To vanishing-points give proper care—
Enumerate, reciprocate,
Nor forget to delineate,
Traverse the plane from end to end,
And theta-functions freely spend.
[1935]. The student should avoid founding results upon divergent series, as the question of their legitimacy is disputed upon grounds to which no answer commanding anything like general assent has yet been given. But they may be used as means of discovery, provided that their results be verified by other means before they are considered as established.—De Morgan, A.
Trigonometry and Double Algebra (London, 1849), p. 55.
[1936]. There is nothing now which ever gives me any thought or care in algebra except divergent series, which I cannot follow the French in rejecting.—De Morgan, A.
Graves’ Life of W. R. Hamilton (New York, 1882-1889), Vol. 3, p. 249.
[1937]. It is a strange vicissitude of our science that these [divergent] series which early in the century were supposed to be banished once and for all from rigorous mathematics should at its close be knocking at the door for readmission.—Pierpont, J.