Interview with a mathematician: Richard K. Guy

Richard K. Guy is the only mathematician I know working at age 100.

A professor at University of Calgary, Richard is an expert in geometry, number theory, graph theory, and he is especially known for his contributions to combinatorial game theory. A prolific author with over 300 papers, he has worked with the greats such as Paul Erdős, John Conway and Donald Knuth.

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I first met Richard in 1999 at the British Combinatorial Conference in Canterbury. I was struck by how down to earth he was, and how polite and unassuming. While at the NSERC Competition Week this February, Renate Scheidler (a number theorist at the University of Calgary) suggested I interview him. She mentioned that he comes to work every day, often walking from home, and he loves interacting with students (and they adore him). That is the Richard I know by legend, who was and is a great mentor to generations of mathematicians. Besides his mathematical work, he is also an avid hiker and mountain climber.

Richard gave a keynote lecture at the Mathematics of Various Entertaining Subjects (MOVES) conference at the National Museum of Mathematics in New York City in August 2015. His lecture is below, which is quite spectacular coming from a person of any age. My favorite part, and one I’ve never seen before from a mathematician giving a lecture: at 41:30 he breaks out in song!



AB: Your colleague Renate Scheidler mentioned that you come to your office at the University of Calgary every weekday.  Would you describe your typical workday?

RKG: I don’t any longer get in very early.  I work on fairly elementary problems in number theory, combinatorics and Euclidean geometry.  A few graduates and undergraduates drop in to discuss these.

AB: How did you first become interested in studying mathematics at university? Who influenced you to study mathematics as a student?

RKG: At school I was best at chemistry, mathematics, and physics.  The mathematics teacher, Cyril T. Lear Caton, was a strong personality and pushed me that way.

AB: You have been influential in having combinatorial game theory evolve into a full fledge subject in Canada and abroad. Can you describe what combinatorial game theory is for our readers?

RKG: Combinatorial game theory differs from classical game theory in that there are just two players, there is complete information and no chance moves (no dice or tossing coins, etc.)  Examples of a few of these combinatorial games are Go, Chess, and Tic-tac-toe. The study of these and other games led to a mathematical theory which is now a subject in its own right.

Image result for game of go
The game of Go.

AB: Richard Nowakowski described a scene (I think in the 1970s) where he walked by your office at University of Calgary, and you were working on an electromechanical computing machine running on ball bearings. He said it made a lot of noise and that, in part, was how he became interested in your work. What was the machine? What were you computing back then?

RKG: I had two Olivetti 101’s, later 620’s or some such number.  John Selfridge and I were calculating aliquot sequences—and I still am!—in a hopeless pursuit of the Guy-Selfridge conjecture (the opposite of the Catalan-Dickson conjecture).

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The Olivetti 101, which was the first commercially available, programmable desktop computer.

AB: You’ve worked in so many areas such as number theory, combinatorics and graph theory, game theory, and geometry. Which of your results make you the most proud?

RKG: I don’t know if pride comes into it, but the most important, I think, is my (re)discovery of the Sprague-Grundy theory, and hence my influence on John Conway who asked, “What if the options for the two players are not the same?”

Richard, John Conway and Elywn Berlekamp with their influential book Winning Ways.

AB: You’ve worked with many great mathematicians such as Paul Erdős.  What impact did Erdős have on your mathematics?

RKG: Erdős was a remarkable person, as well as a great mathematician. He knew more about you than you knew yourself!  I can best characterize him with the following story:

It was at a combinatorics conference in Rome, 1973 I think.  We were in the hotel Parco dei Principe. Erdős came up to me and said, “Gah-ee—veel you av a kah-vey”. I was amazed that he even knew who I was.  I don’t usually drink coffee, but I dutifully followed the great man to the bar, where he ordered two coffees for $1:00 each—at a time when a cup of coffee was usually only a dime.  Then he said, “Gah-ee—you are eenfeeneetly reech; lend me $100.00.”  Again I was surprised to find myself reaching into my pocket and handing him a hundred-dollar bill.

Ever since then I’ve known that I am infinitely rich—not only in the material sense that I have everything that I need, but also in the spiritual sense that I have mathematics and that I have known Erdős.

AB: You’ve been an avid mountain climber and hiker. Please tell us about your interest in outdoor sports.

RKG: I think this arose from an early interest in map-reading and route-finding.  Solving problems.  Many mathematicians are mountaineers. I think it is just the joy of achievement.

Richard (aged 90 in the photograph) climbing The Towers in Mount Assiniboine Provincial Park in 2006.

AB: What advice would you give to a young person studying mathematics?

RKG: I don’t think that I can any longer give much good advice. Mathematics has changed so completely during the time that I have been studying it.

AB: You’ve had a long and esteemed career in mathematics. What do you think are some of the important directions or influences for the future of our field?

RKG: Similarly, I find the future of mathematics to be quite unpredictable.

Anthony Bonato

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