Percy Alexander Macmahon (1854-1929) was something of an anomaly in the mathematical fraternity of his time. Much of his life was spent in the British military manning the outposts of Empire and teaching in military schools rather than in the established academic preserves. just so, he marched to his own drumbeat in his mathematical researches, and his work was often far ahead of its time. Reviewing Volume I, Combinatorics (1978), in his Scientific American feature column, Martin Gardner noted that "it is remarkable how often results of MacMahon's are rediscovered by mathematicians who until now have not had access to his voluminous writings." Some of the fifty-six papers in Volume II relate to combinatorics, but most of them investigate quite distinct areas and reveal a different side of MacMahons mind and mathematical originality. They are grouped into chapters that cover symmetric functions of several systems of quantities, determinants, repeating patterns, multiplicative number theory, applications (to analysis, astronomy, geometry, and physics), and invariant theory. A final chapter collects expository papers on such subjects as the state of knowledge of combinatory analysis and magic squares "and other problems upon a chess board." The editor has provided an introduction and commentary for each of these chapters that bring historical perspective to the papers and relate them to contemporary developments. Summaries of the papers have also been provided.
This volume of MacMahons collected papers is the twenty-fourth and final volume in The MIT Press Mathematicians of Our Time series, edited by Gian-Carlo Rota.