emeritus
''Emeritus'' (; female: ''emerita'') is an adjective used to designate a retired chair, professor, pastor, bishop, pope, director, president, prime minister, rabbi, emperor, or other person who has been "permitted to retain as an honorary title ...
professor
Professor (commonly abbreviated as Prof.) is an academic rank at universities and other post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin as a "person who professes". Professo ...
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
London South Bank University
London South Bank University (LSBU) is a public university in Elephant and Castle, London. It is based in the London Borough of Southwark, near the South Bank of the River Thames, from which it takes its name. Founded in 1892 as the Borough ...
, England. A self-described metagrobologist, he has a huge personal collection of
mechanical puzzle
A mechanical puzzle is a puzzle presented as a set of mechanically interlinked pieces in which the solution is to manipulate the whole object or parts of it. While puzzles of this type have been in use by humanity as early as the 3rd century BC ...
s and books of brain teasers. He is most famous for being an early adopter and enthusiastic promoter of the
Rubik's Cube
The Rubik's Cube is a Three-dimensional space, 3-D combination puzzle originally invented in 1974 by Hungarians, Hungarian sculptor and professor of architecture Ernő Rubik. Originally called the Magic Cube, the puzzle was licensed by Rubik t ...
. His ''Notes on Rubik's "Magic Cube"'' which he began compiling in 1979 provided the first mathematical analysis of the Cube as well as providing one of the first published solutions. The book contained his cube notation which allowed the recording of
Rubik's Cube
The Rubik's Cube is a Three-dimensional space, 3-D combination puzzle originally invented in 1974 by Hungarians, Hungarian sculptor and professor of architecture Ernő Rubik. Originally called the Magic Cube, the puzzle was licensed by Rubik t ...
moves, and which quickly became the standard.
He is both a puzzle historian and a composer of puzzles, and many of his puzzles have been published in newspapers and magazines. In
combinatorial 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, "Mathe ...
, Singmaster's conjecture states that there is an upper bound on the number of times a number other than 1 can appear in
Pascal's triangle
In mathematics, Pascal's triangle is a triangular array of the binomial coefficients that arises in probability theory, combinatorics, and algebra. In much of the Western world, it is named after the French mathematician Blaise Pascal, although o ...
.
Career
David Singmaster was a student at the
California Institute of Technology
The California Institute of Technology (branded as Caltech or CIT)The university itself only spells its short form as "Caltech"; the institution considers other spellings such a"Cal Tech" and "CalTech" incorrect. The institute is also occasional ...
in the late 1950s. His intention was to become a civil engineer, but he became interested in chemistry and then physics. However he was thrown out of college in his third year for "lack of academic ability". After a year working, he switched to the
University of California, Berkeley
The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant un ...
. He only became really interested in mathematics in his final year when he took some courses in
algebra
Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics.
Elementary ...
and
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 ...
. In the autumn semester, his number theory teacher Dick Lehmer posed a prize problem which Singmaster won. In his last semester, his algebra teacher posed a question the teacher didn't know the answer to and Singmaster solved it, eventually leading to two papers. He gained his
PhD PHD or PhD may refer to:
* Doctor of Philosophy (PhD), an academic qualification
Entertainment
* '' PhD: Phantasy Degree'', a Korean comic series
* '' Piled Higher and Deeper'', a web comic
* Ph.D. (band), a 1980s British group
** Ph.D. (Ph.D. al ...
from Berkeley, in 1966. He taught at the
American University of Beirut
The American University of Beirut (AUB) ( ar, الجامعة الأميركية في بيروت) is a private, non-sectarian, and independent university chartered in New York with its campus in Beirut, Lebanon. AUB is governed by a private, aut ...
, and then lived for a while in
Cyprus
Cyprus ; tr, Kıbrıs (), officially the Republic of Cyprus,, , lit: Republic of Cyprus is an island country located south of the Anatolian Peninsula in the eastern Mediterranean Sea. Its continental position is disputed; while it is ...
.
Singmaster moved to
London
London is the capital and List of urban areas in the United Kingdom, largest city of England and the United Kingdom, with a population of just under 9 million. It stands on the River Thames in south-east England at the head of a estuary dow ...
in 1970. The "Polytechnic of the South Bank" had been created from a merger of institutions in 1970, and Singmaster became a lecturer in the Department of Mathematical Sciences. His academic interests are in
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
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 ...
.
In August 1971 he joined an archaeological expedition off the coast of
, acting as photographer. He went off course one day and noticed a timber sticking up out of the sand. This led to the discovery of the Marsala Punic Ship.
Around 1972, he attended the Istituto di Matematica in
Pisa
Pisa ( , or ) is a city and ''comune'' in Tuscany, central Italy, straddling the Arno just before it empties into the Ligurian Sea. It is the capital city of the Province of Pisa. Although Pisa is known worldwide for its leaning tower, the ci ...
for a year having won a research scholarship. He was promoted to a Readership (a Research Professorship) at the South Bank Polytechnic in September 1984. The polytechnic college became
London South Bank University
London South Bank University (LSBU) is a public university in Elephant and Castle, London. It is based in the London Borough of Southwark, near the South Bank of the River Thames, from which it takes its name. Founded in 1892 as the Borough ...
in 1992, and Singmaster was the professor of mathematics at the "School of Computing, Information Systems and Mathematics". He retired in 1996. He became an honorary research fellow at
University College London
, mottoeng = Let all come who by merit deserve the most reward
, established =
, type = Public research university
, endowment = £143 million (2020)
, budget = ...
. He was designated
emeritus
''Emeritus'' (; female: ''emerita'') is an adjective used to designate a retired chair, professor, pastor, bishop, pope, director, president, prime minister, rabbi, emperor, or other person who has been "permitted to retain as an honorary title ...
at
London South Bank University
London South Bank University (LSBU) is a public university in Elephant and Castle, London. It is based in the London Borough of Southwark, near the South Bank of the River Thames, from which it takes its name. Founded in 1892 as the Borough ...
in 2020.
Rubik's Cubes
Singmaster's association with
Rubik's Cube
The Rubik's Cube is a Three-dimensional space, 3-D combination puzzle originally invented in 1974 by Hungarians, Hungarian sculptor and professor of architecture Ernő Rubik. Originally called the Magic Cube, the puzzle was licensed by Rubik t ...
s dates from August 1978, when he saw a Cube (at that time a rarity) at the
International Congress of Mathematicians
The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU).
The Fields Medals, the Nevanlinna Prize (to be rena ...
in
Helsinki
Helsinki ( or ; ; sv, Helsingfors, ) is the Capital city, capital, primate city, primate, and List of cities and towns in Finland, most populous city of Finland. Located on the shore of the Gulf of Finland, it is the seat of the region of U ...
. Some other mathematicians at the conference, including John Conway and
Roger Penrose
Sir Roger Penrose (born 8 August 1931) is an English mathematician, mathematical physicist, philosopher of science and Nobel Laureate in Physics. He is Emeritus Rouse Ball Professor of Mathematics in the University of Oxford, an emeritus f ...
, already had one.
Singmaster quickly acquired a Cube (in exchange for a copy of an
M. C. Escher
Maurits Cornelis Escher (; 17 June 1898 – 27 March 1972) was a Dutch graphic artist who made mathematically inspired woodcuts, lithographs, and mezzotints.
Despite wide popular interest, Escher was for most of his life neglected in t ...
book) and was able to solve it by early September 1978. He has said that it took him "two weeks, on and off" to find a general solution for the Cube. He devised his notation for recording moves (now known as the Singmaster notation) in December 1978. In June 1979 he wrote one of the first articles about the Cube in ''
The Observer
''The Observer'' is a British newspaper published on Sundays. It is a sister paper to ''The Guardian'' and '' The Guardian Weekly'', whose parent company Guardian Media Group Limited acquired it in 1993. First published in 1791, it is the ...
'' newspaper.
In October 1979, he self-published his ''Notes on the "Magic Cube"''. The booklet contained his mathematical analysis of Rubik's Cube, allowing a solution to be constructed using basic
group theory
In abstract algebra, group theory studies the algebraic structures known as groups.
The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen ...
. In August 1980 he published an expanded 5th edition of the book retitled as ''Notes on Rubik's "Magic Cube"''. It included the results of his correspondence with other "cubologists", and included details on monotwists, U-flips,
Cayley graph
In mathematics, a Cayley graph, also known as a Cayley color graph, Cayley diagram, group diagram, or color group is a graph that encodes the abstract structure of a group. Its definition is suggested by Cayley's theorem (named after Arthur Cay ...
s, and
wreath product
In group theory, the wreath product is a special combination of two groups based on the semidirect product. It is formed by the action of one group on many copies of another group, somewhat analogous to exponentiation. Wreath products are used i ...
s. The book contained his own "step by step solution" for the Cube, and it is accepted that he was a pioneer of the general
Layer by Layer
Layer-by-layer (LbL) deposition is a thin film fabrication technique. The films are formed by depositing alternating layers of oppositely charged materials with wash steps in between. This can be accomplished by using various techniques such as imm ...
approach for solving the Cube. If you managed to solve the Cube using his method then Singmaster suggested that you should:
The book also contained a catalogue of pretty patterns including his "cube in a cube in a cube" pattern which he had discovered himself "and was very pleased with". In 1981, at the height of the Rubik's Cube craze, the book was republished by
Penguin Books
Penguin Books is a British publishing, publishing house. It was co-founded in 1935 by Allen Lane with his brothers Richard and John, as a line of the publishers The Bodley Head, only becoming a separate company the following year.Enslow Publishers. There were also Dutch and Spanish translations. He estimates that he sold around 50 to 60 000 copies of his book. Much of the mathematical content of the book was later reworked by Alexander H. Frey in collaboration with Singmaster to create their ''Handbook of Cubik Math'' published in 1982.
Singmaster has been described as "one of the most enthusiastic and prolific promoters of the Cube". In September 1981 he was said to be devoting "almost 100%" of his time to promoting, reporting, marketing and analysing the Cube. He soon began publishing a quarterly newsletter called the ''Cubic Circular'' which was published between 1981 and 1985.
Puzzles
Singmaster has one of the world's largest collections of books on recreational mathematics which he has accumulated since the late 1970s. In 1996 he reported that the collection contained over 4700 works on recreational mathematics. He also collects books on cartoons, humour, and language. In 2013 his book collection was reported to be "nearly 10000 items". Many of the books are housed in a library added as an extension to Singmaster's study. He has a huge collection of
mechanical puzzle
A mechanical puzzle is a puzzle presented as a set of mechanically interlinked pieces in which the solution is to manipulate the whole object or parts of it. While puzzles of this type have been in use by humanity as early as the 3rd century BC ...
s, which he stated in 2002 contained "perhaps 3000 puzzles, of which about 400 are Rubik's Cube and its variants".
From around 1980 to 1982, he ran his own puzzle company, David Singmaster Ltd, which stocked "over 100 puzzles and books". However the venture lost him "a fair amount of money" and led to prolonged tax negotiations. He referred to this period of his life as "a massive overdose of cubism".
Singmaster is both a puzzle historian and a composer of puzzles, and he describes himself as a "metagrobologist". Many of his puzzles have appeared in publications such as ''
BBC Focus
''BBC Science Focus'' (previously ''BBC Focus'') is a British monthly magazine about science and technology published in Bristol, UK by Immediate Media Company. Edited by Daniel Bennett, it covers all aspects of science and technology and is wri ...
'', ''
Games & Puzzles
''Games & Puzzles'' was a magazine about games and puzzles. The magazine was first published in May 1972 by Edu-Games (UK) Ltd. The first editor was Graeme Levin who recruited a variety of games and puzzles experts as writers and consultant editor ...
'', the ''
Los Angeles Times
The ''Los Angeles Times'' (abbreviated as ''LA Times'') is a daily newspaper that started publishing in Los Angeles in 1881. Based in the LA-adjacent suburb of El Segundo since 2018, it is the sixth-largest newspaper by circulation in the ...
'', and the '' Weekend Telegraph''. He published a collection of his puzzles in his 2016 book ''Problems for Metagrobologists''. From around 2006 Singmaster was a director at the New York-based
Conjuring Arts Research Center The Conjuring Arts Research Center is a not-for-profit organization based in New York City dedicated to the preservation and interpretation of magic
Magic or Magick most commonly refers to:
* Magic (supernatural), beliefs and actions employed to ...
, retiring from the position (becoming Director Emeritus) in 2013. He was instrumental in the re-discovery of one of the world's oldest books on puzzles and magic illusions when he came across a reference to the work in a 19th-century manuscript. The recovered text, ''De viribus quantitatis'' ('' en, On The Powers Of Numbers'') was penned by
Luca Pacioli
Fra Luca Bartolomeo de Pacioli (sometimes ''Paccioli'' or ''Paciolo''; 1447 – 19 June 1517) was an Italian mathematician, Franciscan friar, collaborator with Leonardo da Vinci, and an early contributor to the field now known as accounting ...
, a Franciscan friar who lived around 1500.
Singmaster's conjecture
In
combinatorial 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, "Mathe ...
, Singmaster's conjecture states that there is a finite
upper bound
In mathematics, particularly in order theory, an upper bound or majorant of a subset of some preordered set is an element of that is greater than or equal to every element of .
Dually, a lower bound or minorant of is defined to be an eleme ...
on the number of times a number other than 1 can appear in
Pascal's triangle
In mathematics, Pascal's triangle is a triangular array of the binomial coefficients that arises in probability theory, combinatorics, and algebra. In much of the Western world, it is named after the French mathematician Blaise Pascal, although o ...
.
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 ...
suspected that the conjecture is true, but thought it would probably be very difficult to prove. The
empirical evidence
Empirical evidence for a proposition is evidence, i.e. what supports or counters this proposition, that is constituted by or accessible to sense experience or experimental procedure. Empirical evidence is of central importance to the sciences ...
is consistent with the proposition that the smallest upper bound is 8.
Media appearances
In November 1981, Singmaster appeared on the scifi-themed BBC puzzle show ''
The Adventure Game
''The Adventure Game'' is a game show that was originally broadcast on UK television channels BBC1 and BBC2 between 24 May 1980 and 18 February 1986. The story in each show was that the two celebrity contestants and a member of the public had ...
''. From 1998 to 1999 he was a frequent panelist on the
BBC Radio 4
BBC Radio 4 is a British national radio station owned and operated by the BBC that replaced the BBC Home Service in 1967. It broadcasts a wide variety of spoken-word programmes, including news, drama, comedy, science and history from the BBC's ...
show ''
Puzzle Panel
{{Use dmy dates, date=July 2014
''Puzzle Panel'' was a light-hearted, though cerebral BBC Radio 4 panel game that was broadcast between 1998 and 2005. An additional series was broadcast over the winter-spring of 2011, and a further series was broad ...
''.
Personal life
Singmaster has been married twice, the second time to Deborah in 1972.
They have one daughter, Jessica, adopted in 1976.
Publications
Books
* ''Notes on Rubik's "Magic Cube"'', David Singmaster. Enslow Publishers, 1981.
* ''Handbook of Cubik Math'', by David Singmaster and Alexander H. Frey.
The Lutterworth Press
The Lutterworth Press, one of the oldest independent British publishing houses, has traded since the late eighteenth century - initially as the Religious Tract Society (RTS). The Lutterworth imprint, named after the small English town of Lutte ...
, 1982. . Publisher's description
* ''Rubik's Cubic Compendium'', by
Ernő Rubik
Ernő Rubik (; born 13 July 1944) commonly known by his nickname, "Little Man", is a Hungarian inventor, architect and professor of architecture. He is best known for the invention of mechanical puzzles including the Rubik's Cube (1974), Rub ...
and four others. Edited with an Introduction and Afterword by David Singmaster.
Oxford University Press
Oxford University Press (OUP) is the university press of the University of Oxford. It is the largest university press in the world, and its printing history dates back to the 1480s. Having been officially granted the legal right to print book ...
, 1987.
* ''The Cube: The Ultimate Guide to the World's Bestselling Puzzle'', Jerry Slocum, David Singmaster, Wei-Hwa Huang, Dieter Gebhardt, Geert Hellings, Ernő Rubik. Black Dog & Leventhal, 2009.
* ''Problems for Metagrobologists'', David Singmaster,
World Scientific Publishing Company
World Scientific Publishing is an academic publisher of scientific, technical, and medical books and journals headquartered in Singapore. The company was founded in 1981. It publishes about 600 books annually, along with 135 journals in various ...
, 23 April 2016.
* ''Adventures in Recreational Mathematics (in 2 Volumes)''. David Singmaster. World Scientific Publishing Company. (2021)
Reference works
*''Chronology of Recreational Mathematics'' by David Singmaster. 1996. Available online at anduin.eldar.org)
*''Chronology of Computing'' by David Singmaster. 2000. Available online at the University of Applied Sciences, Darmstadt)
*''Sources in Recreational Mathematics: An Annotated Bibliography'', David Singmaster. 8th preliminary edition. South Bank University. 2004. at the Puzzle Museum)
*''Mathematical Gazetteer of the British Isles'', by David Singmaster. The British Society for the History of Mathematics. 2012. at the Internet Archive)
Newsletters
*''Cubic Circular'' magazine published 1981-5 by David Singmaster
New Scientist
''New Scientist'' is a magazine covering all aspects of science and technology. Based in London, it publishes weekly English-language editions in the United Kingdom, the United States and Australia. An editorially separate organisation publish ...
, 23/30 December 1982
*''The Unreasonable Utility of Recreational Mathematics'' by David Singmaster. First European Congress of Mathematics, Paris, July 1992. Available online at anduin.eldar.org)
* ', by David Singmaster and Andrew Southern. Meffert's Puzzles, 15 May 1997.
* Interview with David Singmaster at ''Twisty Puzzles''. Originally published c. April 2002 . A compilation of materials by David Singmaster for teaching and his own interests. Last updated in 1996. David Singmaster archive at
London South Bank University
London South Bank University (LSBU) is a public university in Elephant and Castle, London. It is based in the London Borough of Southwark, near the South Bank of the River Thames, from which it takes its name. Founded in 1892 as the Borough ...