisan; for example, in chess, only one player can move the white pieces....
s. This he developed with Elwyn Berlekamp
Elwyn Berlekamp
Elwyn Ralph Berlekamp is an American mathematician. He is a professor emeritus of mathematics and EECS at the University of California, Berkeley. Berlekamp is known for his work in information theory and combinatorial game theory....
and Richard Guy, and with them also co-authored the book Winning Ways for your Mathematical Plays
Winning Ways for your Mathematical Plays
Winning Ways for your Mathematical Plays by Elwyn R. Berlekamp, John H. Conway, and Richard K. Guy is a compendium of information on mathematical games...
. He also wrote the book On Numbers and Games
On Numbers and Games
On Numbers and Games is a mathematics book by John Horton Conway. The book is a serious mathematics book, written by a pre-eminent mathematician, and is directed at other mathematicians...
(ONAG) which lays out the mathematical foundations of CGT.
He is also one of the inventors of sprouts
Sprouts (game)
Sprouts is a pencil-and-paper game with interesting mathematical properties. It was invented by mathematicians John Horton Conway and Michael S. Paterson at Cambridge University in 1967.- Rules :...
, as well as philosopher's football
Phutball
Phutball is a two-player board game described in Elwyn Berlekamp, John Horton Conway, and Richard Guy's Winning Ways for your Mathematical Plays.- Rules :...
. He developed detailed analyses of many other games and puzzles, such as the Soma cube
Soma cube
The Soma cube is a solid dissection puzzle invented by Piet Hein in 1933 during a lecture on quantum mechanics conducted by Werner Heisenberg. Seven pieces made out of unit cubes must be assembled into a 3x3x3 cube...
, peg solitaire
Peg solitaire
Peg 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 simply as Solitaire in the United Kingdom where the card games are called Patience...
, and Conway's soldiers
Conway's Soldiers
Conway's Soldiers or the checker-jumping problem is a one-person mathematical game or puzzle devised and analyzed by mathematician John Horton Conway in 1961. A variant of peg solitaire, it takes place on an infinite checkerboard. The board is divided by a horizontal line that extends indefinitely...
. He came up with the angel problem
Angel problem
The angel problem is a question in game theory proposed by John Horton Conway. The game is commonly referred to as the Angels and Devils game. The game is played by two players called the angel and the devil. It is played on an infinite chessboard...
, 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
Donald Knuth
Donald Ervin Knuth is a computer scientist and Professor Emeritus at Stanford University.He is the author of the seminal multi-volume work The Art of Computer Programming. Knuth has been called the "father" of the analysis of algorithms...
. He also invented a nomenclature for exceedingly large numbers, the Conway chained arrow notation
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 → 3 → 4 → 5 → 6.As with most...
. Much of this is discussed in the 0th part of ONAG.
He is also known for the invention of the Game of Life
Conway's Game of Life
The Game of Life, also known simply as Life, is a cellular automaton devised by the British mathematician John Horton Conway in 1970....
, one of the early and still celebrated examples of a cellular automaton
Cellular automaton
A cellular automaton is a discrete model studied in computability theory, mathematics, physics, complexity science, theoretical biology and microstructure modeling. It consists of a regular grid of cells, each in one of a finite number of states, such as "On" and "Off"...
. His early experiments in that field were done with pen and paper, long before personal computers existed.
Geometry
In the mid-1960s with Michael Guy, son of Richard Guy, he established that there are sixty-four convex uniform polychoraUniform polychoron
In geometry, a uniform polychoron is a polychoron or 4-polytope which is vertex-transitive and whose cells are uniform polyhedra....
excluding two infinite sets of prismatic forms. They discovered the grand antiprism
Grand antiprism
In geometry, the grand antiprism or pentagonal double antiprismoid is a uniform polychoron bounded by 320 cells: 20 pentagonal antiprisms, and 300 tetrahedra. It is an anomalous, non-Wythoffian uniform polychoron, discovered in 1965 by Conway and Guy.- Alternate names :* Pentagonal double...
in the process, the only non-Wythoffian uniform polyhedron. Conway has also suggested a system of notation dedicated to describing polyhedra called Conway polyhedron notation
Conway polyhedron notation
Conway polyhedron notation is used to describe polyhedra based on a seed polyhedron modified by various operations.The seed polyhedra are the Platonic solids, represented by their first letter of their name ; the prisms , antiprisms and pyramids...
.
He extensively investigated lattices in higher dimensions, and determined the symmetry group of the Leech lattice
Leech lattice
In mathematics, the Leech lattice is an even unimodular lattice Λ24 in 24-dimensional Euclidean space E24 found by .-History:Many of the cross-sections of the Leech lattice, including the Coxeter–Todd lattice and Barnes–Wall lattice, in 12 and 16 dimensions, were found much earlier than...
.
Geometric topology
Conway's approach to computing the Alexander polynomialAlexander 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...
of knot theory involved skein relation
Skein relation
A central question in the mathematical theory of knots is whether two knot diagrams represent the same knot. One tool used to answer such questions is a knot polynomial which is an invariant of the knot. If two diagrams have different polynomials, they represent different knots. The reverse may not...
s, 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 polynomial
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 introduced by J. W...
s. Conway further developed tangle theory and invented a system of notation for tabulating knots, nowadays known as Conway notation
Conway notation (knot theory)
In knot theory, Conway notation, invented by John Horton Conway, is a way of describing knots that makes many of their properties clear. It composes a knot using certain operations on tangles to construct it.-Tangles:...
, while completing the knot tables up to 10 crossings.
Group theory
He worked on the classification of finite simple groupsClassification of finite simple groups
In mathematics, the classification of the finite simple groups is a theorem stating that every finite simple group belongs to one of four categories described below. These groups can be seen as the basic building blocks of all finite groups, in much the same way as the prime numbers are the basic...
and discovered the Conway group
Conway group
In mathematics, the Conway groups Co1, Co2, and Co3 are three sporadic groups discovered by John Horton Conway.The largest of the Conway groups, Co1, of order...
s. He was the primary author of the ATLAS of Finite Groups
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 , published in December 1985 by Oxford University Press and reprinted with corrections in 2003...
giving properties of many finite simple groups. He, along with collaborators, constructed the first concrete representations of some of the sporadic group
Sporadic group
In the mathematical field of group theory, a sporadic group is one of the 26 exceptional groups in the classification of finite simple groups. A simple group is a group G that does not have any normal subgroups except for the subgroup consisting only of the identity element, and G itself...
s. More specifically, he discovered three sporadic groups based on the symmetry of the Leech lattice
Leech lattice
In mathematics, the Leech lattice is an even unimodular lattice Λ24 in 24-dimensional Euclidean space E24 found by .-History:Many of the cross-sections of the Leech lattice, including the Coxeter–Todd lattice and Barnes–Wall lattice, in 12 and 16 dimensions, were found much earlier than...
, which have been designated the Conway groups.
With Simon P. Norton
Simon P. Norton
Simon Phillips Norton is a mathematician in Cambridge, England, who works on finite simple groups. He constructed the Harada–Norton group, and in 1979 together with John Conway proved there is a connection between the Monster group and the j-function in number theory. They dubbed this monstrous...
he formulated the complex of conjectures relating the monster group
Monster group
In the mathematical field of group theory, the Monster group M or F1 is a group of finite order:...
with modular functions, which was named monstrous moonshine
Monstrous moonshine
In mathematics, monstrous moonshine, or moonshine theory, is a term devised by John Horton Conway and Simon P. Norton in 1979, used to describe the connection between the monster group M and modular functions .- History :Specifically, Conway and Norton, following an initial observationby John...
by them.
Number theory
As a graduate student, he proved the conjectureWaring's problem
In number theory, Waring's problem, proposed in 1770 by Edward Waring, asks whether for every natural number k there exists an associated positive integer s such that every natural number is the sum of at most s kth powers of natural numbers...
by Edward Waring
Edward Waring
Edward Waring was an English mathematician who was born in Old Heath , Shropshire, England and died in Pontesbury, Shropshire, England. 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...
that every integer could be written as the sum of 37 numbers, each raised to the fifth power, though Chen Jingrun
Chen Jingrun
Chen Jingrun was a Chinese mathematician who made significant contributions to number theory.- Personal life :Chen was the third son in a large family from Fuzhou, Fujian, China. His father was a postal worker. Chen Jingrun graduated from the Mathematics Department of Xiamen University in 1953...
solved the problem independently before the work could be published.
Algebra
He has also done work in algebra, particularly with quaternionQuaternion
In mathematics, the quaternions are a number system that extends the complex numbers. They were first described by Irish mathematician Sir William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space...
s. Together with Neil James Alexander Sloane
Neil Sloane
Neil James Alexander Sloane is a British-U.S. mathematician. His major contributions are in the fields of combinatorics, error-correcting codes, and sphere packing...
, he invented the system of icosians.
Algorithmics
For calculating the day of the weekCalculating the day of the week
This article details various mathematical algorithms to calculate the day of the week for any particular date in the past or future.A typical application is to calculate the day of the week on which someone was born or some other special event occurred....
, 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
Finite state machine
A finite-state machine or finite-state automaton , or simply a state machine, is a mathematical model used to design computer programs and digital logic circuits. It is conceived as an abstract machine that can be in one of a finite number of states...
s.
Theoretical physics
In 2004, Conway and Simon B. KochenSimon B. Kochen
Simon Bernhard Kochen is an American mathematician, working in the fields of model theory, number theory and quantum mechanics....
, another Princeton mathematician, proved the Free will theorem
Free will theorem
The free will theorem of John H. Conway and Simon B. Kochen states that, if we have a certain amount of "free will", then, subject to certain assumptions, so must some elementary particles. Conway and Kochen's paper was published in Foundations of Physics in 2006.-Axioms:The proof of the theorem...
, a startling version of the No Hidden Variables
Hidden variable theory
Historically, in physics, hidden variable theories were espoused by some physicists who argued that quantum mechanics is incomplete. These theories argue against the orthodox interpretation of quantum mechanics, which is the Copenhagen Interpretation...
principle of Quantum Mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
. 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
Free will
"To make my own decisions whether I am successful or not due to uncontrollable forces" -Troy MorrisonA pragmatic definition of free willFree will is the ability of agents to make choices free from certain kinds of constraints. The existence of free will and its exact nature and definition have long...
, then so do elementary particles."
Books
He has (co-)written several books including the ATLAS of Finite GroupsATLAS 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 , published in December 1985 by Oxford University Press and reprinted with corrections in 2003...
, Regular Algebra and Finite Machines, Sphere Packings, Lattices and Groups, The Sensual (Quadratic) Form, On Numbers and Games
On Numbers and Games
On Numbers and Games is a mathematics book by John Horton Conway. The book is a serious mathematics book, written by a pre-eminent mathematician, and is directed at other mathematicians...
, Winning Ways for your Mathematical Plays
Winning Ways for your Mathematical Plays
Winning Ways for your Mathematical Plays by Elwyn R. Berlekamp, John H. Conway, and Richard K. Guy is a compendium of information on mathematical games...
, 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
Atlanta, Georgia
Atlanta is the capital and most populous city in the U.S. state of Georgia. According to the 2010 census, Atlanta's population is 420,003. Atlanta is the cultural and economic center of the Atlanta metropolitan area, which is home to 5,268,860 people and is the ninth largest metropolitan area in...
, and in summer 2008 published The Symmetries of Things with Chaim Goodman-Strauss and Heidi Burgiel.
Further reading
- Guy, Richard K.Richard K. GuyRichard Kenneth Guy is a British mathematician, Professor Emeritus in the Department of Mathematics at the University of Calgary....
, "Conway's Prime Producing Machine", Mathematics Magazine, Vol. 56, No. 1 (Jan., 1983), pp. 26-33, Mathematical Association of America
External links
by O'Connor and Robertson- Charles Seife, "Impressions of Conway", The Sciences
- Mark Alpert, "Not Just Fun and Games", Scientific American April 1999. (official online version; 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
- John Conway: "Free Will and Determinism in Science and Philosophy" (Video Lectures)http://www.princeton.edu/WebMedia/flash/lectures/20090420_conway_free_will.shtml
- Video of Conway leading a tour of brickwork patterns in Princeton, lecturing on the ordinals, and lecturing on sums of powers and Bernoulli numbers.
- Photos of John Horton Conway
- "Bibliography of John H. Conway" - Princeton University, Mathematics Department