Hardy in his thirties held the view that the late years of a mathematician's life were spent most profitably in writing books ; I remember a particular conversation about this, and though we never spoke of the matter again it remained an understanding. The level below his best at which a man is prepared to go on working at full stretch is a matter of temperament ; Hardy made his decision and while of course he continued to publish papers his last years were mostly devoted to books ; whatever has been lost, mathematical literature has greatly gained. All his books gave him some degree of pleasure, but this one, his last, was his favourite. When embarking on it he told me that he believed in its value (as he well might), and also that he looked forward to the task with enthusiasm. He had actually given lectures on the subject at intervals ever since he return to Cambridge in 1931, and had at one time or another lectured on everything in the book except Chapter XIII.
The title holds curious of the past, and of Hardy's past. Abel wrote in 1828 : 'Divergent series are the invention of the devil and it is shameful to base on them any demonstration whatsoever.' In the ensuing period of critical revision they were simply rejected. Then came a time when I was found that something after all could be done about them. This is now matter of course, but in the early years of the century the subject, while in no way mystical or unrigorous, was regarded as sensational, and about the present title, now colourless there hung an aroma of paradox and audacity.
J. E. LITTLEWOOD, Preface