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The Life and Work of Major Percy Alexander Macmahon Paul Garcia

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The life and work of Major Percy Alexander MacMahon PhD Thesis by Dr Paul Garcia History of Mathematics Thesis submitted to the Open University in fulfilment of the Degree of Doctor of Philosophy The life and work of Major Percy Alexander MacMahon Paul Garcia B.A. (Hons), MSc (Mathematics), MSc (Information and Knowledge Technology) May 2006 1 The life and work of Major Percy Alexander MacMahon PhD Thesis by Dr Paul Garcia Abstract This thesis describes the life and work of the mathematician Major Percy Alexander MacMahon (1854 - 1929). His early life as a soldier in the Royal Artillery and events which led to him embarking on a career in mathematical research and teaching are dealt with in the first two chapters. Succeeding chapters explain the work in invariant theory and partition theory which brought him to the attention of the British mathematical community and eventually resulted in a Fellowship of the Royal Society, the presidency of the London Mathematical Society, and the award of three prestigious mathematical medals and four honorary doctorates. The development and importance of his recreational mathematical work is traced and discussed. MacMahon’s career in the Civil Service as Deputy Warden of the Standards at the Board of Trade is also described. Throughout the thesis, his involvement with the British Association for the Advancement of Science and other scientific organisations is highlighted. The thesis also examines possible reasons why MacMahon’s work, held in very high regard at the time, did not lead to the lasting fame accorded to some of his contemporaries. Details of his personal and social life are included to give a picture of MacMahon as a real person working hard to succeed in a difficult context. Published work from this thesis. Some of the biographical details discovered during the work for this thesis were used to create an entry for MacMahon in the Dictionary of Nineteenth Century British Scientists, published by Thoemmes in 2004. Biographical details and a summary of MacMahon’s recreational work were used as the introduction to a reprint of MacMahon’s 1921 book New Mathematical Pastimes, published by Tarquin in 2004. Some of the material on recreational mathematics was used in two articles published in the Mathematical Association’s Mathematics in School magazine: The mathematical pastimes of Major Percy Alexander MacMahon: Part 1 - slab stacking, Mathematics in School 34(2) (2005) 23 - 25, and Part 2 - triangles and beyond, Mathematics in School 34(4) (2005) 20 - 22; and an article in the magazine Infinity published by Tarquin: From puzzles to tiling patterns, Infinity, 2005(2) (2005) 28 - 32. 2 The life and work of Major Percy Alexander MacMahon PhD Thesis by Dr Paul Garcia History of Mathematics Thesis submitted to the Open University in fulfilment of the Degree of Doctor of Philosophy The life and work of Major Percy Alexander MacMahon Paul Garcia B.A. (Hons), MSc (Mathematics), MSc (Information and Knowledge Technology) April 2006 3 The life and work of Major Percy Alexander MacMahon PhD Thesis by Dr Paul Garcia 4 The life and work of Major Percy Alexander MacMahon PhD Thesis by Dr Paul Garcia Acknowledgements “Remember, it’s supposed to be fun” Richard Feynman, quoted in Some time with Feynman, L. Mlodinow, 2003 I have pieced together this story of MacMahon’s life and work from the writings of his three obituarists (H. F. Baker, H. H. Turner and A. R. Forsyth), notices of his death published in The Times, and information from various other sources, most notably St John's College, Cambridge, Winchester College, The Royal Military Academy (Sandhurst Collection), the Royal Irish Academy, Aberdeen University, St. Andrew's University, Trinity College, Dublin, the Royal Society, the Royal Astronomical Society, and the London Mathematical Society. The librarians at Cambridge University Library, the Bodleian Library, the British Library, the Public Record Office at Kew, the Family Record Office in Islington, Claire Harrington of the Glasgow City Council Library Service, and Maria Martinez, a genealogist in Monte Vista, Colorado, have all provided invaluable help and pointed me at material I might otherwise have taken decades to discover. I would also like to thank all the people who have helped and shown great kindness and patience over the 7 years I have been working on MacMahon. In particular, George Andrews (the editor of MacMahon's Collected Papers); Anthony Unwin; the Humphreys family (Charles & Rosie Humphreys, Mick Humphreys, and Clare Middleton, all descendants of MacMahon’s brothers); the late John Fauvel for his encouragement and advice in my first year of study; my supervisors, Robin Wilson for all the time and advice he has lavished on me, and June Barrow-Green for many interesting and helpful conversations. Special thanks are due to Professor Margaret Farrell for details of the Mayblox puzzle, and Professor Robert N. Andersen for donating his aunt’s Mayblox puzzle to my collection of MacMahon memorabilia , and to Kev Stenning of Rapido UK who helped me make a copy of the bronze bust of MacMahon. Finally, I would like to thank my wife Mary, for putting up with this obsession for so many years. 5 The life and work of Major Percy Alexander MacMahon PhD Thesis by Dr Paul Garcia Contents Chapter 1 Introduction................................................................................... 9 Scope of the thesis........................................................................................... 9 Content.......................................................................................................... 11 Sources.......................................................................................................... 13 Chapter 2 Early years and India 1854 - 1881................................................... 14 Early education............................................................................................... 14 Royal Military Academy, Woolwich................................................................... 15 India............................................................................................................. 20 Chapter 3 Woolwich 1881 - 1889..................................................................... 23 Instructor at RMA Woolwich............................................................................ 23 Teaching........................................................................................................ 26 MacMahon’s mathematical work........................................................................ 28 Symmetric functions............................................................................ 28 Invariant Theory.................................................................................. 29 Partition theory................................................................................... 37 Personal events............................................................................................... 40 Chapter 4 Royal Artillery College 1890 - 1898.................................................. 42 Royal Artillery College.................................................................................... 42 The Royal Society........................................................................................... 43 The London Mathematical Society...................................................................... 44 1896 Presidential address to the London Mathematical Society.................... 44 The Royal Astronomical Society........................................................................ 50 Honorary degree.............................................................................................. 51 Savilian Professorship, Oxford........................................................................... 52 Mathematical work.......................................................................................... 55 Partition Theory.................................................................................. 55 The Master Theorem............................................................................. 62 Recreational mathematics...................................................................... 62 Puzzle Patents..................................................................................... 63 Magic Squares.................................................................................... 69 Probability......................................................................................... 70 Retirement..................................................................................................... 73 Chapter 5 London 1898 - 1906....................................................................... 75 Royal Medal...................................................................................... 75 Winchester College............................................................................. 75 British Association for the Advancement of Science.............................................. 76 Views on education............................................................................. 78 Other meetings................................................................................... 82 Evidence of Esteem......................................................................................... 83 Cambridge......................................................................................... 83 St John’s College..............................................................................
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