Richard Kenneth Guy (30 September 1916 – 9 March 2020) was a British mathematician. He was a professor in the Department of

Mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

at the

University of Calgary The University of Calgary (U of C or UCalgary) is a public research university located in Calgary, Alberta, Canada. The University of Calgary started in 1944 as the Calgary branch of the University of Alberta, founded in 1908, prior to being ins ...

. He is known for his work in

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Ma ...

geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

recreational mathematics Recreational mathematics is mathematics carried out for recreation (entertainment) rather than as a strictly research and application-based professional activity or as a part of a student's formal education. Although it is not necessarily limited ...

combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many a ...

, and

graph theory In mathematics, graph theory is the study of '' graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are conn ...

. He is best known for co-authorship (with John Conway and

Elwyn Berlekamp Elwyn Ralph Berlekamp (September 6, 1940 – April 9, 2019) was a professor of mathematics and computer science at the University of California, Berkeley.Contributors, ''IEEE Transactions on Information Theory'' 42, #3 (May 1996), p. 1048. DO1 ...

) of '' Winning Ways for your Mathematical Plays'' and authorship of ''Unsolved Problems in Number Theory''. He published more than 300 scholarly articles. 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. For this paper he received the MAA Lester R. Ford Award.

Biography

Early life

Guy was born 30 September 1916 in

Nuneaton Nuneaton ( ) is a market town in the borough of Nuneaton and Bedworth in northern Warwickshire, England, close to the county border with Leicestershire and West Midlands County.OS Explorer Map 232 : Nuneaton & Tamworth: (1:25 000) : Nuneaton ...

Warwickshire Warwickshire (; abbreviated Warks) is a county in the West Midlands region of England. The county town is Warwick, and the largest town is Nuneaton. The county is famous for being the birthplace of William Shakespeare at Stratford-upon-Avo ...

, 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 Warwick School is a selective, independent day and boarding school in Warwick, England in the public school tradition. Known until about 1900 as King's School, Warwick, it is believed to have been founded by Æthelflæd of Mercia in 914 AD ...

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 ''History of the Theory of Numbers'' is a three-volume work by L. E. Dickson summarizing work in number theory up to about 1920. The style is unusual in that Dickson mostly just lists results by various authors, with little further discussion. ...

''. He said it was better than "the whole works of Shakespeare", solidifying his lifelong interest in mathematics. In 1935 Guy entered

Gonville and Caius College, Cambridge Gonville and Caius College, often referred to simply as Caius ( ), is a constituent college of the University of Cambridge in Cambridge, England. Founded in 1348, it is the fourth-oldest of the University of Cambridge's 31 colleges and one of t ...

, 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 problem A chess problem, also called a chess composition, is a puzzle set by the composer using chess pieces on a chess board, which presents the solver with a particular task. For instance, a position may be given with the instruction that White is to ...

s. In 1938, he was 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. Although his parents strongly advised against it, Guy decided to become a teacher and got a teaching diploma at the

University of Birmingham , mottoeng = Through efforts to heights , established = 1825 – Birmingham School of Medicine and Surgery1836 – Birmingham Royal School of Medicine and Surgery1843 – Queen's College1875 – Mason Science College1898 – Mason Univers ...

. He met his future wife, Nancy Louise Thirian, through her brother Michael, who was a fellow scholarship winner at Gonville and Caius. He and Louise shared loves of mountain climbing and dancing. They married in December 1940.

War years

In November 1942, Guy received an emergency commission in the Meteorological Branch of the

Royal Air Force The Royal Air Force (RAF) is the United Kingdom's air and space force. It was formed towards the end of the First World War on 1 April 1918, becoming the first independent air force in the world, by regrouping the Royal Flying Corps (RFC) an ...

, with the rank of

flight lieutenant Flight lieutenant is a junior Officer (armed forces)#Commissioned officers, commissioned rank in air forces that use the Royal Air Force (RAF) RAF officer ranks, system of ranks, especially in Commonwealth of Nations, Commonwealth countries. I ...

. He was posted to Reykjavik, and later to

Bermuda ) , anthem = "God Save the King" , song_type = National song , song = "Hail to Bermuda" , image_map = , map_caption = , image_map2 = , mapsize2 = , map_caption2 = , subdivision_type = Sovereign state , subdivision_name = , es ...

, as a

meteorologist A meteorologist is a scientist who studies and works in the field of meteorology aiming to understand or predict Earth's atmospheric phenomena including the weather. Those who study meteorological phenomena are meteorologists in research, while t ...

. 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. When Guy returned to England after the war, he went back to teaching, this time at

Stockport Grammar School Stockport Grammar School is a co-educational independent day school in Stockport, England. Founded in 1487 by former Lord Mayor of London Sir Edmund Shaa, it is the second oldest in the North of England, after Lancaster Royal Grammar School, ...

, but stayed only two years. In 1947 the family moved to London, where he got a job teaching mathematics at Goldsmiths' College.

Later life and death

In 1951 he moved to Singapore, where he taught at the

University of Malaya The University of Malaya ( ms, Universiti Malaya, UM; abbreviated as UM or informally the Malayan University) is a public research university located in Kuala Lumpur, Malaysia. It is the oldest and highest ranking Malaysian institution of highe ...

until 1962. He then spent a few years at the

Indian Institute of Technology The Indian Institutes of Technology (IITs) are central government owned public technical institutes located across India. They are under the ownership of the Ministry of Education of the Government of India. They are governed by the Insti ...

Delhi, India Delhi, officially the National Capital Territory (NCT) of Delhi, is a city and a union territory of India containing New Delhi, the capital of India. Straddling the Yamuna river, primarily its western or right bank, Delhi shares borders w ...

. While they were in India, he and Louise went mountaineering in the foothills of the

Himalayas The Himalayas, or Himalaya (; ; ), is a mountain range in Asia, separating the plains of the Indian subcontinent from the Tibetan Plateau. The range has some of the planet's highest peaks, including the very highest, Mount Everest. Over 10 ...

. Guy moved to Canada in 1965, settling down at the

in Alberta, where he obtained a professorship. Although he officially retired in 1982, he still went to the office five days a week to work, even as he passed the age of 100. Along with George Thomas and John Selfridge, Guy taught at

Canada/USA Mathcamp Canada/USA Mathcamp is a five-week academic summer program for middle and high school students in mathematics. Mathcamp was founded in 1993 by Dr. George Thomas, who believed that students interested in mathematics frequently lacked the resources ...

during its early years. In 1991 the University of Calgary awarded him an

honorary doctorate An honorary degree is an academic degree for which a university (or other degree-awarding institution) has waived all of the usual requirements. It is also known by the Latin phrases ''honoris causa'' ("for the sake of the honour") or ''ad hono ...

. Guy said that they gave him the degree out of embarrassment, although 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." 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 The Alpine Club of Canada (ACC) is an amateur athletic association with its national office in Canmore, Alberta that has been a focal point for Canadian mountaineering since its founding in 1906. The club was co-founded by Arthur Oliver Wheeler, ...

for the training of amateur leaders. In turn, the Alpine Club has honoured them by building the ''Louise and Richard Guy Hut'' near the base of Mont des Poilus. They had three children, among them computer scientist and mathematician Michael J. T. Guy. Guy died on 9 March 2020 at the age of 103.

Mathematics

While teaching in Singapore in 1960 Guy met the Hungarian mathematician

Paul Erdős Paul Erdős ( hu, Erdős Pál ; 26 March 1913 – 20 September 1996) was a Hungarian mathematician. He was one of the most prolific mathematicians and producers of mathematical conjectures of the 20th century. pursued and proposed problems in ...

. Erdős was noted for posing and solving difficult mathematical problems and shared several of them with Guy. Guy later recalled "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." Eventually he wrote four papers with Erdős, giving him an

Erdős number The Erdős number () describes the "collaborative distance" between mathematician Paul Erdős and another person, as measured by authorship of mathematical papers. The same principle has been applied in other fields where a particular individual ...

of 1, and solved one of Erdős' problems. Guy was intrigued by unsolved problems and wrote two books devoted to them. Many number theorists got their start trying to solve problems from Guy's book ''Unsolved problems in number theory''. Guy described himself as an amateur mathematician, although his work was widely respected by professionals. In a career that spans eight decades he wrote or co-authored more than a dozen books and collaborated with some of the most important mathematicians of the twentieth century.

John H. Conway John Horton Conway (26 December 1937 – 11 April 2020) was an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He also made contributions to many branches o ...

Donald Knuth Donald Ervin Knuth ( ; born January 10, 1938) is an American computer scientist, mathematician, and professor emeritus at Stanford University. He is the 1974 recipient of the ACM Turing Award, informally considered the Nobel Prize of computer sc ...

, and

Martin Gardner Martin Gardner (October 21, 1914May 22, 2010) was an American popular mathematics and popular science writer with interests also encompassing scientific skepticism, micromagic, philosophy, religion, and literatureespecially the writings of Lew ...

were among his collaborators, as were

, John L. Selfridge, Kenneth Falconer,

Frank Harary Frank Harary (March 11, 1921 – January 4, 2005) was an American mathematician, who specialized in graph theory. He was widely recognized as one of the "fathers" of modern graph theory. Harary was a master of clear exposition and, together wit ...

Lee Sallows Lee Cecil Fletcher Sallows (born April 30, 1944) is a British electronics engineer known for his contributions to recreational mathematics. He is particularly noted as the inventor of golygons, self-enumerating sentences, and geomagic squares. ...

Gerhard Ringel Gerhard Ringel (October 28, 1919 in Kollnbrunn, Austria – June 24, 2008 in Santa Cruz, California) was a German mathematician. He was one of the pioneers in graph theory and contributed significantly to the proof of the Heawood conjecture (now ...

Béla Bollobás Béla Bollobás FRS (born 3 August 1943) is a Hungarian-born British mathematician who has worked in various areas of mathematics, including functional analysis, combinatorics, graph theory, and percolation. He was strongly influenced by Pau ...

, C. B. Lacampagne, Bruce Sagan, and

Neil Sloane __NOTOC__ Neil James Alexander Sloane (born October 10, 1939) is a British-American mathematician. His major contributions are in the fields of combinatorics, error-correcting codes, and sphere packing. Sloane is best known for being the creator ...

. Over the course of his career Guy published more than 100 research papers in mathematics, including four with Erdős. Guy was influential in the field of

. He collaborated with Berlekamp and Conway on two volumes of ''Winning Ways'', which

described in 1998 as "the greatest contribution to recreational mathematics in this century". Guy was considered briefly as a replacement for Gardner when the latter retired from the Mathematical Games column at ''Scientific American''. Guy conducted extensive research on

Conway's Game of Life The Game of Life, also known simply as Life, is a cellular automaton devised by the British mathematician John Horton Conway in 1970. It is a zero-player game, meaning that its evolution is determined by its initial state, requiring no furthe ...

, and in 1970, discovered the game's glider. Around 1968, Guy discovered a unistable polyhedron with 19 faces; no such construct with fewer faces was found until 2012. As of 2016 Guy still was active in conducting mathematical work. 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 Gathering 4 Gardner (G4G) is an educational foundation and non-profit corporation (Gathering 4 Gardner, Inc.) devoted to preserving the legacy and spirit of prolific writer Martin Gardner. G4G organizes conferences where people who have been inspi ...

. Guy was one of the original directors of the Number Theory Foundation and played an active role in supporting their efforts to "foster a spirit of cooperation and goodwill among the family of number theorists" for more than twenty years.

Chess problems

From 1947 to 1951 Guy was the endings editor for ''

British Chess Magazine ''British Chess Magazine'' is the world's oldest chess journal in continuous publication. First published in January 1881, it has appeared at monthly intervals ever since. It is frequently known in the chess world as ''BCM''. The founder an ...

''. He is known for almost 200

endgame studies In the game of chess, an endgame study, or just study, is a composed position—that is, one that has been made up rather than played in an actual game—presented as a sort of puzzle, in which the aim of the solver is to find the essentially uniq ...

. 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 including '' EG'' use it to classify endgame types and to index endgame studies.Hooper, David; Whyld, Kenneth (1992) ''

The Oxford Companion to Chess ''The Oxford Companion to Chess'' is a reference book on the game of chess written by David Vincent Hooper and Kenneth Whyld. The book is written in an encyclopedia format. The book belongs to the Oxford Companions series. Details The first e ...

'', "GBR code", p. 353, Oxford University Press, Solution: 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

* 1975 (with John L. Selfridge) ''Optimal coverings of the square'', North-Holland, Amsterdam, OCLC Number: 897757276. * 1976 ''Packing

, n The comma is a punctuation mark that appears in several variants in different languages. It has the same shape as an apostrophe or single closing quotation mark () in many typefaces, but it differs from them in being placed on the baseline o ...

with solutions of ax + by = cz — the unity of combinatorics'' ''Atti dei Conv. Lincei'', 17, Tomo II, 173–179 * 1981 ''Unsolved problems in number theory'', Springer-Verlag in New York, * 1982 ''Sets of integers whose subsets have distinct sums'', North-Holland, OCLC Number: 897757256. * 1982 (with

and

) ''Winning Ways for your Mathematical Plays'', Academic Press, . * 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, . * 1991 ''Graphs and the strong law of small numbers'' in 'Graph Theory, Combinatorics, and Applications, Wiley, OCLC Number: 897682607. * 1994 (with Hallard T. Croft and Kenneth Falconer) ''Unsolved problems in geometry'', Springer-Verlag, . * 1996 (with

) ''The book of numbers'', Copernicus, . * 2002 (with Paul Vaderlind and Loren C. Larson) ''The inquisitive problem solver'', Mathematical Association of America, . * 2020 (with Ezra A. Brown) ''The Unity of Combinatorics'', Mathematical Association of America,

Papers

* * * * * * * * * * * * * * * * * * * * * * * * * * * * *

References

Sources

* Albers, Donald J.; Alexanderson, Gerald L. (1985).
Mathematical People: Profiles and Interviews
', John Horton Conway by Richard K. Guy: pp. 36–46, Princeton University Press, * Albers, Donald J.; Alexanderson, Gerald L. (2011).
Fascinating Mathematical People : interviews and memoirs
', Interview with Richard K. Guy: pp. 165–192, Princeton University Press, * Berlekamp, Elwyn R. (2014).
The Mathematical Legacy of Martin Gardner
'

Society for Industrial and Applied Mathematics Society for Industrial and Applied Mathematics (SIAM) is a professional society dedicated to applied mathematics, computational science, and data science through research, publications, and community. SIAM is the world's largest scientific soci ...

(SIAM), 2 September 2014 * Fortney, Valerie (2015).
Richard Guy to visit his namesake alpine hut
'' The Calgary Herald'', 10 September 2015 * Guiltenane, Erin (2016)
Emeritus professor marks a century of life and learning
University of Calgary: Faculty of Science, 29 September 2016 * MMA (2016).
Happy Birthday, Richard Guy!
'

Mathematical Association of America The Mathematical Association of America (MAA) is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university, college, and high school teachers; graduate and undergraduate students; pure a ...

, 30 September 2016 * Mulcahy, Colm (2016).
Richard K. Guy turns 100
' MMA: CardColm, 30 September 2016 * Roberts, Siobhan (2016).
An “Infinitely Rich” Mathematician Turns 100
', 30 September 2016 * Scott, Chic (2012).
Young at Heart: The Inspirational Lives of Richard and Louise Guy
', Pub by The

, Canmore, Alberta,

External links

Richard K. Guy
author profile on

MathSciNet MathSciNet is a searchable online bibliographic database created by the American Mathematical Society in 1996. It contains all of the contents of the journal ''Mathematical Reviews'' (MR) since 1940 along with an extensive author database, links ...

Personal web page
* * {{DEFAULTSORT:Guy, Richard K. 1916 births 2020 deaths 20th-century English mathematicians 21st-century English mathematicians Academics of the University of London Alumni of Gonville and Caius College, Cambridge Chess composers Combinatorial game theorists English centenarians IIT Delhi faculty Mathematics popularizers Men centenarians National University of Singapore faculty Number theorists People from Nuneaton Recreational mathematicians Royal Air Force personnel of World War II University of Calgary faculty English expatriates in Canada English expatriates in Singapore Royal Air Force officers