# John Horton Conway

## Synopsis

Born in England in 1937, John Horton Conway began his mathematics career at Cambridge University. By the 1970s, he was known for his discoveries of the Leech lattice symmetry group and surreal numbers, along with his creation of the Game of Life. Conway later moved to a high-profile position at Princeton University, where he continued his pursuits in such areas as sphere packing, game theory and theoretical physics.

## Early Years and Education

John Horton Conway was born on December 26, 1937, in Liverpool, England. The third child of parents Agnes and Cyril, Horton demonstrated remarkable math prowess early in his life; by age 4, he was reciting the powers of 2.

Aiming to become a mathematician at the University of Cambridge, Conway was a star math pupil at Liverpool's Holt High School for Boys. However, he was also a painfully shy introvert. After being accepted to Cambridge, the school of his dreams, he decided to overcome his social inhibitions and developed a more outgoing personality.

Conway earned his B.A. in mathematics at Cambridge's Gonville and Caius College in 1959, and embarked on graduate studies in number theory. During this time he married his first wife, teacher Eileen Howe, and developed his longtime interest in games. Upon earning his doctorate in 1964, he was named lecturer in pure mathematics at Cambridge and earned a fellowship at Sidney Sussex College.

## Conway Group and Other Discoveries

Known for his entertaining lectures, Conway nevertheless felt he was accomplishing very little and worried about his job security. That changed when he was confronted with the yet-undetermined symmetry group of the Leech Lattice, a 24-dimensional packing of spheres discovered by the University of Stirling's John Leech. Conway calculated the number of symmetries to be 8,315,553,613,086,720,000 and uncovered three sporadic simple groups. His findings of what was termed the Conway group were published in the *Bulletin of the London Mathematical Society* in 1969.

Thus began what Conway termed his "annus mirabilis," a year of groundbreaking discoveries that transformed him into a rock star mathematician. His fascination with games led to his proudest achievement, the realization of a continuum of real, infinite and infinitesimal numbers that became known as surreal numbers. Around this time he also developed the Game of Life, one of the first cellular automatons, and in 1973 introduced his Doomsday Algorithm, which determined the day of the week for any date in time via the Gregorian calendar.

Conway was honored with the London Mathematical Society's Berwick Prize in 1971, and in 1981 he was named a fellow at the esteemed Royal Society of London. In between, he was promoted from lecturer to reader in pure mathematics at Cambridge, gaining more celebrity for his electric presentations and game inventions. He also wrote his first book, *On Numbers and Games* (1976), later following with the popular *Winning Ways for Your Mathematical Plays* (1982). In 1983, Conway was officially appointed professor of mathematics at Cambridge.

## Princeton and Later Years

The 1980s was a decade of transition for Conway, along with more prolific output. He married a second time, to fellow mathematician Larissa Queen, and left Cambridge for the position of John von Neumann chair of mathematics at Princeton University. Following some 15 years of development, the *ATLAS of Finite Groups* was published in 1985 and became one of the definitive works on group theory. In addition, Conway earned a patent with AT&T mathematician Neil Sloane for applying sphere packing theory to telecommunications.

Conway underwent a difficult period in the early 1990s, marked by another divorce, a heart attack and a suicide attempt. He recovered to pen *The Book of Numbers* in 1996 with the University of Calgary's Richard Guy, and won a series of awards over the following years. In 2001, he married his third wife, Diana.

Slowed by a stroke in 2006, Conway nevertheless continued his intellectual pursuits. That year he and Princeton colleague Simon B. Kochen published their free will theorem, essentially stating that if people have free will, then elementary particles have free will as well. He also co-authored the book *Symmetries of Things* (2008), and collaborated on several projects with Alex Ryba of the City University of New York's Queens College.

Conway stepped down from his longtime position at Princeton in 2013, but he remains a professor emeritus and an outsized presence at the Ivy League school. His celebrated career and eccentricities were profiled in the 2015 biography *Genius At Play: The Curious Mind of John Horton Conway*, by Siobhan Roberts.

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