Report on Dan Rutherford's lecture to the Edinburgh Mathematical Society given in the Mathematical Institute, Chambers Street, Edinburgh, on Saturday 1 November 1941. This is taken from the Society's Minute Book.
Dr Rutherford delivered his presidential address, entitled "Substitutional Analysis" - and account of the life-work of the late Alfred Young. Young's principal papers on this subject appeared at intervals between 1900 and 1933, but there was a long gap (1902-1927) in which none appeared; from which the lecturer drew the moral that when a problem defeats us we should keep it at hand, persevere with it, never despair. He then described how quantitative substitutional operators are built from permutations, and - by means of a trivial example - what is meant by a substitutional equation and its solution; and he expounded the elaborate calculus which Young constructed - based on standard tableaux - and applied it to the solution of a particular equation.
In the discussion which followed, Dr Aitken referred to the connections of this subject with the theory of groups, matrices and invariants; and more particularly its connection with determinants, permanents and intermediate expansions which he called substituents. - Professor Born showed how the problems dealt with arose in important physical problems. - Professor Turnbull commented on the great difficulty of reading and comprehending Young's papers, and the hard work which the lecturer had performed in studying it and in preparing a lecture in which it was rendered so intelligible.