Richard K. Guy

Richard Kenneth Guy (born 30 September 1916) is a British mathematician and professor emeritus in the Department of Mathematics at the University of Calgary.[1] He is known for his work in number theory, geometry, recreational mathematics, combinatorics, and graph theory.[2][3] He is best known for co-authorship (with John Conway and Elwyn Berlekamp) of Winning Ways for your Mathematical Plays and authorship of Unsolved Problems in Number Theory.[4] He has also published over 300 papers.[5] Guy proposed the partially tongue-in-cheek "Strong Law of Small Numbers," which says there are not enough small integers available for the many tasks assigned to them – thus explaining many coincidences and patterns found among numerous cultures.[6] For this paper he received the MAA Lester R. Ford Award.[7]

R. K. Guy
Richard Kenneth Guy

(1916-09-30) 30 September 1916
Nuneaton, England
Alma materGonville and Caius College, Cambridge
Cambridge [B.A. in 1938, M.A. in 1941]
Known fornumber theory
Recreational mathematics
Strong Law of Small Numbers
unistable polyhedron
Scientific career
InstitutionsUniversity of Calgary
WebsiteUniversity of Calgary: Celebrating Richard Guy


Early life

Guy was born 30 September 1916 in Nuneaton, Warwickshire, England, to Adeline Augusta Tanner and William Alexander Charles Guy. Both of his parents were teachers, rising to the rank of headmistress and headmaster, respectively. He attended Warwick School for Boys, the third oldest school in Britain, but was not enthusiastic about most of the curriculum. He was good at sports, however, and excelled in mathematics. At the age of 17 he read Dickson's History of the Theory of Numbers. He said it was better than "the whole works of Shakespeare", solidifying his lifelong interest in mathematics.[8]

In 1935 Guy entered Gonville and Caius College, Cambridge as a result of winning several scholarships. To win the most important of these he had to travel to Cambridge and write exams for two days. His interest in games began while at Cambridge where he became an avid composer of chess problems.[9] In 1938, he graduated with a second-class honours degree; he would later state that his failure to get a first may have been related to his obsession with chess.[10] Although his parents strongly advised against it, Guy decided to become a teacher and got a teaching diploma at the University of Birmingham. He met his future wife Nancy Louise Thirian through her brother Michael, who was a fellow scholarship winner at Gonville and Caius College. He and Louise shared loves of mountain climbing and dancing. They would marry in December of 1940.

The war years

In November 1942, Guy received an emergency commission in the Meteorological Branch of the Royal Air Force, with the rank of flight lieutenant.[11] He was posted to Reykjavik, and later to Bermuda, as a meteorologist. He tried to get permission for Louise to join him but was refused. While in Iceland, he did some glacier travel, skiing and mountain climbing, marking the beginning of another long love affair, this one with snow and ice.[12] When Guy returned to England after the war, he went back to teaching, this time at Stockport Grammar School, but stayed only two years. In 1947 the family moved to London, where he got a job teaching math at Goldsmiths' College.[13]

1950s to present

In 1951 he moved to Singapore, where he taught at the University of Malaya until 1962. He then spent a few years at the Indian Institute of Technology in Delhi, India. While they were in India, he and Louise went mountaineering in the foothills of the Himalayas.[14] Guy moved to Canada in 1965, settling down at the University of Calgary in Alberta, where he obtained a professorship.[15][16] Though he officially retired in 1982, he still goes to the office five days a week to work, even as he passed the age of 100.[17]

In 1991 the University of Calgary awarded him an Honorary Doctorate. Guy claims that they gave him the degree out of embarrassment, though the university stated that "his extensive research efforts and prolific writings in the field of number theory and combinatorics have added much to the underpinnings of game theory and its extensive application to many forms of human activity."[18] Guy and his wife Louise (who died in 2010) remained very committed to mountain hiking and environmentalism even in their later years. In 2014, he donated $100,000 to the Alpine Club of Canada for the training of amateur leaders.[19] The Alpine Club has in turn honoured them by building the Louise & Richard Guy Hut near the base of Mont des Poilus.[20] He has three children, among them computer scientist and mathematician Michael J. T. Guy.


I love mathematics so much, and I love anybody who can do it well, so I just like to hang on and try to copy them as best I can, even though I'm not really in their league.[21]

–R. K. Guy

While teaching in Singapore in 1960 Guy met the Hungarian mathematician Paul Erdős. Erdős was noted for posing and solving difficult mathematical problems and shared several of them with Guy.[22] Guy says, "I made some progress in each of them. This gave me encouragement, and I began to think of myself as possibly being something of a research mathematician, which I hadn't done before."[23] Eventually he wrote four papers with Erdős, giving him an Erdős number of 1.[24] He even solved one of Erdős' problems.[25] Guy has always been intrigued by unsolved problems and has written two books devoted to them.[26][27] Many number theorists got their start trying to solve problems from Unsolved problems in number theory.[28]

Guy describes himself as an amateur mathematician[29], though his work enjoys broad respect, beyond that of amateur status.[30] In a career that spans eight decades he has written or co-authored over a dozen books and collaborated with some of the most important mathematicians of the 20th century.[31] Paul Erdős, John H. Conway, Donald Knuth, and Martin Gardner are among his collaborators, as are Elwyn Berlekamp, John L. Selfridge, Kenneth Falconer, Frank Harary, Lee Sallows, Gerhard Ringel, Béla Bollobás, C. B. Lacampagne, Bruce Sagan, and Neil Sloane.[32]

Guy is one of the key people in the field of recreational mathematics. In 1998 Martin Gardner wrote, "Conway later collaborated with fellow mathematicians Richard Guy and Elwyn Berlekamp on what I consider the greatest contribution to recreational mathematics in this century, a two-volume work called Winning Ways."[33][34] In fact, Guy was briefly considered as a replacement for Gardner when the latter retired from the Mathematical Games column at Scientific American.[35] Along with Bill Gosper, Guy has been one of the principal researchers in John H. Conway's Game of Life, and in 1970 discovered the glider, one of the key discoveries in that field.[36][37] Around 1968, Guy discovered a unistable polyhedron having only 19 faces; no such construct with fewer faces was found until 2012. As of 2016 Guy was still active in conducting mathematical work.[38] To mark his 100th birthday friends and colleagues organised a celebration of his life and a tribute song and video was released by Gathering 4 Gardner.[39]

Chess problems

From 1947 to 1951 Guy was the endings editor for the British Chess Magazine.[40] He is known for almost 200 endgame studies. Along with Hugh Blandford and John Roycroft, he is one of the inventors of the GBR code (Guy–Blandford–Roycroft code), a system of representing the position of chess pieces on a chessboard. Publications such as EG magazine use it to classify endgame types and to index endgame studies.[41]

Richard Guy endgame composition: 1938

1. Kd1 Ka3
2. Kc1 a5
3. h4 a4
4. h5 Ka2
5. h6 a3
6. h7 Ka1
7. h8=N a2
8. Ng6 fxg6
9. f7 g5
10. f8=N g4
11. Ne6 dxe6
12. d7 e5
13. d8=N e4
14. Nc6 bxc6
15. b7 c5
16. Kd1 Kb2
17. b8=Q+ 1-0

Selected publications

Books by R. K. Guy

  • 1975 (with John L. Selfridge) Optimal coverings of the square, North-Holland, Amsterdam, OCLC Number: 897757276.
  • 1976 Packing with solutions of ax+by= cz The unity of combinatorics, OCLC Number: 883501309
  • 1981 Unsolved problems in number theory, Springer-Verlag in New York, ISBN 0-387-90593-6
  • 1982 Sets of integers whose subsets have distinct sums, North-Holland, OCLC Number: 897757256.
  • 1982 (with John H. Conway and Elwyn Berlekamp) Winning Ways for your Mathematical Plays, Academic Press, ISBN 0120911507.
  • 1987 Six phases for the eight-lambdas and eight-deltas configurations, North-Holland, OCLC Number: 897693235.
  • 1989 Fair game how to play impartial combinatorial games, COMAP in Arlington, MA, ISBN 0912843160.
  • 1991 Graphs and the strong law of small numbers, Wiley, OCLC Number: 897682607.
  • 1994 (with Hallard T. Croft and Kenneth Falconer) Unsolved problems in geometry, Springer-Verlag, ISBN 0387975063.
  • 1996 (with John H. Conway) The book of numbers, Copernicus, ISBN 9780387979939.
  • 2002 (with Paul Vaderlind and Loren C. Larson) The inquisitive problem solver, Mathematical Association of America, ISBN 0883858061.



  1. Albers & Alexanderson (2011) p. 320
  2. MMA (2016)
  3. Author biography from Winning Ways for your Mathematical Plays, Vol. I, 2nd ed., AK Peters, 2001.
  4. Roberts (2016)
  5. Scott (2012) p. 29
  6. Guy, Richard K. (October 1988). "The Strong Law of Small Numbers" (PDF). Am. Math. Mon. 95 (8): 697–712. doi:10.2307/2322249. ISSN 0002-9890. JSTOR 2322249.
  7. MMA (2016)
  8. Scott (2012) p. 6
  9. Roberts (2016)
  10. Albers & Alexanderson (2011) p. 169
  11. "No. 35894". The London Gazette (Supplement). 5 February 1943. p. 707.
  12. Scott (2012) p. 29: Richard has often told me that he has had three loves in his life: Louise and mountains of course are two of them, but his first love was mathematics.
  13. Scott (2012) p. 11
  14. Guiltenane (2016)
  15. University of Calgary (2016)
  16. Roberts (2016)
  17. Guiltenane (2016): Guy has said, "I didn't retire, they just stopped paying me.
  18. Scott (2012) p. 31
  19. Scott (2012) p. 39
  20. Alpine Club of Canada (30 October 2014). "Introducing the Louise & Richard Guy Hut". Archived from the original on 11 October 2016.
  21. Roberts (2016) p.30
  22. Roberts (2016)
  23. Albers & Alexanderson (2011) p. 176
  24. Coauthors of Paul Erdos
  25. Brent Wittmeier, "Math genius left unclaimed sum," Edmonton Journal, 28 September 2010.
  26. Unsolved problems in number theory and Unsolved problems in combinatorial games
  27. Albers (2011): p. 165
  28. Scott (2016) p. 30: It is no exaggeration to say that Unsolved Problems in Number Theory has inspired generations of aspiring Number Theorists!
  29. Scot (2012) p. 29
  30. Roberts (2016): "He pushes the boundaries of that definition."
  31. Scott (2016)
  32. Albers (2011)
  33. A Quarter-Century of Recreational Mathematics by Martin Gardner, Scientific American, August 1998
  34. Scott (2016) p. 30: Mathematician Michael Bennett calls Winning Ways for your Mathematical Plays the bible of Combinatorial Game Theory.
  35. Mulcahy (2016): 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!".
  36. Mulcahy (2016)
  37. Gardner, Martin (1970). The fantastic combinations of John Conway's new solitaire game "life" Scientific American: Mathematical Games. October 1970.
  38. Kenneth Falconer (3 October 2016). "Richard Guy at 100". London Mathematical Society Newsletter. Archived from the original on 29 December 2017.
  39. Richard Guy 100th Birthday Tribute Song video
  40. The Chess Endgame Study: A Comprehensive Introduction By A. J. Roycroft, New York : Dover Publications, 1981, p. 58, ISBN 0486241866
  41. Hooper, David; Whyld, Kenneth (1992) The Oxford Companion to Chess, "GBR code", p. 353, Oxford University Press, ISBN 0-19-280049-3


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