Richard K. Guy turns 100

Richard Guy. Photo Copyright Colm Mulcahy.

Richard K. Guy has long reached an age when most people would be sitting back having left work behind for a few decades, but he's still very active mathematically as he turns 100 on Friday, Sep 30, 2016. Until just a few years ago he was also a keen hiker. (The Alpine Club of Canada has published a wonder account of his life called Young at Heart.) The photo to the right, taken in New York City in August 2015, shows him wearing his trademark "Peace is a disarming concept" button.

A few years ago he was quoted as saying, "I clearly look like and old man and I no doubt behave like an old man but I feel like a kid." As former MAA President Ron Graham notes, "Richard is quite a guy!" Many Canadian institutions are celebrating Richard Guy Day with relevant lectures this month.

Richard was born in Nuneaton, Warwickshire, England on Saturday, September 30, 1916. He reportedly came home from his first day at kindergarten to tell his parents, "The teacher doesn't know much. She asked me what shape the world was and all sorts of things that I thought she would have known."

Following a BA (1938) and MA (1941) from Cambridge, Richard taught at various levels for over two decades, including stints in Singapore and India. He finally settled down in the early 1960s, at the University of Calgary in Alberta. His main interests are geometry, combinatorics and number theory, as well as chess and numerous other games. He's also a great believer in the value of recreational mathematics.

Richard's extensive list of publications includes many books, most famously Unsolved Problems in Number Theory (Springer, originally 1981, much expanded in later editions), Winning Ways for your Mathematical Plays (Academic Press, with Berkekamp & Conway, 1982, originally two volumes and now expanded to four), and Unsolved Problems in Geometry (Springer, with Croft & Falconer, 1994). Richard is also well known for his Strong Law of Small Numbers observation from the 1980s: "There aren't enough small numbers to meet the many demands made of them"!

Richard discussing triangle geometry with John H. Conway at the 2016 Gathering for Gardner in Atlanta.
Photo Copyright Colm Mulcahy.

"Writing with Richard was continual hilarity" recalls Conway. In recent years, as already reported by the MAA, he's been giving talks on new aspects of triangle geometry that reflect fresh research of his, using the provocative title "A Triangle Has Eight Vertices (But Only One Centre)." When he gave it at MoMath's MOVES conference, Aug 2015, his friend and co-author John H. Conway was heard to shout out, "That's beautiful, Richard!"

At the end of some of these talks, Richard has led a spirited singalong to the tune of "My Bonnie Lies Over the Ocean", whose chorus goes "Bring back that ge-om-met-try" (instead of "Bring back my Bonnie to me"). Readers can listen to one of those here.

Now a new song has been launched to mark his centennial, in the form of an imaginary (one-sided) telephone conversation of Richard's with the late Hungarian mathematician Paul Erdős (1913-1996).

"Is There Still News For Me in that Old Geometry" borrows the tune of the 1916 hit "Is There Still Room for Me 'Neath the Old Apple Tree", and is performed by Robert Schneider of indie rock band Apples in stereo, who is currently a PhD student of Ken Ono's at Emory University.

The premise of this affectionate tribute is that Richard is asking Erdős about progress on a geometry problem he's been thinking about since the 1950s. Richard discovered a unistable polyhedron which had 19 faces—see John H. Conway, Michael Goldberg and Richard K. Guy, Problem 66-12, SIAM Review 11 (1969, 78.82)—unistable (or monostatic) shapes in 3D are ones which only sit stably on the plane on one of their many faces. Video of a wobbling model of Richard's discovery may be viewed here. In 2012, Alex Reshetov found such a shape with only 14 faces, and it remains an open question whether one exists with fewer faces. (The Wolfram Demonstrations Project has a Mathematica notebook demo of Reshetov's Unistable Polyhedra with 14, 15, 16, and 17 Faces.)

Elwyn Berlekamp and Richard at the 2016 Gathering for Gardner in Atlanta.
Photo Copyright Colm Mulcahy.

In 2014, Gathering 4 Gardner conducted extensive interviews with Richard, leading to sixteen revealing videos here. In the one on Conway & Gardner, Richard discusses working closely with Conway on the Game of Life cellular automaton, back in 1970, and discovering the glider. He helped to get Martin Gardner interested in the topic, which resulted in a highly influential Scientific American article.

In this video Richard also reveals a little known fact about the end of Gardner's quarter-century column run for that publication, "There was serious consideration given to my taking over the column from him. I'm glad that it didn't happen, because you can't follow Martin Gardner!" In the Numbers, Pictures G4G video, Richard comments about one of the guiding principles of his approach to mathematics, "When I hear a problem, I like to draw a picture, when I can; I have to see the problem." He adds, "I have to actually have some numbers, of some picture, to work with."

Richard has left his mark on chess as well as on many branches of mathematics and game theory. His extensive experience and studies in this arena is reflected in the Guy–Blandford–Roycroft code, a system for representing chess piece positions in endgames.

As for celebrating his own birthday, Richard is once more spending it at his beloved his beloved Mount Assiniboine Provincial Park, home of "the Matterhorn of the Rockies," where he hiked so often with his late wife of seven decades, Louise. Rumour has it that it'll be a repeat of last year's expedition, when he finally got to the summit, by helicopter. "I've never climbed it (there was a failed attempt once)" he recalls wistfully, "But now I can say that I've been within 100 feet of the top!"

Richard Guy on top of the world (The Towers, Mount Assiniboine) at age 90, ten years ago.
Photo Credit: The Guy Family