Page:An introduction to Combinatory analysis (Percy MacMahon, 1920, IA Introductiontoco00macmrich).djvu/11



HIS little book is intended to be an Introduction to the two volumes of Combinatory Analysis which were published by the Cambridge University Press in 1915–16. It has appeared to me to be necessary from the circumstance that some of my mathematical critics have found that the presentation of the general problem through the medium of the algebra of symmetric functions is difficult or troublesome reading. I was reminded that the great Euler wrote a famous algebra which was addressed to his man-servant, and had the object of anticipating and removing every conceivable difficulty and obscurity. Posterity gives the verdict that, in accomplishing this he was wonderfully successful.

From a general point of view it seems to me there is advantage on the one hand in explaining a complicated if not difficult matter to an untrained mind, and on the other in propounding a simple theory for the benefit of those who are highly trained. In this way certain vantage points may be reached which are not commonly attainable by the usual plan of addressing students in a style which is in proportion to their attainments. The advantage which has been spoken of accrues both to the writer and to the reader. The writer for example is likely to be led to points of view of whose existence he was previously unaware or aware of only sub-consciously. In attempting what is here proposed it is inevitable that much must be written that will appear to the reader to be self-evident and unworthy of statement. The intention is by a succession of such statements to arrive at facts which, by a quicker progression, would be difficult or troublesome to grasp. It is in analogy with a succession of likenesses of a person taken at small intervals of time such that little or no difference can be detected between any two successive pictures but between pictures taken at