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Remembering Richard K. Guy and John Horton Conway

Don Albers remembers mathematical luminaries Richard K. Guy and John Horton Conway and introduces an article collection to further explore their work. 

In the space of six weeks over March and April of 2020, the mathematical world lost John Horton Conway and Richard K. Guy — two of its luminaries.  I knew John for 29 years and Richard for 40 years. The combined span of their interests, expertise in several areas, and impressive number of results was reinforced by strong friendship. They both loved to tell others in and out of the classroom about wonderful problems in geometry, number theory, combinatorics, and especially games. I had the pleasure of observing them teach undergraduates at Princeton and Calgary, respectively. Their enthusiasm for teaching was abundantly clear.

It’s hard to remember any dull moments with either of them. They even seemed to enjoy conducting one-person classes, with me being the student. I recall one visit to John’s office, which over the years seemed to migrate to the lounge of the Math Department Office. During his first years at Princeton he had two facing offices on the ground floor. One was full of what might some describe as toys hanging from the ceiling – geometric solids formed from colored paper, tennis balls, and colored ropes which he had passing undergraduates use to do a special Conway designed  “square dance” and in the process learn about the “theory of tangles”.

The facing office had a large table in one corner covered with FedEx packages to a height of about three feet. I looked at them, and said to John, “None of these packages seem to be opened”. He responded, “I’m afraid if I open anyone of them, the sender will want me to do something”. I said, “I’m pretty sure that one of them is from me, asking you to make corrections to the manuscript of The Sensual Quadratic Form, a book that I signed you to write four years ago” . The main reason that I was in Princeton that day was to sit down with John and work through the manuscript page by page.

I signed John to write The Sensual Quadratic Form over dinner at the Joint AMS/MAA summer meeting in Orono, Maine in 1991. John had given the Hedrick Lectures, which were a big hit. It was my good fortune to be seated across the dinner table from him following the last lecture. I complimented him on his lectures, and told him that they would make an excellent Carus Mathematical Monograph, the MAA’s premier book series. He seemed interested, so I told him that I could write a contract with him on my table napkin right now. He seemed to like the idea of a contract on a table napkin. Then he hesitated, and said “I’ll need some help with proof reading and other details”. I responded, “No problem, I’ve got just the right person for you seated next to me. Meet Francis Fung, who will be a graduate student in mathematics at Princeton in a few weeks”. John agreed, and Francis went on earn his Ph.D. with John as his advisor.

On another visit to meet with John, we were to walk across campus to lunch. Before leaving his office in the Lounge, I asked him about a graph theory problem. He quickly answered my question, and then for the next hour he filled up several whiteboards with a dazzling array of extensions and generalizations to my question. He simply enjoyed the question and was eager to share his pleasure in carrying out generalizations on the spot. John was clearly a happy showman who delivered the goods. It’s easy to see why he was so often tapped to teach freshman mathematics at Princeton. He possessed great ability to attract them to mathematics, and that was a boon to the department. John possessed great mathematical power and insight as borne out by his discovery of the Conway Group, the Game of Life, and Surreal Numbers, which stand out as accomplishments of the first magnitude.

Richard’s great writing skills and ability to work well with Conway can be seen in vivid detail in their joint authorship with Berklekamp in The Book of Numbers, and with Elwyn R. Berlekamp and Conway in the three volume opus Winning Ways for Your Mathematical Plays, which Martin Gardner described as “the greatest contribution to recreational mathematics in the 20th century”. In addition to several books, Richard wrote over 300 papers, several of which won prizes. Paul Erdos, Donald Knuth, John Selfridge, Kenneth Falconer, Frank Harary, Bela Bollobas, and Neil Sloane were among his many collaborators. Richard was a master teacher, who carried in his head a vast collection of solved and unsolved problems in geometry, number theory, geometry, games, and combinatorics. If you asked him about a problem, he would happily bring you up to date on solutions and attempted solutions, often over dinner.

In 1992, early in my tenure as MAA Director of Publications, Richard summoned me to Calgary to help finish The Lighter Side of Mathematics, a lovely manuscript on recreational mathematics. I arrived to find him and John Selfridge poring over the manuscript and arguing with gusto about the finer points of English usage. Richard, born and bred in England, the son of a headmaster and headmistress, and a graduate of Cambridge, not surprisingly insisted on following Fowler’s A Dictionary of English Usage.

Selfridge, a native of Alaska with his Ph.D. from UCLA, disagreed. After an hour of observing and being asked for my opinion, I became worried about finishing. I finally said as diplomatically as possible, “This book is being published by an American publisher and aimed at the American market.”Four days later, we finished, and on my last full day in Alberta, Richard and I went hiking in the beautiful mountains surrounding Lake Louise. Although I was 26 years younger than Richard, he provided me with a humbling demonstration of power hiking. Let’s just say that he left me in the dust. I fell far behind him, and was thoroughly exhausted when I got back to the car where I found him napping. He woke up, and said “You’re driving us back.” Over the years on other hikes with him and his wife, Louise, my standing did not improve.

I hope that you enjoy the articles provided in this special digital issue which provides more details about the lives and work of John Horton Conway and Richard K. Guy, truly remarkable mathematicians.

Don Albers
Former MAA Associate Executive Director and Director of Publications

Richard K. Guy

Article Title Author(s)Journal Volume Issue
The Strong Law of Small NumbersRichard K. Guy The American Mathematical Monthly958
Nothing's New in Number Theory?Richard K. Guy The American Mathematical Monthly10510
What's Left?Richard K. Guy Math Horizons54
John Horton Conway: Mathematical MagusRichard K. Guy The Two-Year College Mathematics Journal135
Conway's Subprime Fibonacci SequencesRichard K. Guy,
Tanya Khovanova,
Julian Salazar
Mathematics Magazine875
Conway's Prime Producing MachineRichard K. Guy Mathematics Magazine561
A Quarter Century of Monthly Unsolved Problems, 1969–1993Richard K. GuyThe American Mathematical Monthly10010
A Conversation with Richard K. GuyDonald J. Albers & Gerald L. AlexandersonThe College Mathematics Journal 242

John Horton Conway

Article Title Author(s)Journal Volume Issue
On Unsettleable Arithmetical ProblemsJohn ConwayThe American Mathematical Monthly1203
Symmetrically Bordered SurfacesWilliam Cavendish & John H. ConwayThe American Mathematical Monthly1177
All Games Bright and BeautifulJohn ConwayThe American Mathematical Monthly846
A Headache-Causing ProblemJohn Conway, M. S. Paterson & USSR MoscowThe American Mathematical Monthly 1274
A Gamut of Game TheoriesJohn H. ConwayMathematics Magazine511
Surreal NumbersJohn Conway & Richard K. GuyMath Horizons42
John Horton Conway—Talking a Good GameDon AlbersMath Horizons12