Percy Alexander MacMahon - Revision history

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← Older revision		Revision as of 23:14, 5 December 2022
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	{{Use dmy dates\|date=July ~~2022~~}}		{{Use dmy dates\|date=July 2017}}
	{{Infobox scientist		{{Infobox scientist
	\| name = Percy A. MacMahon		\| name = Percy A. MacMahon
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	== References ==		== References ==
	{{Dual\|source=freespace.virgin.net/p.garcia/\|sourcepath=http://freespace.virgin.net/p.garcia/Ch%202.pdf\|sourcearticle=Life and Work of Major Percy Alexander MacMahon\|date=21 June ~~2022~~}}		{{Dual\|source=freespace.virgin.net/p.garcia/\|sourcepath=http://freespace.virgin.net/p.garcia/Ch%202.pdf\|sourcearticle=Life and Work of Major Percy Alexander MacMahon\|date=21 June 2010}}
	* {{Cite thesis \|degree=PhD \|title=Life and Work of Major Percy Alexander MacMahon \|arxiv=1607.01321 \|last=Garcia \|first=Paul \|year=2006 \|publisher=[[The Open University]] \|bibcode=2016arXiv160701321G }}		* {{Cite thesis \|degree=PhD \|title=Life and Work of Major Percy Alexander MacMahon \|arxiv=1607.01321 \|last=Garcia \|first=Paul \|year=2006 \|publisher=[[The Open University]] \|bibcode=2016arXiv160701321G }}

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← Older revision		Revision as of 23:14, 5 December 2022
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	{{EngvarB\|date=July ~~2017~~}}		{{EngvarB\|date=July 2022}}
	{{Use dmy dates\|date=July ~~2017~~}}		{{Use dmy dates\|date=July 2022}}
	{{Infobox scientist		{{Infobox scientist
	\| name = Percy A. MacMahon		\| name = Percy A. MacMahon
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	\| doctoral_advisor = <!--(or \| doctoral_advisors = )-->		\| doctoral_advisor = <!--(or \| doctoral_advisors = )-->
	\| doctoral_students =		\| doctoral_students =
	\| known_for =		\| known_for = [[MacMahon's master theorem\|His master theorem]]
	\| awards =		\| awards =
	\| signature = Percy signature.jpeg<!--(filename only)-->		\| signature = Percy signature.jpeg<!--(filename only)-->
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	==Early life==		==Early life==

	Percy MacMahon was born in Malta to a British military family. His father was a colonel at the time, retired in the rank of the [[Brigadier (United Kingdom)\|brigadier]].<ref>P.R. ~~Stein, "~~Book Review" of P.A. MacMahon's "Collected Papers"~~, ''~~[[Advances in Mathematics]]~~'', vol.~~ 31:3 (~~1979~~)~~, 350–355.~~</ref>		Percy MacMahon was born in Malta to a British military family. His father was a colonel at the time, retired in the rank of the [[Brigadier (United Kingdom)\|brigadier]].<ref>{{cite journal
			\| last1=Stein \| first1=Paul R.
			\| title=Book Review of P.A. MacMahon's "Collected Papers"
			\| journal=[[Advances in Mathematics]]
			\| volume=31
			\| issue=3
			\| date=1979
			\| pages=350—355
			\| doi=10.1016/0001-8708(79)90050-1 \| doi-access=free}}</ref>
	MacMahon attended the Proprietary School in [[Cheltenham]]. At the age of 14 he won a Junior Scholarship to [[Cheltenham College]], which he attended as a day boy from 10 February 1868 until December 1870. At the age of 16 MacMahon was admitted to the [[Royal Military Academy, Woolwich]] and passed out after two years.		MacMahon attended the Proprietary School in [[Cheltenham]]. At the age of 14 he won a Junior Scholarship to [[Cheltenham College]], which he attended as a day boy from 10 February 1868 until December 1870. At the age of 16 MacMahon was admitted to the [[Royal Military Academy, Woolwich]] and passed out after two years.

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	MacMahon was elected a fellow of the [[Royal Society]] in 1890. He received the [[Royal Society Royal Medal]] in 1900, the [[Sylvester Medal]] in 1919, and the [[LMS De Morgan Medal\|Morgan Medal]] by the [[London Mathematical Society]] in 1923. MacMahon was the President of the London Mathematical Society from 1894 to 1896.		MacMahon was elected a fellow of the [[Royal Society]] in 1890. He received the [[Royal Society Royal Medal]] in 1900, the [[Sylvester Medal]] in 1919, and the [[LMS De Morgan Medal\|Morgan Medal]] by the [[London Mathematical Society]] in 1923. MacMahon was the President of the London Mathematical Society from 1894 to 1896.

	MacMahon is best known for his study of [[symmetric function]]s and enumeration of [[plane partition]]s; see [[MacMahon Master theorem]]. His two volume ''Combinatory analysis'', published in 1915/16,<ref>{{cite journal\|author=Lovitt, W. V.\|title=Review: Percy MacMahon, ''Combinatory Analysis''\|journal=Bull. Amer. Math. Soc.\|year=1916\|volume=23\|issue=2\|pages=97–101\|url=https://www.ams.org/journals/bull/1916-23-02/S0002-9904-1916-02878-3/\|doi=10.1090/s0002-9904-1916-02878-3\|doi-access=free}}</ref> is the first major book in [[enumerative combinatorics]]. MacMahon also did pioneering work in recreational mathematics and patented several successful puzzles. One of the best known puzzles is an [[edge-matching puzzle]] known as "MacMahon Squares" which he published his 1921 treatise ''New Mathematical Pastimes,''<ref>{{Cite book\|last=MacMahon\|first=Percy Alexander\|url=http://archive.org/details/newmathematicalp00macmuoft\|title=New mathematical pastimes\|date=1921\|publisher=Cambridge, University Press\|others=Gerstein - University of Toronto}}</ref> consisting of the unique set of 24 squares that can be made by colouring the edges with one of three colours.<ref>{{Cite web\|last=Steckles\|first=Katie\|date=2012-03-29\|title=MacMahon Squares\|url=https://aperiodical.com/2012/03/macmahon-squares/\|access-date=2020-11-11\|website=The Aperiodical\|language=en}}</ref>		MacMahon is best known for his study of [[symmetric function]]s and enumeration of [[plane partition]]s; see [[MacMahon Master theorem]]. His two volume ''Combinatory analysis'', published in 1915/16,<ref>{{cite journal\|author=Lovitt, W. V.\|title=Review: Percy MacMahon, ''Combinatory Analysis''\|journal=Bull. Amer. Math. Soc.\|year=1916\|volume=23\|issue=2\|pages=97–101\|url=https://www.ams.org/journals/bull/1916-23-02/S0002-9904-1916-02878-3/\|doi=10.1090/s0002-9904-1916-02878-3\|doi-access=free}}</ref> is the first major book in [[enumerative combinatorics]]. MacMahon also did pioneering work in recreational mathematics and patented several successful puzzles. One of the best known puzzles is an [[edge-matching puzzle]] known as [[MacMahon Squares]] which he published his 1921 treatise ''New Mathematical Pastimes,''<ref>{{Cite book\|last=MacMahon\|first=Percy Alexander\|url=http://archive.org/details/newmathematicalp00macmuoft\|title=New mathematical pastimes\|date=1921\|publisher=Cambridge, University Press\|others=Gerstein - University of Toronto}}</ref> consisting of the unique set of 24 squares that can be made by colouring the edges with one of three colours.<ref>{{Cite web\|last=Steckles\|first=Katie\|date=2012-03-29\|title=MacMahon Squares\|url=https://aperiodical.com/2012/03/macmahon-squares/\|access-date=2020-11-11\|website=The Aperiodical\|language=en}}</ref>

	== Tribute ==		== Tribute ==
	A reviewer in "Science Progress in the Twentieth Century", writes:		A reviewer in "Science Progress in the Twentieth Century", writes:
	: ''It is, I believe, a loss to England and to mathematics that Major MacMahon has not directed a great school of research; the gain to the youthful mathematicians of such a leader is obvious; they would have received an impetus which the printed page will only give to a few. Is it not possible also that the quality of work done in such circumstances may not, like mercy, be doubly blest? [..] it is impossible to resist the feeling that there are countries in which mathematical teaching is better organised than it is in England.''<ref>[https://www.jstor.org/stable/43432465?seq=1#page_scan_tab_contents Review of ''Combinatory Analysis''], in J. Murray, Science Progress in the Twentieth Century: A Quarterly Journal of Scientific Work & Thought, Vol. 10, No. 40 (April 1916), pp. 601–606.</ref>		: ''It is, I believe, a loss to England and to mathematics that Major MacMahon has not directed a great school of research; the gain to the youthful mathematicians of such a leader is obvious; they would have received an impetus which the printed page will only give to a few. Is it not possible also that the quality of work done in such circumstances may not, like mercy, be doubly blest? [..] it is impossible to resist the feeling that there are countries in which mathematical teaching is better organised than it is in England.''<ref>[https://www.jstor.org/stable/43432465?seq=1#page_scan_tab_contents Review of ''Combinatory Analysis''], in J. Murray, Science Progress in the Twentieth Century: A Quarterly Journal of Scientific Work & Thought, Vol. 10, No. 40 (April 1916), pp. 601–606.</ref>

	[[Richard P. Stanley]] considers MacMahon as the most influential mathematician in enumerative combinatorics pre-1960.<ref>[https://arxiv.org/pdf/2105.07884.pdf Enumerative and Algebraic Combinatorics in the		[[Richard P. Stanley]] considers MacMahon as the most influential mathematician in enumerative combinatorics pre-1960.<ref>[https://arxiv.org/pdf/2105.07884.pdf Enumerative and Algebraic Combinatorics in the 1960’s and 1970’s], (17 June 2021)</ref>
	1960’s and 1970’s], (17 June 2021)</ref>

	== Portrayal in film ==		== Portrayal in film ==
	In the movie ''[[The Man Who Knew Infinity (film)\|The Man Who Knew Infinity]]'' [[Kevin McNally]] plays as MacMahon. The film accurately depicts the first meeting of MacMahon and [[Srinivasa Ramanujan]], where Ramanujan successfully completes some mathematical calculations.<ref name="Andrews AMS">{{cite journal\|last1=Andrews\|first1=George E.\|author-link1=George Andrews (mathematician)\|title=The Man Who Knew Infinity : A Report on the Movie\|journal=Notices of the AMS\|volume=63\|issue=2\|date=February 2016\|publisher=American Mathematical Society}}</ref> [[Gian-Carlo Rota]] notes in his introduction to Volume I of ~~MacMahon’s~~ Collected Papers: {{block quote\|It would have been fascinating to be present at one of the battles of arithmetical wits at Trinity College, when MacMahon would regularly trounce Ramanujan by the display of superior ability for fast mental calculation (as reported by [[Donald C. Spencer\|D. C. Spencer]], who heard it from [[G. H. Hardy]]). The written accounts of the lives of these characters, however, omit any mention of this episode, since it clashes against our prejudices.<ref name="Andrews AMS"/>}}		In the movie ''[[The Man Who Knew Infinity (film)\|The Man Who Knew Infinity]]'' [[Kevin McNally]] plays as MacMahon. The film accurately depicts the first meeting of MacMahon and [[Srinivasa Ramanujan]], where Ramanujan successfully completes some mathematical calculations.<ref name="Andrews AMS">{{cite journal\|last1=Andrews\|first1=George E.\|author-link1=George Andrews (mathematician)\|title=The Man Who Knew Infinity : A Report on the Movie\|journal=Notices of the AMS\|volume=63\|issue=2\|date=February 2016\|publisher=American Mathematical Society}}</ref> [[Gian-Carlo Rota]] notes in his introduction to Volume I of MacMahon's Collected Papers: {{block quote\|It would have been fascinating to be present at one of the battles of arithmetical wits at Trinity College, when MacMahon would regularly trounce Ramanujan by the display of superior ability for fast mental calculation (as reported by [[Donald C. Spencer\|D. C. Spencer]], who heard it from [[G. H. Hardy]]). The written accounts of the lives of these characters, however, omit any mention of this episode, since it clashes against our prejudices.<ref name="Andrews AMS"/>}}

	==See also==		==See also==
	*[[Cairo pentagonal tiling]], a tiling of the plane by pentagons also called "MacMahon's net"		*[[Cairo pentagonal tiling]], a tiling of the plane by pentagons also called "MacMahon's net"
	*[[Edge-matching puzzle]]
	*[[Eternity II puzzle]]
	*[[TetraVex]]
	*[[Wang tile]]

	== Notes ==		== Notes ==
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	== References ==		== References ==
	{{Dual\|source=freespace.virgin.net/p.garcia/\|sourcepath=http://freespace.virgin.net/p.garcia/Ch%202.pdf\|sourcearticle=Life and Work of Major Percy Alexander MacMahon\|date=21 June ~~2010~~}}		{{Dual\|source=freespace.virgin.net/p.garcia/\|sourcepath=http://freespace.virgin.net/p.garcia/Ch%202.pdf\|sourcearticle=Life and Work of Major Percy Alexander MacMahon\|date=21 June 2022}}
	* {{Cite thesis \|degree=PhD \|title=Life and Work of Major Percy Alexander MacMahon \|arxiv=1607.01321 \|last=Garcia \|first=Paul \|year=2006 \|publisher=[[The Open University]] \|bibcode=2016arXiv160701321G }}		* {{Cite thesis \|degree=PhD \|title=Life and Work of Major Percy Alexander MacMahon \|arxiv=1607.01321 \|last=Garcia \|first=Paul \|year=2006 \|publisher=[[The Open University]] \|bibcode=2016arXiv160701321G }}

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← Older revision		Revision as of 03:29, 25 March 2022
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	\| signature_alt = MacMahon's signature		\| signature_alt = MacMahon's signature
	}}		}}
			'''Percy Alexander MacMahon''' (26 September 1854 – 25 December 1929) was a [[mathematician]], especially noted in connection with the [[integer partition\|partitions of numbers]] and [[enumerative combinatorics]].
	'''Percy Alexander MacMahon''' (26 September 1854 – 25 December 1929) was a [[~~mathematics\|~~mathematician]], especially noted in connection with the [[integer partition\|partitions of numbers]] and [[enumerative combinatorics]].

	==Early life==		==Early life==
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	== References ==		== References ==
	* {{Dual\|source=freespace.virgin.net/p.garcia/\|sourcepath=http://freespace.virgin.net/p.garcia/Ch%202.pdf\|sourcearticle=Life and Work of Major Percy Alexander MacMahon\|date=21 June 2010}}		{{Dual\|source=freespace.virgin.net/p.garcia/\|sourcepath=http://freespace.virgin.net/p.garcia/Ch%202.pdf\|sourcearticle=Life and Work of Major Percy Alexander MacMahon\|date=21 June 2010}}
	* {{Cite thesis \|degree=PhD \|title=Life and Work of Major Percy Alexander MacMahon \|arxiv=1607.01321 \|last=Garcia \|first=Paul \|year=2006 \|publisher=[[The Open University]] \|bibcode=2016arXiv160701321G }}		* {{Cite thesis \|degree=PhD \|title=Life and Work of Major Percy Alexander MacMahon \|arxiv=1607.01321 \|last=Garcia \|first=Paul \|year=2006 \|publisher=[[The Open University]] \|bibcode=2016arXiv160701321G }}

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	[[Category:De Morgan Medallists]]		[[Category:De Morgan Medallists]]
	[[Category:Presidents of the Royal Astronomical Society]]		[[Category:Presidents of the Royal Astronomical Society]]
			[[Category:Maltese military personnel]]
			[[Category:Academics of the Royal Military Academy, Woolwich]]

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{{EngvarB|date=July 2017}}
{{Use dmy dates|date=July 2017}}
{{Infobox scientist
| name = Percy A. MacMahon
| image = Percy MacMahon.jpg
| image_size = 200px
| image_upright =
| alt =
| caption = Percy Alexander MacMahon
| birth_date = {{birth date |1854|9|26|df=yes}}
| birth_place = [[Sliema]], [[British Malta]]
| death_date = {{death date and age |1929|12|25 |1854|9|26|df=yes}}
| death_place = [[Bognor Regis]], England
| death_cause =
| nationality = [[United Kingdom|British]]
| fields = [[Mathematics]]
| workplaces =
| alma_mater =
| thesis_title = 
| thesis_url = 
| thesis_year = 
| doctoral_advisor = 
| doctoral_students =
| known_for =
| awards =
| signature = Percy signature.jpeg
| signature_alt = MacMahon's signature
}}

'''Percy Alexander MacMahon''' (26 September 1854 – 25 December 1929) was a [[mathematics|mathematician]], especially noted in connection with the [[integer partition|partitions of numbers]] and [[enumerative combinatorics]].

==Early life==

Percy MacMahon was born in Malta to a British military family. His father was a colonel at the time, retired in the rank of the [[Brigadier (United Kingdom)|brigadier]].<ref>P.R. Stein, "Book Review" of P.A. MacMahon's "Collected Papers", ''[[Advances in Mathematics]]'', vol. 31:3 (1979), 350–355.</ref>
MacMahon attended the Proprietary School in [[Cheltenham]]. At the age of 14 he won a Junior Scholarship to [[Cheltenham College]], which he attended as a day boy from 10 February 1868 until December 1870. At the age of 16 MacMahon was admitted to the [[Royal Military Academy, Woolwich]] and passed out after two years.

==Military career==

On 12 March 1873, MacMahon was posted to [[Madras]], India, with the 1st Battery 5th
Brigade, with the temporary rank of lieutenant. The Army List showed that in October 1873 he was posted to the 8th Brigade in [[Lucknow]]. MacMahon's final posting was to the No. 1 Mountain Battery with the Punjab Frontier Force at Kohat on the North West Frontier. He was appointed Second Subaltern on 26 January and joined the Battery on 25 February 1877. In the ''Historical Record of the No. 1 (Kohat) Mountain Battery, Punjab Frontier Force'' it is recorded that he was sent on sick leave to Muree (or Maree), a town north of Kohat on the banks of the Indus river, on 9 August 1877. On 22 December 1877 he started 18 months leave on a medical certificate granted under GGO number 1144. The nature of his illness is unknown.

This period of sick leave was one of the most significant occurrences in MacMahon's life. Had he remained in India he would undoubtedly have been caught up in [[Roberts's War]] against the Afghans. In early 1878 MacMahon returned to England and the sequence of events began which led to him becoming a mathematician rather than a soldier. The Army List records a transfer to the 3rd Brigade in Newbridge at the beginning of 1878, and then shows MacMahon as 'supernumerary' from May 1878 until March 1879.

In January 1879 MacMahon was posted to the 9th Brigade in [[Dover]], moving to [[Sheerness]] in 1880. In the same year he enrolled in the Advanced Class for Artillery Officers at Woolwich. This was a two-year course covering technical subjects and a foreign language. Successful completion of the course resulted in the award of the letters "p.a.c" (passed advanced class) after MacMahon's name in the Army List.

After he passed the Advanced Course and had been promoted to the rank of captain on 29 October 1881, MacMahon took up a post as instructor at the [[Royal Military Academy, Woolwich|Royal Military Academy]] on 23 March 1882. Here he met [[Alfred George Greenhill]], professor of mathematics at the
Royal Artillery College. [[Joseph Larmor]], in a letter to ''The Times'' published after MacMahon's death, wrote, 'The young Captain threw himself with indomitable zeal and insight into the great problems of the rising edifice of algebraic forms, as was being developed by [[Arthur Cayley|Cayley]], [[James Joseph Sylvester|Sylvester]] and [[George Salmon|Salmon]].’

In 1891 MacMahon took up a new post as military instructor in electricity at the Royal Artillery College, Woolwich. Some sources (e.g. his three obituarists) have said that this post was 'professor of physics', but this is not correct, as Greenhill held that post until his own retirement.

MacMahon retired from the military in 1898.

==Mathematical career==
MacMahon was elected a fellow of the [[Royal Society]] in 1890. He received the [[Royal Society Royal Medal]] in 1900, the [[Sylvester Medal]] in 1919, and the [[LMS De Morgan Medal|Morgan Medal]] by the [[London Mathematical Society]] in 1923. MacMahon was the President of the London Mathematical Society from 1894 to 1896.

MacMahon is best known for his study of [[symmetric function]]s and enumeration of [[plane partition]]s; see [[MacMahon Master theorem]]. His two volume ''Combinatory analysis'', published in 1915/16,<ref>{{cite journal|author=Lovitt, W. V.|title=Review: Percy MacMahon, ''Combinatory Analysis''|journal=Bull. Amer. Math. Soc.|year=1916|volume=23|issue=2|pages=97–101|url=https://www.ams.org/journals/bull/1916-23-02/S0002-9904-1916-02878-3/|doi=10.1090/s0002-9904-1916-02878-3|doi-access=free}}</ref> is the first major book in [[enumerative combinatorics]]. MacMahon also did pioneering work in recreational mathematics and patented several successful puzzles. One of the best known puzzles is an [[edge-matching puzzle]] known as "MacMahon Squares" which he published his 1921 treatise ''New Mathematical Pastimes,''<ref>{{Cite book|last=MacMahon|first=Percy Alexander|url=http://archive.org/details/newmathematicalp00macmuoft|title=New mathematical pastimes|date=1921|publisher=Cambridge, University Press|others=Gerstein - University of Toronto}}</ref> consisting of the unique set of 24 squares that can be made by colouring the edges with one of three colours.<ref>{{Cite web|last=Steckles|first=Katie|date=2012-03-29|title=MacMahon Squares|url=https://aperiodical.com/2012/03/macmahon-squares/|access-date=2020-11-11|website=The Aperiodical|language=en}}</ref>
== Tribute ==
A reviewer in "Science Progress in the Twentieth Century", writes:
: ''It is, I believe, a loss to England and to mathematics that Major MacMahon has not directed a great school of research; the gain to the youthful mathematicians of such a leader is obvious; they would have received an impetus which the printed page will only give to a few. Is it not possible also that the quality of work done in such circumstances may not, like mercy, be doubly blest? [..] it is impossible to resist the feeling that there are countries in which mathematical teaching is better organised than it is in England.''<ref>[https://www.jstor.org/stable/43432465?seq=1#page_scan_tab_contents Review of ''Combinatory Analysis''], in J. Murray, Science Progress in the Twentieth Century: A Quarterly Journal of Scientific Work & Thought, Vol. 10, No. 40 (April 1916), pp. 601–606.</ref>

[[Richard P. Stanley]] considers MacMahon as the most influential mathematician in enumerative combinatorics pre-1960.<ref>[https://arxiv.org/pdf/2105.07884.pdf Enumerative and Algebraic Combinatorics in the
1960’s and 1970’s], (17 June 2021)</ref>

== Portrayal in film ==
In the movie ''[[The Man Who Knew Infinity (film)|The Man Who Knew Infinity]]'' [[Kevin McNally]] plays as MacMahon. The film accurately depicts the first meeting of MacMahon and [[Srinivasa Ramanujan]], where Ramanujan successfully completes some mathematical calculations.<ref name="Andrews AMS">{{cite journal|last1=Andrews|first1=George E.|author-link1=George Andrews (mathematician)|title=The Man Who Knew Infinity : A Report on the Movie|journal=Notices of the AMS|volume=63|issue=2|date=February 2016|publisher=American Mathematical Society}}</ref> [[Gian-Carlo Rota]] notes in his introduction to Volume I of MacMahon’s Collected Papers: {{block quote|It would have been fascinating to be present at one of the battles of arithmetical wits at Trinity College, when MacMahon would regularly trounce Ramanujan by the display of superior ability for fast mental calculation (as reported by [[Donald C. Spencer|D. C. Spencer]], who heard it from [[G. H. Hardy]]). The written accounts of the lives of these characters, however, omit any mention of this episode, since it clashes against our prejudices.<ref name="Andrews AMS"/>}}

==See also==
*[[Cairo pentagonal tiling]], a tiling of the plane by pentagons also called "MacMahon's net"
*[[Edge-matching puzzle]]
*[[Eternity II puzzle]]
*[[TetraVex]]
*[[Wang tile]]

== Notes ==
{{reflist}}

== References ==
* {{Dual|source=freespace.virgin.net/p.garcia/|sourcepath=http://freespace.virgin.net/p.garcia/Ch%202.pdf|sourcearticle=Life and Work of Major Percy Alexander MacMahon|date=21 June 2010}}
* {{Cite thesis |degree=PhD |title=Life and Work of Major Percy Alexander MacMahon |arxiv=1607.01321 |last=Garcia |first=Paul |year=2006 |publisher=[[The Open University]] |bibcode=2016arXiv160701321G }}

==External links==
{{wikisource author}}
*PhD thesis by Dr Paul Garcia,"[https://arxiv.org/abs/1607.01321]"
*{{MacTutor Biography|id=MacMahon}}
* P.A. MacMahon, ''[http://www.hti.umich.edu/cgi/t/text/text-idx?c=umhistmath;idno=ABU9009 Combinatory analysis]'', 2 vols, Cambridge University Press, 1915–16.
* [http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?db_key=AST&bibcode=1930MNRAS..90Q.373.&letter=Q&classic=YES&defaultprint=YES&whole_paper=NO&page=373&epage=378&send=Send+PDF&filetype=.pdf Obituary Notices] – ''[[Monthly Notices of the Royal Astronomical Society]]'' '''90''', 373–378.
*[http://www.mathematische-basteleien.de/macmahon.htm MacMahon's Coloured Cubes] – a puzzle with coloured cubes

{{De Morgan Medallists}}
{{Authority control}}

{{DEFAULTSORT:Macmahon, Percy Alexander}}
[[Category:19th-century English mathematicians]]
[[Category:20th-century English mathematicians]]
[[Category:British Indian Army officers]]
[[Category:1854 births]]
[[Category:1929 deaths]]
[[Category:Combinatorialists]]
[[Category:People educated at Cheltenham College]]
[[Category:Graduates of the Royal Military Academy, Woolwich]]
[[Category:Fellows of the Royal Society]]
[[Category:Royal Medal winners]]
[[Category:De Morgan Medallists]]
[[Category:Presidents of the Royal Astronomical Society]]