John Horton Conway

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Lore & Background

Conway was born in Liverpool on 26 December 1937, the son of Cyril Horton Conway and Agnes Boyce. He became interested in mathematics at a very early age, and by age 11 his ambition was to become a mathematician. After sixth form, he studied mathematics at Gonville and Caius College, Cambridge. Describing himself as a 'terribly introverted adolescent' in school, he used his admission to Cambridge as an opportunity to transform into an extrovert, a change that later earned him the nickname 'the world's most charismatic mathematician'. He earned a BA in 1959 and, supervised by Harold Davenport, began research in number theory, solving an open problem on writing numbers as sums of fifth powers. His interest in games began during his Cambridge years, where he became an avid backgammon player. He was awarded his doctorate in 1964 and became a College Fellow and Lecturer at Sidney Sussex College, Cambridge. In 1986 he moved to the United States to hold the John von Neumann Professorship at Princeton University, where he also won the Princeton University Pi Day pie-eating contest.

Reader's Guide

Conway's career was deeply intertwined with that of Martin Gardner. When Gardner featured Conway's Game of Life in his Mathematical Games column in October 1970, it became the most widely read of all his columns and made Conway an instant celebrity. Conway invented the Game of Life, one of the early examples of a cellular automaton, initially experimenting with pen and paper long before personal computers existed. The game is known to be Turing complete. Conway contributed to combinatorial game theory, co-authoring the book Winning Ways for your Mathematical Plays with Elwyn Berlekamp and Richard Guy, and writing On Numbers and Games, which lays out the mathematical foundations of the field. He invented the surreal numbers and the Conway chained arrow notation for exceedingly large numbers. In geometry, he established with Michael Guy that there are sixty-four convex uniform polychora and discovered the grand antiprism. He devised the Conway criterion for tessellations and investigated the Leech lattice, determining its symmetry group and discovering three sporadic groups now called the Conway groups. In knot theory, he formulated the Conway polynomial and developed tangle theory and the Conway notation for tabulating knots. He also invented the Doomsday algorithm for calculating the day of the week. Conway died on 11 April 2020 at age 82 from complications of COVID-19.

Did You Know?

• Conway could calculate the day of the week for any date in under two seconds using his Doomsday algorithm.
• He won the Princeton University Pi Day pie-eating contest after moving there in 1986.
• Conway and Simon B. Kochen proved the free will theorem in 2004, stating that if experimenters have free will, then so do elementary particles.
• He invented the base 13 function as a counterexample to the converse of the intermediate value theorem.
• Conway discovered three sporadic groups based on the symmetry of the Leech lattice, now called the Conway groups.