Continuierliche Gruppen—Scheffers (Leipzig, 1893), p. 665.
[1753]. Universal Algebra has been looked on with some suspicion by many mathematicians, as being without intrinsic mathematical interest and as being comparatively useless as an engine of investigation.... But it may be shown that Universal Algebra has the same claim to be a serious subject of mathematical study as any other branch of mathematics.—Whitehead, A. N.
Universal Algebra (Cambridge, 1898), Preface, p. vi.
[1754]. [Function] theory was, in effect, founded by Cauchy; but, outside his own investigations, it at first made slow and hesitating progress. At the present day, its fundamental ideas may be said almost to govern most departments of the analysis of continuous quantity. On many of them, it has shed a completely new light; it has educed relations between them before unknown. It may be doubted whether any subject is at the present day so richly endowed with variety of method and fertility of resource; its activity is prodigious, and no less remarkable than its activity is its freshness.—Forsyth, A. R.
Presidential Address British Association for the Advancement of Science (1897); Nature, Vol. 56, p. 378.
[1755]. Let me mention one other contribution which this theory [Theory of functions of a complex variable] has made to knowledge lying somewhat outside our track. During the rigorous revision to which the foundations of the theory have been subjected in its re-establishment by Weierstrass, new ideas as regards number and continuity have been introduced. With him and with others influenced by him, there has thence sprung a new theory of higher arithmetic; and with its growth, much has concurrently been effected in the elucidation of the general notions of number and quantity.... It thus appears to be the fact that, as with Plato, or Descartes, or Leibnitz, or Kant, the activity of pure mathematics is again lending some assistance to the better comprehension of those notions of time, space, number, quantity, which underlie a philosophical conception of the universe.—Forsyth, A. R.
Presidential Address British Association for the Advancement of Science (1897); Nature, Vol. 56, p. 378.