# John Horton Conway : biography

### Algebra

He has also done work in algebra, particularly with quaternions. Together with Neil James Alexander Sloane, he invented the system of icosian.

### Algorithmics

For calculating the day of the week, 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 machines.

### Theoretical physics

In 2004, Conway and Simon B. 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 finishing *The Triangle Book* written with 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.

## Biography

Conway’s parents were Agnes Boyce and Cyril Horton Conway. He was born in Liverpool. He became interested in mathematics at a very early age and his mother recalled that he could recite the powers of two when he was four years old. 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 four 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.

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