Alan was no foreigner to an interest in the physical world. But at this point, what he needed most was a grip on rigour, on intellectual toughness, on something that was absolutely right. While the Cambridge Tripos – half 'pure' and half 'applied' – kept him in touch with science, it was to pure mathematics that he turned as to a friend, to stand against the disappointments of the world.

Alan did not have many other friends – particularly in this first year, in which he still mentally belonged to Sherborne. The King's scholars mostly formed a self-consciously élite group, but he was one of the exceptions. He was a shy boy of nineteen, who had had an education more to do with learning silly poems by rote, or writing formal letters, than with ideas or self-expression. His first friend, and link with the others of the group, was David Champernowne, one of the other two mathematical scholars. He came from the mathematical sixth form of Winchester College, where he had been a scholar, and was more confident socially then Alan. But the two shared a similar 'sense of humour', being alike unimpressed by institutions or traditions. They also shared a hesitancy in speech, although David Champernowne's was more slight than Alan's. It was and remained a rather detached, public school kind of friendship, but important to Alan was that 'Champ' was not shocked by unconventionality. Alan told him about Christopher, showing him a diary that he had kept of his feelings since the death.

They would go to college tutorials together. To begin with, it was a case of Alan catching up, for David Champernowne had been much better taught, and Alan's work was still poorly expressed and muddled. Indeed, his friend 'Champ' had the distinction of publishing a paper11 while still an undergraduate, which was more than Alan did. The two supervisors of mathematics at King's were A.E. Ingham, serious but with a wry humour, the embodiment of mathematical rigour, and Philip Hall, only recently elected a Fellow, under whose shyness lay a particular friendly disposition. Philip Hall liked taking Alan, and found him full of ideas, talking excitedly in his own strange way, in which his voice went up and down in pitch rather than in stress. By January 1932 Alan was able to write in an impressively off-hand way:

I pleased one of my lecturers rather the other day by producing a theorem, which he found had previously only been proved by one Sierpinski, using a rather difficult method. My proof is quite simple so Sierpinski* is scored off.