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.
Among amateur mathematicians, he is perhaps most widely known for his combinatorial game theory and for the invention of the game of life. He is also one of the inventors of sprouts, as well as philosopher's football, and he developed detailed analyses of many other games and puzzles, such as the Soma cube. He came up with the still unsolved 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.
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.
He has (co-)written several books including the Atlas of Finite Groups, 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.
- O'Connor, John J., and Edmund F. Robertson. "John Conway". MacTutor History of Mathematics archive. by O'Connor and Robertson
- Mark Alpert, "Not Just Fun and Games", Scientific American April 1999. online version
- Jasvir Nagra, "Conway's Proof Of The Free Will Theorem"