Everything about John Horton Conway totally explained
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 automaton, 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).
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.
He left Cambridge in 1986 to take up the appointment to the
John von Neumann Chair of Mathematics at
Princeton University. He is also a regular visitor at
Mathcamp and MathPath
(External Link
), summer math programs for high schoolers and middle schoolers, respectively.
Conway resides in Princeton, New Jersey, United States with his wife and youngest son. He has six other children from his two previous marriages and three grandchildren.
Game theory
Among amateur mathematicians, he's 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,
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.
He is also known for the invention of the
Game of Life, one of the early and still celebrated examples of a
cellular automaton.
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.
Geometric topology
Conway's approach to computing the
Alexander polynomial of knot theory involved
skein relations, 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 polynomials. Conway further developed
tangle theory and invented a system of notation for tabulating knots, while completing the knot tables up to 10 crossings.
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.
Algebra
He has also done work in algebra particularly with quaternions.
Algorithmics
For
calculating the day of the week, he invented the
Doomsday algorithm. The algorithm is simple enough for anyone with basic arithemetic 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 machines.
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, 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".
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. He is currently co-writing
The Triangle Book with Steve Sigur, math teacher at Paideia School in Atlanta Georgia, and
The Symmetries of Things with
Chaim Goodman-Strauss and Heidi Burgiel.
Further Information
Get more info on 'John Horton Conway'.
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