Percy Alexander MacMahon (26 September 1854 – 25 December 1929) was a

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

, especially noted in connection with the partitions of numbers and

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. More generally, given an infin ...

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 Brigadier is a military rank, the seniority of which depends on the country. In some countries, it is a senior rank above colonel, equivalent to a brigadier general or commodore, typically commanding a brigade of several thousand soldiers. ...

. MacMahon attended the Proprietary School in

Cheltenham Cheltenham (), also known as Cheltenham Spa, is a spa town and borough on the edge of the Cotswolds in the county of Gloucestershire, England. Cheltenham became known as a health and holiday spa town resort, following the discovery of mineral s ...

. At the age of 14 he won a Junior Scholarship to

Cheltenham College ("Work Conquers All") , established = , closed = , type = Public school Independent School Day and Boarding School , religion = Church of England , president = , head_label = Head , head = Nicola Hugget ...

, 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 The Royal Military Academy (RMA) at Woolwich, in south-east London, was a British Army military academy for the training of commissioned officers of the Royal Artillery and Royal Engineers. It later also trained officers of the Royal Corps of S ...

and passed out after two years.

Military career

On 12 March 1873, MacMahon was posted to

Madras Chennai (, ), formerly known as Madras ( the official name until 1996), is the capital city of Tamil Nadu, the southernmost Indian state. The largest city of the state in area and population, Chennai is located on the Coromandel Coast of th ...

, 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 Lucknow (, ) is the capital and the largest city of the Indian state of Uttar Pradesh and it is also the second largest urban agglomeration in Uttar Pradesh. Lucknow is the administrative headquarters of the eponymous district and divis ...

. 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 Dover () is a town and major ferry port in Kent, South East England. It faces France across the Strait of Dover, the narrowest part of the English Channel at from Cap Gris Nez in France. It lies south-east of Canterbury and east of Maids ...

, moving to

Sheerness Sheerness () is a town and civil parish beside the mouth of the River Medway on the north-west corner of the Isle of Sheppey in north Kent, England. With a population of 11,938, it is the second largest town on the island after the nearby tow ...

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 Sir Alfred George Greenhill, FRS FRAeS (29 November 1847 in London – 10 February 1927 in London), was a British mathematician. George Greenhill was educated at Christ's Hospital School and from there he went to St John's College, Cambridge ...

, professor of mathematics at the Royal Artillery College.

Joseph Larmor Sir Joseph Larmor (11 July 1857 – 19 May 1942) was an Irish and British physicist and mathematician who made breakthroughs in the understanding of electricity, dynamics, thermodynamics, and the electron theory of matter. His most influen ...

, 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 Sylvester or Silvester is a name derived from the Latin adjective ''silvestris'' meaning "wooded" or "wild", which derives from the noun ''silva'' meaning "woodland". Classical Latin spells this with ''i''. In Classical Latin, ''y'' represented ...

and

Salmon Salmon () is the common name for several commercially important species of euryhaline ray-finned fish from the family Salmonidae, which are native to tributaries of the North Atlantic (genus '' Salmo'') and North Pacific (genus '' Onco ...

.’ 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 The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...

in 1890. He received the Royal Society Royal Medal in 1900, the

Sylvester Medal The Sylvester Medal is a bronze medal awarded by the Royal Society (London) for the encouragement of mathematical research, and accompanied by a £1,000 prize. It was named in honour of James Joseph Sylvester, the Savilian Professor of Geometry a ...

in 1919, and the Morgan Medal by the

London Mathematical Society The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh Mathematical ...

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 In mathematics, a function of n variables is symmetric if its value is the same no matter the order of its arguments. For example, a function f\left(x_1,x_2\right) of two arguments is a symmetric function if and only if f\left(x_1,x_2\right) = f ...

s and enumeration of

plane partition In mathematics and especially in combinatorics, a plane partition is a two-dimensional array of nonnegative integers \pi_ (with positive integer indices ''i'' and ''j'') that is nonincreasing in both indices. This means that : \pi_ \ge \pi_ and \ ...

s; see

MacMahon Master theorem In mathematics, MacMahon's master theorem (MMT) is a result in enumerative combinatorics and linear algebra. It was discovered by Percy MacMahon and proved in his monograph ''Combinatory analysis'' (1916). It is often used to derive binomial i ...

. His two volume ''Combinatory analysis'', published in 1915/16, is the first major book in

. MacMahon also did pioneering work in recreational mathematics and patented several successful puzzles. One of the best known puzzles is an

edge-matching puzzle An edge-matching puzzle is a type of tiling puzzle involving tiling an area with (typically regular) polygons whose edges are distinguished with colours or patterns, in such a way that the edges of adjacent tiles match. Edge-matching puzzles are k ...

known as MacMahon Squares which he published his 1921 treatise ''New Mathematical Pastimes,'' consisting of the unique set of 24 squares that can be made by colouring the edges with one of three colours.

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.'' Richard P. Stanley considers MacMahon as the most influential mathematician in enumerative combinatorics pre-1960.Enumerative and Algebraic Combinatorics in the 1960’s and 1970’s
(17 June 2021)

Portrayal in film

In the movie ''

The Man Who Knew Infinity ''The Man Who Knew Infinity'' is a 2015 British biographical drama film about the Indian mathematician Srinivasa Ramanujan, based on the 1991 book of the same name by Robert Kanigel. The film stars Dev Patel as Srinivasa Ramanujan, a real-life ...

Kevin McNally Kevin Robert McNally (born 27 April 1956) is an English actor and writer. He is known for portraying Joshamee Gibbs in the ''Pirates of the Caribbean'' film series. Early life Born in Bristol, McNally spent his early years in Birmingham, atte ...

plays as MacMahon. The film accurately depicts the first meeting of MacMahon and

Srinivasa Ramanujan Srinivasa Ramanujan (; born Srinivasa Ramanujan Aiyangar, ; 22 December 188726 April 1920) was an Indian mathematician. Though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical analysis, ...

, where Ramanujan successfully completes some mathematical calculations.

Gian-Carlo Rota Gian-Carlo Rota (April 27, 1932 – April 18, 1999) was an Italian-American mathematician and philosopher. He spent most of his career at the Massachusetts Institute of Technology, where he worked in combinatorics, functional analysis, proba ...

notes in his introduction to Volume I of MacMahon's Collected Papers:

Notes

References

External links

*PhD thesis by Dr Paul Garcia

* * P.A. MacMahon,
Combinatory analysis
', 2 vols, Cambridge University Press, 1915–16.
Obituary Notices
– ''

Monthly Notices of the Royal Astronomical Society ''Monthly Notices of the Royal Astronomical Society'' (MNRAS) is a peer-reviewed scientific journal covering research in astronomy and astrophysics. It has been in continuous existence since 1827 and publishes letters and papers reporting orig ...

'' 90, 373–378.
MacMahon's Coloured Cubes
– a puzzle with coloured cubes {{DEFAULTSORT:Macmahon, Percy Alexander 19th-century English mathematicians 20th-century English mathematicians British Indian Army officers 1854 births 1929 deaths Combinatorialists People educated at Cheltenham College Graduates of the Royal Military Academy, Woolwich Fellows of the Royal Society Royal Medal winners De Morgan Medallists Presidents of the Royal Astronomical Society Maltese military personnel Academics of the Royal Military Academy, Woolwich