Percy A. MacMahon | |
|---|---|
 Percy Alexander MacMahon | |
| Born | (1854-09-26)26 September 1854 |
| Died | 25 December 1929(1929-12-25) (aged 75) Bognor Regis, England |
| Known for | MacMahon's master theorem |
| Scientific career | |
| Fields | Mathematics |
| Signature | |
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Percy Alexander MacMahonFRS (26 September 1854 – 25 December 1929) was an Englishmathematician, especially noted in connection with thepartitions of numbers andenumerative combinatorics.
Percy MacMahon was born in Malta to a British military family. His father was a colonel at the time, retired in the rank of thebrigadier.[1]MacMahon attended the Proprietary School inCheltenham. At the age of 14 he won a Junior Scholarship toCheltenham College, which he attended as a day boy from 10 February 1868 until December 1870. At the age of 16 MacMahon was admitted to theRoyal Military Academy, Woolwich and passed out after two years.
On 12 March 1873, MacMahon was posted toMadras, 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 inLucknow. 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 theHistorical 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 inRoberts'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 inDover, moving toSheerness 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 theRoyal Military Academy on 23 March 1882. Here he metAlfred George Greenhill, professor of mathematics at theRoyal Artillery College.Joseph Larmor, in a letter toThe 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 byCayley,Sylvester andSalmon.’
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.
MacMahon was elected a fellow of theRoyal Society in 1890. He received theRoyal Society Royal Medal in 1900, theSylvester Medal in 1919, and theMorgan Medal by theLondon Mathematical Society in 1923. MacMahon was the President of the London Mathematical Society from 1894 to 1896.
MacMahon is best known for his study ofsymmetric functions and enumeration ofplane partitions; seeMacMahon Master theorem. His two volumeCombinatory analysis, published in 1915/16,[2] is the first major book inenumerative combinatorics.
MacMahon also did pioneering work in recreational mathematics and developed several successfulpuzzle games. His 1921 treatiseNew Mathematical Pastimes[3] extended the linearedge-matching puzzle game ofdominoes to two- and three-dimensional shapes includingequilateral triangles (a set of 24, with each edge coloured one of four possible colours was patented by MacMahon in 1892; similar triangle-tile domino games have since been published commercially, includingContack [1939],Triominoes [1965], andTrioker [1970]),[4] squares (MacMahon Squares; a set of 24 unique patterns results from colouring each of the four edges one of three possible colours),[5] and cubes (a set of 30 is made by assigning each face one of six possible colours without repeating a colour).[6]
A reviewer in "Science Progress in the Twentieth Century", writes:
Richard P. Stanley considers MacMahon as the most influential mathematician in enumerative combinatorics pre-1960.[8]
In the movieThe Man Who Knew InfinityKevin McNally plays as MacMahon. The film accurately depicts the first meeting of MacMahon andSrinivasa Ramanujan, where Ramanujan successfully completes some mathematical calculations.[9]Gian-Carlo Rota notes in his introduction to Volume I of MacMahon's Collected Papers:
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 byD. C. Spencer, who heard it fromG. H. Hardy). The written accounts of the lives of these characters, however, omit any mention of this episode, since it clashes against our prejudices.[9]
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