It was Mr. Littlewood (I believe) who remarked that "every positive integer was one of his personal friends." - John Edensor Littlewood

G. H. Hardy said he thought on paper ('with my pen'). He wrote everything out (in his invariably admirable handwriting), scrapping and copying whenever a page got into a mess. When I am thinking about a difficult problem everything goes onto a single page - all over the place with odd equations, diagrams, rings. However appalling the mess, I feel that to scrap this page would somehow break threads in the unconscious.

It is possible for a mathematician to be 'too strong' for a given occasion. He forces through, where another might be driven to a different, and possibly more fruitful, approach. (So a rock climber might force a dreadful crack, instead of finding a subtle and delicate route.)

The derivates theorem enables one to reject certain parts of the thing one wants to tend to zero. One day I was playing round with this, and a ghost of an idea entered my mind of making r, the number of differentiations, large. At that moment the spring cleaning that was in progress reached the room I was working in, and there was nothing for it but to go walking for 2 hours, in pouring rain. The problem seethed violently in my mind: the material was disordered and cluttered up with irrelevant complications cleared away in the final version, and the 'idea' was vague and elusive. Finally I stopped, in the rain, gazing blankly for minutes on end over a little bridge into a stream (near Kenwith wood), and presently a flooding certainty came into my mind that the thing was done. The 40 minutes before I got back and could verify were none the less tense.