A Treatise on Universal Algebra, with Applications

Abstract

THIS work affords a sad illustration of the spirit of lawlessness which has invaded one of our ancient Universities since the time when she rashly began to tamper with her Tripos Regulations. In the good old times two and two were four, and two straight lines in a plane would meet if produced, or, if not, they were parallel; but it would seem that we have changed all that. Here is a large treatise, issued with the approval of the Cambridge authorities, which appears to set every rule and principle of algebra and geometry at defiance. Sometimes ba is the same thing as ab, sometimes it isn't; a + a a may be 2a or a according to circumstances; straight lines in a plane may be produced to an infinite distance without meeting, yet not be parallel; and the sum of the angles of a triangle appears to be capable of assuming any value that suits the author's convenience. It is a pity that we have not had an opportunity of showing the book to some country rector who graduated with mathematical honours, say, forty years ago; it is easy to imagine his feelings of surprise, bewilderment, possibly of indignation, as he turned over the pages and encountered such a variety of paradoxical statements and unfamiliar formulæ.

A Treatise on Universal Algebra, with Applications.

By Alfred North Whitehead Vol. 1. Pp. xxvi + 586. (Cambridge: at the University Press, 1898.)