John Horton Conway

Obituary John Horton Conway (1937–2020) Playful master of games who transformed mathematics. ohn Horton Conway was one of the Monstrous Moonshine conjectures. These, most versatile mathematicians of the for the first time, seriously connected finite past century, who made influential con- symmetry groups to analysis — and thus dis- tributions to group theory, analysis, crete maths to non-discrete maths. Today, topology, number theory, geometry, the Moonshine conjectures play a key part Jalgebra and combinatorial game theory. His in physics — including in the understanding deep yet accessible work, larger-than-life of black holes in string theory — inspiring a personality, quirky sense of humour and wave of further such discoveries connecting ability to talk about mathematics with any and algebra, analysis, physics and beyond. all who would listen made him the centre of Conway’s discovery of a new knot invariant attention and a pop icon everywhere he went, — used to tell different knots apart — called the among mathematicians and amateurs alike. Conway polynomial became an important His lectures about numbers, games, magic, topic of research in topology. In geometry, he knots, rainbows, tilings, free will and more made key discoveries in the study of symme- captured the public’s imagination. tries, sphere packings, lattices, polyhedra and Conway, who died at the age of 82 from tilings, including properties of quasi-periodic complications related to COVID-19, was a tilings as developed by Roger Penrose. lover of games of all kinds. He spent hours In algebra, Conway discovered another in the common rooms of the University of important system of numbers, the icosians, Cambridge, UK, and Princeton University with his long-time collaborator Neil Sloane. DITH PRAN/NYT/REDUX/EYEVINE in New Jersey playing backgammon, Go and In number theory, Conway showed that every other diversions, some of his own creation. chemistry laboratory technician at a local high whole number is the sum of at most 37 fifth Several of Conway’s most celebrated contribu- school attended by George Harrison and Paul powers. He also developed the 15-theorem tions were made while he was thinking about McCartney. Conway, like his mother, was an (with his student William Schneeberger) and games and their strategies. Perhaps his great- avid reader. He showed early interests in math- the 290-conjecture; these were vast general- est discovery was a surprising correspondence ematics; by the age of 11, he wanted to be a izations of the four-squares theorem, proved between numbers and games that led him to mathematician at Cambridge. He received his by eighteenth-century mathematician Joseph- a truly gigantic system, the surreal numbers, PhD from the University of Cambridge in 1964 Louis Lagrange, which states that every positive which stunned the mathematics community. under the advisership of Harold Davenport, whole number is the sum of four square num- It contained not only the positive and negative was subsequently hired at Cambridge as a lec- bers (for example, 21 is the sum of 16, 4, 1 and 0). real numbers that we all know, but also new turer, and became professor in 1983. In 1987, Conway was a memorable teacher and infinitely large numbers, infinitesimally small he moved to Princeton. speaker, and the many tricks he performed ones, and all sorts of new numbers in between. to illustrate mathematical concepts included: Conway’s work on surreal numbers emerged “His lectures about numbers, stating immediately the day of the week for from the influential research project and book any date in history, twirling a hanger with a Winning Ways for your Mathematical Plays games, magic, knots, penny balanced on its inside edge, contorting (1982), a compendium of information on the rainbows and more captured his tongue into a variety of shapes, balancing theory of games, written with Elwyn Berlekamp the public’s imagination.” objects on his chin, and delivering entire lec- and Richard Guy. This fascination with games tures in which every word he said had only also led Conway to develop the Game of Life, one syllable. a cellular automaton in which the pattern of Conway first attained fame in 1968 for He loved to talk about mathematics and live or dead cells in a two-dimensional grid determining all 8,315,553,613,086,720,000 games, as well as history, etymology and evolves according to a set of rules for the ‘birth’ symmetries of the Leech lattice — a remark- philosophy. His contributions to culture, and ‘death’ of each cell, based on the status of ably regular arrangement of points in through his work and outreach, will have a last- its nearest neighbours. The simplicity and 24-dimensional space discovered by John ing impact. For the remarkable profundity of accessibility of this game was popularized in Leech in 1967. This led to his discovery of the his mathematical discoveries — and the playful 1970 by Scientific American columnist Martin Conway simple groups, which were funda- and generous way in which he shared these Gardner. By the mid-1970s, it was estimated that mental in the classification of finite simple with others — he will be sorely missed. one-quarter of the world’s computers were run- groups — one of the capstone achievements ning Conway’s Game of Life as their screensaver. of twentieth-century mathematics. Manjul Bhargava is the R. Brandon Fradd Conway, who was the John von Neumann Conway had a primary role in researching professor of mathematics at Princeton professor of mathematics at Princeton and assembling the iconic symmetry book University, New Jersey, USA. He was a first-year University before his retirement in 2013, was ATLAS of Finite Groups (1985). His deep graduate advisee, and later colleague, of John born in Liverpool, UK, in 1937. His father made knowledge of symmetries led him to propose, H. Conway at Princeton. his living playing cards, and later worked as a with his ATLAS co-author Simon Norton, the e-mail: [email protected] Nature | Vol 582 | 4 June 2020 | 27 ©2020 Spri nger Nature Li mited. All rights reserved. .

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