Percy Alexander MacMahon
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Percy Alexander MacMahon (b. 26 September 1854, Sliema, Malta – 25 December 1929, Bognor Regis, England) was a mathematician, especially noted in connection with the partition of numbers and analysis.
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[edit] Early Life
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 1861 until December 1870. At the age of 16 MacMahon was admitted to the Royal Military Academy, Woolwich and passed out after two years.
[edit] 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. 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.
[edit] 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 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 functions and enumeration of plane partitions. 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. His total output on recreational topics comprised seven papers and one book, New Mathematical Pastimes, published in 1921 (and reprinted in 2004 as part of his 150th birthday celebration). In addition to his papers, MacMahon was granted three patents for puzzles. The first patent for which he applied (number 21,118) was a puzzle comprising nine wooden blocks linked by flexible tapes to form a chain. The length of the links was to be such that the blocks could be formed into a stack in 452764 different ways. A design applied to the edges of the blocks would have to be reconstructed by finding the correct stacking. This patent was accepted on 8 October 1892, but there are no records to indicate whether the puzzle was ever manufactured commercially.
In 1892, MacMahon and Major J. R. Jocelyn jointly applied for two patents. The first of these, patent number 3927, was for Appliances to be used in playing a new class of games. The provisional specification was submitted on 29 February 1892, and the patent was granted on 28 January 1893. The patent described equilateral triangular pieces divided into three compartments, numbered or coloured in a manner analogous to dominoes. The rules of two different edge-matching games to be played by two players on specially marked boards were described in the patent in some detail, and a suggestion was made for a puzzle where the pieces were to be fitted together to form a hexagon with (say) a single colour around the perimeter, this latter idea was to be expanded upon in greater detail in New Mathematical Pastimes some 29 years later. It is not known whether any sets of pieces were manufactured or sold.
The second joint patent application was made on 2 May 1892. It described how a set of 27 coloured cubes could be constructed using three colours, the puzzle being to assemble the set into a larger cube with a uniform colour on each external face and matching between the internal faces. The existence of a set of 30 cubes that could be made with six colours was also mentioned, and the puzzle described was to select two ‘associated’ cubes, with the same pairs of colours on opposite faces, and then to locate amongst the remaining 28 cubes a set of sixteen cubes in which none of those opposites occurs. These sixteen can then be assembled into two larger copies of the two associated cubes, where internal faces must also match. A puzzle called Mayblox was manufactured by R. Journet and Co. of London (best known for their glass-topped dexterity puzzles) with the legend “Invented by Major P. A. MacMahon F. R. S.” on the box. This version of the puzzle, described by Margaret A. Farrell in the Journal of Recreational Mathematics in 1969, asked the solver to construct a large cube from 8 smaller cubes as in MacMahon’s puzzle, but without the benefit of the target cube.
[edit] External links
- PhD thesis by Dr Paul Garcia,"The life and work of Percy Alexander MacMahon"
- O'Connor, John J. & Robertson, Edmund F., “Percy Alexander MacMahon”, MacTutor History of Mathematics archive
- P.A. MacMahon, Combinatory analysis, 2 vols, Cambridge University Press, 1915-16.
- Obituary Notices – Monthly Notices of the Royal Astronomical Society 90, 373-378.
- MacMahon squares – a puzzle.
- MacMahon's Coloured Cubes - a puzzle with coloured cubes
