Editing David Singmaster

{{Short description|British mathematician (1938–2023)}}
{{Use dmy dates|date=April 2022}}
{{Infobox scientist
| honorific_prefix  = 
| name              = David Singmaster
| image             = David Singmaster 2006.jpg
| image_size        = 240px
| caption           = Singmaster in 2006
| birth_date        = {{birth date|1938|12|14|df=y}}<ref name="g4g2018b">{{cite interview |last=Singmaster |first=David |subject= |subject-link= |interviewer=[[Dana S. Richards]] |title=An Extended Interview with David Singmaster |type= |url=https://www.youtube.com/watch?v=7ZolXFbWkRM&t=20m15s  |archive-url=https://ghostarchive.org/varchive/youtube/20211212/7ZolXFbWkRM| archive-date=2021-12-12 |url-status=live|format= |work=G4G Celebration |publisher=[[Gathering 4 Gardner]] |location= |date=April 2018 |access-date=3 June 2019 |quote=}}{{cbignore}}</ref><ref name=ams>{{cite journal|title=AMS Updates: Death of AMS Members|journal=Notices of the American Mathematical Society|date=August 2023|volume=70|issue=7|page=1147|url=https://www.ams.org/journals/notices/202307/noti2744/noti2744.html}}</ref>
| birth_place       = [[Ferguson, Missouri]], U.S.<ref>{{Cite web |last=O'Connor |first=J J |last2=Robertson |first2=E F |date=September 2023 |title=David Singmaster |url=https://mathshistory.st-andrews.ac.uk/Biographies/Singmaster/ |url-status=live |archive-url=https://web.archive.org/web/20240528103115/https://mathshistory.st-andrews.ac.uk/Biographies/Singmaster/ |archive-date=2024-05-28 |access-date=2024-09-27 |publisher=[[University of St Andrews]] |language=en}}</ref>
| death_date        = {{death date and age|2023|02|13|1938|12|14|df=y}}
| death_place       = 
| death_cause       = 
| fields            = [[Mathematics]]
| workplaces        = [[London South Bank University]]
| patrons           = 
| education         = 
| alma_mater        = [[University of California, Berkeley]]
| thesis_title      = On Means of Differences of Consecutive Integers Relatively Prime to m
| thesis_url        = 
| thesis_year       = 1966
| doctoral_advisors = [[Derrick Henry Lehmer|Dick Lehmer]], [[Russell Sherman Lehman|Russell Lehman]]
| academic_advisors = 
| doctoral_students = 
| notable_students  = 
| known_for         = [[Singmaster's conjecture]]<br />[[Singmaster notation]]<br />History of mathematics<br />Mathematics of puzzles, especially the [[Rubik's cube]]
| influences        = 
| influenced        = 
| awards            = 
| signature         = <!--(filename only)-->
}}

'''David Breyer Singmaster''' (14 December 1938 – 13 February 2023) was an American-British mathematician who was emeritus professor of mathematics at [[London South Bank University]], England. He had a huge personal collection of [[mechanical puzzle]]s and books of [[brain teaser]]s. He was most famous for being an early adopter and enthusiastic promoter of the [[Rubik's Cube]]. 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 [[Singmaster notation|his cube notation]] which allowed the recording of [[Rubik's Cube]] moves, and which quickly became the standard.

Singmaster was both a puzzle historian and a composer of puzzles, and many of his puzzles were published in newspapers and magazines. In [[combinatorial number theory]], [[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]].

==Career==
David Singmaster was a student at the [[California Institute of Technology]] in the late 1950s.<ref>{{Cite news|url=http://caltechcampuspubs.library.caltech.edu/449/1/1958_02_20_59_17.pdf|title=Candidates' statements - treasurer|page=9|publisher=The California Tech|date=20 February 1958}}</ref> His intention was to become a civil engineer, but he became interested in chemistry and then physics.<ref name="twisty"/><ref name="g4g2018">{{cite interview |last=Singmaster |first=David |subject= |subject-link= |interviewer=Dana Richards |title=An Interview with David Singmaster |type= |url=https://youtube.com/watch?v=abWpHc1XGyo  |archive-url=https://ghostarchive.org/varchive/youtube/20211212/abWpHc1XGyo| archive-date=2021-12-12 |url-status=live|format= |work=G4G Celebration |publisher=[[Gathering 4 Gardner]] |location= |date=April 2018 |access-date=25 June 2018 |quote=}}{{cbignore}}</ref> However he was thrown out of college in his third year for "lack of academic ability".<ref name="g4g2018"/> After a year working, he switched to the [[University of California, Berkeley]].<ref name="g4g2018"/> He only became really interested in mathematics in his final year when he took some courses in [[algebra]] and [[number theory]].<ref name="twisty"/> In the autumn semester, his number theory teacher [[Derrick Henry Lehmer|Dick Lehmer]] posed a prize problem which Singmaster won.<ref name="twisty"/><ref name="g4g2018"/> 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.<ref name="twisty"/> He gained his [[PhD]] from Berkeley, in 1966.<ref>{{MathGenealogy|id=32103}}</ref> He taught at the [[American University of Beirut]], and then lived for a while in [[Cyprus]].<ref name="airm">{{cite book |last=Singmaster |first=David |date=2021 |title=Adventures In Recreational Mathematics |page=xiii |publisher=World Scientific Publishing Company |isbn=9789811225642}}</ref>

Singmaster moved to [[London]] in 1970.<ref>{{Cite web|url=http://www.footnotesaudiowalks.co.uk/about.php|title=About the Footnotes team|publisher=Footnotes audio walks|access-date=23 January 2017}}</ref> 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.<ref name="morallessons"/> His academic interests were in [[combinatorics]] and [[number theory]].<ref name="airm"/>

In August 1971 he joined an archaeological expedition off the coast of [[Sicily]], acting as photographer.<ref name="punic">{{Cite web|url=https://artsandculture.google.com/story/the-discovery-of-the-marsala-punic-ship-honor-frost-foundation/2QWhIN7Uu9SK-Q?hl=en|title=The Discovery of the Marsala Punic Ship|publisher=Honor Frost Foundation|website=Google Arts & Culture|access-date=29 May 2022}}</ref> He went off course one day and noticed a timber sticking up out of the sand. This led to the discovery of the [[Marsala Ship|Marsala Punic Ship]].<ref name="punic"/>

Around 1972, he attended the Istituto di Matematica in [[Pisa]] for a year having won a research scholarship.<ref name="twisty"/> He was promoted to a Readership (a Research Professorship) at the South Bank Polytechnic in September 1984.<ref name="circ78"/> The polytechnic college became [[London South Bank University]] in 1992, and Singmaster was the professor of mathematics at the "School of Computing, Information Systems and Mathematics". He retired in 1996.<ref name="airm"/> He became an honorary research fellow at [[University College London]].<ref>{{Cite web|url=https://www.ucl.ac.uk/news/news-articles/0701/07011002|title=A lecture to get your head around|date=10 January 2007|publisher=University College London}}</ref> He was designated [[emeritus]] at [[London South Bank University]] in 2020.<ref name="airm"/>

==Rubik's Cubes==
{{quote box
| bgcolor = #c6dbf7
| width=26em
| quote = The power of [[Conjugacy class|conjugation]] ... was the last point I understood; I remember lying awake thinking about it, seeing that I could move any four edges into the working locations and realising that this completed the general method for restoring the cube to its original state.
| source=&ndash;David Singmaster, ''[https://books.google.com/books?id=_n1vr0_RbXoC&pg=PA786 Moral and Mathematical Lessons from a Rubik Cube]'', [[New Scientist]], 1982
}}
Singmaster's association with [[Rubik's Cube]]s dates from August 1978, when he saw a Cube (at that time a rarity) at the [[International Congress of Mathematicians]] in [[Helsinki]].<ref name="twisty">{{Cite web|url=http://www.twistypuzzles.com/articles/spotlight-singmaster/|title=Interview with David Singmaster|publisher=Twisty Puzzles|access-date=4 January 2017}}</ref> Some other mathematicians at the conference, including [[John Horton Conway|John Conway]] and [[Roger Penrose]], already had one.<ref name="twisty"/>

Singmaster quickly acquired a Cube (in exchange for a copy of an [[M. C. Escher]] book) and was able to solve it by early September 1978.<ref name="twisty"/> He said that it took him "two weeks, on and off" to find a general solution for the Cube.<ref>{{Cite news|url=http://www.upi.com/Archives/1981/08/24/Now-meet-Rubiks-snake-Bigger-than-Rubiks-cube/9742367473600/|last=Jensen|first=Gregory|title=Now meet Rubik's snake – 'Bigger than Rubik's cube!'|date=24 August 1981|publisher=United Press International}}</ref> He devised his notation for recording moves (now known as the Singmaster notation) in December 1978.<ref name="morallessons">{{Cite news|last=Singmaster|first=David|title=Moral and Mathematical Lesson from a Rubik Cube|page=787|date=23 December 1982|newspaper=New Scientist|url=https://books.google.com/books?id=_n1vr0_RbXoC&pg=PA786}}</ref> In June 1979 he wrote one of the first articles about the Cube in ''[[The Observer]]'' newspaper.<ref>{{Cite news|author=David Singmaster|title=Six-sided magic|publisher=The Observer|date=17 June 1979}}</ref>

In October 1979, he self-published his ''Notes on the "Magic Cube"''.<ref name="publ">{{Cite web|url=http://anduin.eldar.org/~problemi/singmast/pubchron.html|title=Publications of David Singmaster|date=4 August 1996|publisher=anduin.eldar.org|archive-url=https://web.archive.org/web/20170116155532/http://anduin.eldar.org/~problemi/singmast/pubchron.html|archive-date=2017-01-16}}</ref> The booklet contained his mathematical analysis of Rubik's Cube, allowing a solution to be constructed using basic [[group theory]].<ref name="review">{{Cite news|author=<!--Staff writer(s); no by-line.-->|title=Review – Restore your cube|page=802|date=24 September 1981|newspaper=New Scientist|url=https://books.google.com/books?id=_0beD5LVNugC&pg=PA802|access-date=30 August 2017|archive-date=18 August 2020|archive-url=https://web.archive.org/web/20200818162232/https://books.google.com/books?id=_0beD5LVNugC&pg=PA802|url-status=dead}}</ref> In August 1980 he published an expanded 5th edition of the book retitled as ''Notes on Rubik's "Magic Cube"''.<ref name="publ"/> It included the results of his correspondence with other "cubologists", and included details on monotwists, U-flips, [[Cayley graph]]s, and [[wreath product]]s.<ref name="review"/> The book contained his own "step by step solution" for the Cube,<ref name="linkedresources" /> and it is accepted that he was a pioneer of the general [[Layer by Layer]] approach for solving the Cube.<ref name="ryanheise-beginner"/> 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".<ref>{{Cite web|url=http://www.cube20.org/cubelovers/CL26/015.txt|author=David Singmaster|date=8 October 1998|title=Davenport's pattern|publisher=cube20.org}}</ref> In 1981, at the height of the Rubik's Cube craze, the book was republished by [[Penguin Books]], with a US edition by [[Enslow Publishers]].<ref name="publ"/> There were also Dutch and Spanish translations.<ref name="publ"/> He estimated that he sold around 50 to 60&nbsp;000 copies of his book.<ref name="twisty"/> 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 was described as "one of the most enthusiastic and prolific promoters of the Cube".<ref>{{Cite book|last=Lees-Maffei|first=Grace|title=Iconic Designs: 50 Stories about 50 Things|page=140|year=2015|publisher=Bloomsbury|isbn=978-0857853530}}</ref> In September 1981 he was said to be devoting "almost 100%" of his time to promoting, reporting, marketing and analysing the Cube.<ref name="herman">{{Cite news|url=https://books.google.com/books?id=jpr_dn_0IfEC&pg=PA678|last=Herman|first=Ros|title=Cubic mastery|date=10 September 1981|newspaper=New Scientist|access-date=4 January 2017|archive-date=19 August 2020|archive-url=https://web.archive.org/web/20200819133107/https://books.google.com/books?id=jpr_dn_0IfEC&pg=PA678|url-status=dead}}</ref> He soon began publishing a quarterly newsletter called the ''Cubic Circular'' which was published between 1981 and 1985.<ref name="twisty"/><ref name="herman"/>

==Puzzles==
Singmaster had one of the world's largest collections of books on recreational mathematics which he had accumulated starting in the late 1970s.<ref name="allsquared1">{{cite podcast | url= http://aperiodical.com/2013/05/all-squared-number-5-favourite-maths-books-part-1/ | title=All Squared, Number 5: Favourite maths books (part 1) | host=All Squared | website=The Aperiodical | date=11 May 2013 | access-date=25 June 2018 }}</ref> In 1996 he reported that the collection contained over 4700 works.<ref name="list">{{Cite web|url=http://anduin.eldar.org/~problemi/singmast/material.html|title=David Singmaster: List of Available Material|date=1 October 1996|publisher=anduin.eldar.org|archive-url=https://web.archive.org/web/20170309090104/http://anduin.eldar.org/~problemi/singmast/material.html|archive-date=2017-03-09}}</ref> He also collected books on cartoons, humour, and language.<ref name="twisty"/> In 2013 his book collection was reported to be "nearly 10000 items".<ref name="allsquared1"/> Many of the books were housed in a library added as an extension to Singmaster's study.<ref name="allsquared1"/> He had a huge collection of [[mechanical puzzle]]s, which he started in 2002 containing "perhaps 3000 puzzles, of which about 400 are about Rubik's Cube and its variants".<ref name="twisty"/>

From around 1980 to 1982, he ran his own puzzle company, David Singmaster Ltd, which stocked "over 100 puzzles and books".<ref>{{Cite news|title=For Sale|publisher=New Scientist|url=https://books.google.com/books?id=YWj2f6Rir28C&pg=PA395|date=6 May 1982|page=395}}</ref> However the venture lost him "a fair amount of money" and led to prolonged tax negotiations.<ref name="circ78">{{Cite web|author=David Singmaster|title=Cubic Circular Issues 7 & 8|date=1985|url=http://www.jaapsch.net/puzzles/cubic7.htm}}</ref> He referred to this period of his life as "a massive overdose of cubism".<ref name="circ78"/>

Singmaster was both a puzzle historian and a composer of puzzles, and he described himself as a "metagrobologist". Many of his puzzles appeared in publications such as ''[[BBC Focus]]'', ''[[Games & Puzzles]]'', the ''[[Los Angeles Times]]'', and the ''[[The Daily Telegraph|Weekend Telegraph]]''.<ref name="meta">{{Cite web|url=http://books.telegraph.co.uk/Product/David-Singmaster/Problems-For-Metagrobologists-A-Collection-Of-Puzzles-Wit/19147161|title=Problems For Metagrobologists|publisher=Telegraph bookshop|access-date=4 January 2017}}</ref> He published a collection of his puzzles in his 2016 book ''Problems for Metagrobologists''.<ref name="meta"/> From around 2006 Singmaster was a director at the New York-based [[Conjuring Arts Research Center]], retiring from the position (becoming Director Emeritus) in 2013.<ref>[http://conjuringarts.org/about/board-of-directors/ Board of Directors], Conjuring Arts. Retrieved 4 January 2017</ref> He was instrumental in the re-discovery of one of the world's oldest books on puzzles and [[Magic (illusion)|magic illusions]] when he came across a reference to the work in a 19th-century manuscript. The recovered text, ''De viribus quantitatis'' (''{{langx|en|On The Powers Of Numbers}}'') was penned by [[Luca Pacioli]], a Franciscan friar who lived around 1500.<ref>{{Cite news|url=https://www.theguardian.com/world/2007/apr/10/italy.books|title=And that's renaissance magic ...| newspaper=[[The Guardian]] |date=10 April 2007}}</ref>

==Singmaster's conjecture==
{{Main|Singmaster's conjecture}}
In [[combinatorial number theory]], Singmaster's conjecture states that there is a finite [[upper bound]] on the number of times a number other than 1 can appear in [[Pascal's triangle]]. [[Paul Erdős]] suspected that the conjecture is true, but thought it would probably be very difficult to prove. The [[empirical evidence]] is consistent with the proposition that the smallest upper bound is&nbsp;8.

==Media appearances==
In November 1981, Singmaster appeared on the scifi-themed [[BBC]] puzzle show ''[[The Adventure Game]]''.<ref name="twisty"/> From 1998 to 1999 he was a frequent panelist on the [[BBC Radio 4]] show ''[[Puzzle Panel]]''.<ref name="twisty"/>

==Personal life and death==
Singmaster was married twice, the second time to Deborah in 1972. They had one daughter, Jessica, adopted in 1976.<ref name="twisty"/>

Singmaster died on 13 February 2023, at the age of 84.<ref>{{Cite tweet |user=robeastaway |number=1625836667046076416 |access-date=15 February 2023 |title=I have sad news to report. David Singmaster, the great puzzle collector, historian and Rubik's Cube guru, died on Monday morning after a long illness. He was a unique character with an infectious, child-like enthusiasm for puzzles of every kind. He will be greatly missed. |via=Twitter |language=en |date=15 February 2023}}</ref><ref>{{cite web |title=David Singmaster |url=https://xmau.com/wp/notiziole/2023/02/15/david-singmaster/ |website=Xmau |access-date=16 February 2023 |date=15 February 2023}}</ref>

==Publications==

===Books===
* ''Notes on Rubik's "Magic Cube"'', David Singmaster. [[Enslow Publishers]], 1981. {{ISBN|0-89490-043-9}}
* ''Handbook of Cubik Math'', by David Singmaster and Alexander H. Frey. [[The Lutterworth Press]], 1982. {{ISBN|0-7188-2555-1}}. Publisher's description {{Webarchive|url=https://web.archive.org/web/20170314084959/http://www.lutterworth.com/product_info.php?products_id=1356 |date=14 March 2017 }}
* ''Rubik's Cubic Compendium'', by [[Ernő Rubik]] and four others. Edited with an Introduction and Afterword by David Singmaster. [[Oxford University Press]], 1987. {{ISBN|0-19-853202-4}}
* ''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 Publishers|Black Dog & Leventhal]], 2009. {{ISBN|157912805X}}
* ''Problems for Metagrobologists'', David Singmaster, [[World Scientific Publishing Company]], 23 April 2016. {{ISBN|9814663638}}
* ''Adventures in Recreational Mathematics (in 2 Volumes)''. David Singmaster. World Scientific Publishing Company. (2021) {{ISBN|9789811225642}}

===Reference works===
*''Chronology of Recreational Mathematics'' by David Singmaster. 1996. ([https://web.archive.org/web/20170226070507/http://anduin.eldar.org/~problemi/singmast/recchron.html Available online] at anduin.eldar.org)
*''Chronology of Computing'' by David Singmaster. 2000. ([https://web.archive.org/web/20170223043445/https://www.fbi.h-da.de/fileadmin/vmi/chronologie/ 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. ([http://www.puzzlemuseum.com/singma/singma-index.htm Available online] at the Puzzle Museum)
*''Mathematical Gazetteer of the British Isles'', by David Singmaster. The British Society for the History of Mathematics. 2012. ([https://web.archive.org/web/20120514145358/http://www.dcs.warwick.ac.uk/bshm/gazetteer.html Available online] at the Internet Archive)

===Newsletters===
*''Cubic Circular'' magazine published 1981-5 by David Singmaster ([http://www.jaapsch.net/puzzles/cubic.htm available online at Jaap's Puzzle Page])

===Articles===
*[https://books.google.com/books?id=_n1vr0_RbXoC&pg=PA786 Moral and Mathematical Lessons from a Rubik Cube] by David Singmaster, [[New Scientist]], 23/30 December 1982
*''The Unreasonable Utility of Recreational Mathematics'' by David Singmaster. First European Congress of Mathematics, Paris, July 1992. ([https://web.archive.org/web/20170202012030/http://anduin.eldar.org/~problemi/singmast/ecmutil.html Available online] at anduin.eldar.org)
*''[http://www.mefferts.com/puzzles/jpmsol.html Solution to Meffert's Pyramorphix] {{Webarchive|url=https://web.archive.org/web/20210506005347/http://www.mefferts.com/puzzles/jpmsol.html |date=6 May 2021 }}'', by David Singmaster and Andrew Southern. Meffert's Puzzles, 15 May 1997.

==See also==
* [[wikibooks:How to solve the Rubik's Cube|''How to solve the Rubik's Cube'']] – Wikibook

==References==
{{reflist|2|refs =

<ref name="linkedresources">{{cite web
 |url = http://www.linkedresources.com/teach/rubik/solution.php
 |title = A Step by Step Solution of Rubik's "Magic Cube"
 |author = David Singmaster
 |date = 1980-08-06
 |publisher = Jeffrey W Baumann & LinkedResources
 |archive-url = https://web.archive.org/web/20060304183050/http://www.linkedresources.com/teach/rubik/solution.php
 |archive-date = 2006-03-04
}}</ref>

<ref name="ryanheise-beginner">{{cite web
 |url = http://www.ryanheise.com/cube/beginner.html
 |title = Beginner's Rubik's Cube Solution
 |quote = The general layer-by-layer approach described above is credited to mathematician David Singmaster and was first published in his 1980 book "Notes on Rubik's Magic Cube"
 |author = Ryan Heise
 |archive-url = https://web.archive.org/web/20150926083418/http://www.ryanheise.com/cube/beginner.html
 |archive-date = 2015-09-26
}}</ref>

}}

==External links==
*{{MathGenealogy|id=32103}}
*[http://www.twistypuzzles.com/articles/spotlight-singmaster/ Interview with David Singmaster] at ''Twisty Puzzles''. Originally published c. April 2002 ([https://web.archive.org/web/20020403133052/http://www.zeta.org.au/~sausage/twistymegasite/interview-singmaster.html archive]).
*[https://web.archive.org/web/20170309090104/http://anduin.eldar.org/~problemi/singmast/material.html David Singmaster: List of Available Material]. A compilation of materials by David Singmaster for teaching and his own interests. Last updated in 1996.
*[http://www.calmview2.eu/LSBU/CalmView/Record.aspx?src=CalmView.Catalog&id=DS&pos=1 David Singmaster] archive at [[London South Bank University]].

{{Rubik's Cube}}

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{{DEFAULTSORT:Singmaster, David}}
[[Category:1938 births]]
[[Category:2023 deaths]]
[[Category:Recreational mathematicians]]
[[Category:Mathematics popularizers]]
[[Category:Rubik's Cube]]
[[Category:California Institute of Technology alumni]]
[[Category:University of California, Berkeley alumni]]
[[Category:American expatriates in England]]
[[Category:20th-century British mathematicians]]
[[Category:21st-century British mathematicians]]
[[Category:Academics of London South Bank University]]
[[Category:People from St. Louis County, Missouri]]