John Horton Conway

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John Horton Conway

Born	December 26, 1937 Liverpool, England
Residence	USA
Nationality	English
Field	Mathematician
Institution	Princeton University
Alma mater	University of Cambridge
Academic advisor	Harold Davenport
Notable students	Richard Borcherds Robert Wilson
Known for	Game of life , Look-and-say sequence
Notable prizes	Polya Prize (1987)

John Horton Conway (born December 26, 1937, Liverpool, England) 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 Game of Life (the cellular automata, not the board game).

Conway is currently professor of mathematics at Princeton University. He studied at Cambridge, where he started research under Harold Davenport. He has an Erdős number of one. He received the Berwick Prize (1971), was elected a Fellow of the Royal Society (1981), and was the first recipient of the Pólya Prize (LMS) (1987).

Contents 1 Biography 2 Game theory 3 Geometry 4 Geometric topology 5 Group theory 6 Algorithmics 7 Theoretical physics 8 Books 9 See also 10 External links and references

[edit] Biography

Conway's parents were Agnes Boyce and Cyril Horton Conway. John had two older sisters, Sylvia and Joan. Cyril Conway was a chemistry laboratory assistant. John became interested in mathematics at a very early age and his mother Agnes recalled that he could recite the powers of two when aged four years. John's young years were difficult for he grew up in Britain at a time of wartime shortages. At primary school John was outstanding and he topped almost every class. 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 Lecturer in Study at the University of Cambridge.

Conway has been married to wife Diana since 2001 and has a son Gareth (b. 2001). Their home is in Princeton, New Jersey, United States. With previous wives he has sons Oliver (b. 1988) and Alex (b. 1983); daughters Susan (b. 1962), (Rose b. 1963), Elena (b. 1965) and Ann-Louise (b. 1968). He has three grandchildren: John, Ellen and Joseph Wayman. .

[edit] Game theory

Among amateur mathematicians, he is perhaps most widely known for his contributions to combinatorial game theory, a theory of partisan games. This he developed with Elwyn Berlekamp and Richard Guy.

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, and peg solitaire. He came up with the just recently (2006) solved Angel problem.

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.

He is also known for the invention of the Game of Life, one of the early and still celebrated examples of a cellular automaton.

[edit] Geometry

In the mid-1960s with Michael Guy, son of Richard Guy, he established that there are sixty-four convex uniform polychora excluding two infinite sets of prismatic forms. Conway has also suggested a system of notation dedicated to describing polyhedra called Conway polyhedron notation.

[edit] Geometric topology

Conway's approach to computing the Alexander polynomial of knot theory, in a variant now called the Alexander-Conway polynomial, involved a skein relation. After lying dormant for more than a decade, this concept became central to work in the 1980s on the novel knot polynomials. Conway further developed tangle theory and invented a system of notation for tabulating knots.

[edit] Group theory

He worked on the classification of finite simple groups and discovered the Conway groups. He was the primary author of the Atlas of Finite Groups giving properties of many finite simple groups. He with collaborators constructed the first concrete representations of some of the sporadic groups.

With Simon Norton he formulated the complex of conjectures relating the monster group with modular functions, which was christened monstrous moonshine by them.

[edit] Algorithmics

For calculating the day of the week, he invented the Doomsday algorithm. The algorithm is simple enough for Conway to do the calculations in his head. He 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 machines.

[edit] Theoretical physics

In 2004, Conway and Simon Kochen, 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 (that almost every physicist agrees are true), 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. Or, in Conway's provocative wording, if experimenters have free will, then so do elementary particles.

[edit] Books

He has (co-)written several books including the Atlas of Finite Groups, 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.

[edit] See also

• Conway polyhedron notation
• Conway's LUX method for magic squares
• Conway's orbifold notation
• Conway chained arrow notation
• Conway's Game of Life
• Phutball
• Look-and-say sequence
• 15 theorem
• Conway's thrackle conjecture

[edit] External links and references

• O'Connor, John J., and Edmund F. Robertson. "John Horton Conway". MacTutor History of Mathematics archive. 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" [1]
• Conway, J. H.; Curtis, R. T.; Norton, S. P.; Parker, R. A.; and Wilson, R. A.: "Atlas of Finite Groups: Maximal Subgroups and Ordinary Characters for Simple Groups." Oxford, England 1985.
• John Horton Conway at the Mathematics Genealogy Project
• 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

Persondata
NAME	Conway, John Horton
ALTERNATIVE NAMES
SHORT DESCRIPTION	Mathematician
DATE OF BIRTH	December 26, 1937
PLACE OF BIRTH	Liverpool, England
DATE OF DEATH
PLACE OF DEATH