Percy Alexander MacMahon
Encyclopedia
Percy Alexander MacMahon (b. 26 September 1854, Sliema
, Malta
– 25 December 1929, Bognor Regis
, England
) was a mathematician
, especially noted in connection with the partitions of numbers and enumerative combinatorics
.
Junior Scholarship to Cheltenham College
, which he attended as a day boy from 10
February 1861 until December 1870. At the age of 16 MacMahon was admitted to the Royal Military Academy, Woolwich and passed out after two years.
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. Officers did not receive discharge papers in the same way as ordinary soldiers, whose documents contain a wealth of interesting information.
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, a bloody adventure which lasted two years and achieved nothing, neither in a military nor a political sense. 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 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 Cayley
, Sylvester
and 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.
in 1890. He received the Royal Society Royal Medal in 1900, the Sylvester Medal
in 1919, and the 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 partitions; see MacMahon Master theorem
. His two volume Combinatory analysis, published in 1915/16, is the first major book in enumerative combinatorics
. MacMahon also did pioneering work in recreational mathematics and patented several successful puzzles.
Sliema
Tas-Sliema is a city located on the northeast coast of Malta. It is a centre for shopping, restaurants and café life. Tas-Sliema is also a major commercial and residential area and houses several of Malta's most modern hotels. Tas-Sliema, which means 'peace, comfort', was once a quiet fishing...
, Malta
Malta
Malta , officially known as the Republic of Malta , is a Southern European country consisting of an archipelago situated in the centre of the Mediterranean, south of Sicily, east of Tunisia and north of Libya, with Gibraltar to the west and Alexandria to the east.Malta covers just over in...
– 25 December 1929, Bognor Regis
Bognor Regis
Bognor Regis is a seaside resort town and civil parish in the Arun district of West Sussex, on the south coast of England. It is south-south-west of London, west of Brighton, and south-east of the city of Chichester. Other nearby towns include Littlehampton east-north-east and Selsey to the...
, England
England
England is a country that is part of the United Kingdom. It shares land borders with Scotland to the north and Wales to the west; the Irish Sea is to the north west, the Celtic Sea to the south west, with the North Sea to the east and the English Channel to the south separating it from continental...
) was a mathematician
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, especially noted in connection with the partitions of numbers and enumerative combinatorics
Enumerative combinatorics
Enumerative combinatorics is an area of combinatorics that deals with the number of ways that certain patterns can be formed. Two examples of this type of problem are counting combinations and counting permutations...
.
Early life
MacMahon attended the Proprietary School in Cheltenham. At the age of 14 he won aJunior Scholarship to Cheltenham College
Cheltenham College
Cheltenham College is a co-educational independent school, located in Cheltenham, Gloucestershire, England.One of the public schools of the Victorian period, it was opened in July 1841. An Anglican foundation, it is known for its classical, military and sporting traditions.The 1893 book Great...
, which he attended as a day boy from 10
February 1861 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 5thBrigade, with the temporary rank of Lieutenant. The Army List showed that in October 1873 he was posted to the 8th Brigade in Lucknow
Lucknow
Lucknow is the capital city of Uttar Pradesh in India. Lucknow is the administrative headquarters of Lucknow District and Lucknow Division....
. 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. Officers did not receive discharge papers in the same way as ordinary soldiers, whose documents contain a wealth of interesting information.
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, a bloody adventure which lasted two years and achieved nothing, neither in a military nor a political sense. 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
Dover
Dover is a town and major ferry port in the home county of Kent, in South East England. It faces France across the narrowest part of the English Channel, and lies south-east of Canterbury; east of Kent's administrative capital Maidstone; and north-east along the coastline from Dungeness and Hastings...
, moving to Sheerness
Sheerness
Sheerness is a town located beside the mouth of the River Medway on the northwest corner of the Isle of Sheppey in north Kent, England. With a population of 12,000 it is the largest town on the island....
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 on
23 March 1882. Here he met Alfred George Greenhill
Alfred George Greenhill
Sir George Greenhill, F.R.S. , was a British mathematician.George Greenhill was educated at Christ's Hospital School and from there he went up to St John's College, Cambridge in 1866. In 1876, Greenhill was appointed professor of mathematics at the Royal Military Academy at Woolwich, London, UK...
, 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 Cayley
Arthur Cayley
Arthur Cayley F.R.S. was a British mathematician. He helped found the modern British school of pure mathematics....
, Sylvester
James Joseph Sylvester
James Joseph Sylvester was an English mathematician. He made fundamental contributions to matrix theory, invariant theory, number theory, partition theory and combinatorics...
and Salmon
George Salmon
The Reverend George Salmon was an Irish mathematician and theologian. His publications in algebraic geometry were widely read in the second half of the 19th century, but he devoted himself mostly to theology for the last forty years of his life...
.’
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 SocietyRoyal Society
The Royal Society of London for Improving Natural Knowledge, known simply as the Royal Society, is a learned society for science, and is possibly the oldest such society in existence. Founded in November 1660, it was granted a Royal Charter by King Charles II as the "Royal Society of London"...
in 1890. He received the Royal Society Royal Medal in 1900, the Sylvester Medal
Sylvester Medal
The Sylvester Medal is a bronze medal awarded by the Royal Society for the encouragement of mathematical research, and accompanied by a £1,000 prize...
in 1919, and the Morgan Medal by the London Mathematical Society
London Mathematical Society
-See also:* American Mathematical Society* Edinburgh Mathematical Society* European Mathematical Society* List of Mathematical Societies* Council for the Mathematical Sciences* BCS-FACS Specialist Group-External links:* * *...
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
Symmetric function
In algebra and in particular in algebraic combinatorics, the ring of symmetric functions, is a specific limit of the rings of symmetric polynomials in n indeterminates, as n goes to infinity...
s and enumeration of plane partitions; see MacMahon Master theorem
MacMahon Master theorem
The MacMahon Master theorem is a result in enumerative combinatorics and linear algebra, both branches of mathematics. It was discovered by Percy MacMahon and proved in his monograph Combinatory analysis...
. His two volume Combinatory analysis, published in 1915/16, is the first major book in enumerative combinatorics
Enumerative combinatorics
Enumerative combinatorics is an area of combinatorics that deals with the number of ways that certain patterns can be formed. Two examples of this type of problem are counting combinations and counting permutations...
. MacMahon also did pioneering work in recreational mathematics and patented several successful puzzles.
External links
- PhD thesis by Dr Paul Garcia,"The life and work of Percy Alexander MacMahon"
- P.A. MacMahon, Combinatory analysis, 2 vols, Cambridge University Press, 1915-16.
- Obituary Notices – Monthly Notices of the Royal Astronomical SocietyMonthly Notices of the Royal Astronomical SocietyMonthly Notices of the Royal Astronomical Society is one of the world's leading scientific journals in astronomy and astrophysics. It has been in continuous existence since 1827 and publishes peer-reviewed letters and papers reporting original research in relevant fields...
90, 373-378. - MacMahon squares – a puzzle.
- MacMahon's Coloured Cubes - a puzzle with coloured cubes