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In Memoriam: John Horton Conway 1937-2020

By Lawrence M. Fisher

April 13, 2020

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Mathematician and Princeton University John von Neumann Professor Emeritus John Horton Conway died April 11 of coronavirus at his home in New Jersey. He was 82.

Princeton neuroscience scientist Sam Wang tweeted that Conway's fever started on the morning of Wednesday April 8; three days later, he died.

"I am sorry to confirm the passing of my colleague John Conway. An incomparable mathematician, a pleasant neighbor, and an excellent coffee acquaintance," Wang tweeted. "Part of coronavirus's hard toll in New Jersey."

Conway was an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory.

His most notable contribution to his field may have been his invention of the Game of Life, which led to the popularization of cellular automaton. Done on pen and paper long before the invention of personal computers, the game became integral for both theoretical interest and practical exercise in data programming and display.

Born in Liverpool, England, Conway became interested in mathematics at a very early age. He attended Gonville and Caius College of Cambridge University to study mathematics, and he was awarded his Bachelor of Arts degree there in 1959. He was awarded his doctorate in 1964, and was appointed College Fellow and Lecturer in Mathematics at Sidney Sussex College, Cambridge. He remained at Cambridge until 1986, when he was appointed to the John von Neumann Chair of Mathematics at Princeton University.

Conway wrote a number of textbooks and did original work in algebra, focusing particularly on quaternions and octonions. Together with mathematician Neil Sloane, he invented the icosians, a set of Hamiltonian quaternions with the same symmetry as the 600-cell.

He invented a base 13 function as a counterexample to the converse of the intermediate value theorem: the function takes on every real value in each interval on the real line, so it has a Darboux property, but is not continuous.

For calculating the day of the week, he invented the Doomsday algorithm, which provides a perpetual calendar because the Gregorian calendar moves in cycles of 400 years.

The Web page for Princeton's Dean of Faculty said that, notwithstanding Horton's "serious chops, John is equally if not more renowned for his persistent playing around, which makes him a great teacher and a wonderful speaker, especially to a general audience. Forever the showman, always seeking the center of attention, he gained a reputation for carrying on his person ropes, pennies, coat hangers, cards, dice, games, puzzles, models, sometimes a Slinky— props deployed to extend his winning and charismatic imagination. In this sense, John is one of his discipline's best ambassadors, bringing mathematics to the masses—be it at summer math camps teaching some of his more trivial and eccentric mathematical inventions to wide-eyed students, or delivering public lectures on Archimedes and Escher and the like to standing-room-only crowds at McCosh Hall. At the drop of a hat, he can also discuss the conversion of the Hebrew calendar to the Roman one, as well as constellations and phases of the moon, the strange etymology of English words (such as "floccinaucinihilipilification"), or the symmetry of brick patterns in walls."

In 2004, Conway and Princeton mathematician Simon B. Kochen proved the free will theorem, writing, "if experimenters have free will, then so do elementary particles."

Yet Conway was perhaps best known for his contributions to combinatorial game theory, a theory of partisan games. In addition to multiple books in this realm, he invented several games (sprouts, philosopher's football (or Phutball), and Conway's soldiers) and developed detailed analyses of many others. He also invented the Game of Life, a zero-player game one interacts with by creating an initial configuration and observing how it evolves; it is Turing complete and can simulate a universal constructor or any other Turing machine.

He formulated the angel problem (also known as the Angels and Devils game), a problem in combinatorial game theory which was solved in 2006. His surreal numbers inspired a mathematical novel by Donald Knuth called "Surreal Numbers," which includes the line: "Conway said to the numbers, 'Be fruitful and multiply'." He also invented a naming system for exceedingly large numbers, the Conway chained arrow notation.

In 1981, when Conway was elected a Fellow of the Royal Society, his nomination described him as "a versatile mathematician who combines a deep combinatorial insight with algebraic virtuosity, particularly in the construction and manipulation of 'off-beat' algebraic structures which illuminate a wide variety of problems in completely unexpected ways.

"He has made distinguished contributions to the theory of finite groups, to the theory of knots, to mathematical logic (both set theory and automata theory) and to the theory of games (as also to its practice)."

Other awards Conway received in his lifetime include the London Mathematical Society's Berwick Prize (1971) and Pólya Prize (1987), Northwestern University's Nemmers Prize in Mathematics (1998), and the American Mathematical Society's Leroy P. Steele Prize for Mathematical Exposition (2000). He was elected a fellow of the Royal Society of London in 1981, and a fellow of the American Academy of Arts and Sciences in 1992.

A biography of Conway ("Genius At Play: The Curious Mind of John Horton Conway") describes him as " a singular mathematician with a lovely loopy brain. He is Archimedes, Mick Jagger, Salvador Dali, and Richard Feynman all rolled into one -- a singular mathematician, with a rock star's charisma, a sly sense of humor, a polymath's promiscuous curiosity, and a burning desire to explain everything about the world to everyone in it."

Stanford University mathematician Persi Diaconis once said in an interview, "John Conway is a genius. And the thing about John is he'll think about anything.… He has a real sense of whimsy. You can't put him in a mathematical box."

Lawrence M. Fisher is Senior Editor/News for ACM Magazines.


David Bendory

I'm trying to find a record of Professor Conway's algorithm for converting between Gregorian dates and the Hebrew calendar, which I understand he could do via mental arithmetic in about 5 seconds.

If anyone knows his algorithm or knows a written version of it, please post here.


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