That is why A Mathematician’s Apology is, if read with the textual attention it deserves, a book of haunting sadness. Yes, it is witty and sharp with intellectual high spirits: yes, the crystalline clarity and candour are still there: yes, it is the testament of a creative artist.

Hardy was, in Newton’s phrase, ‘in the prime of his age for invention’, and this came in his early forties, unusually late for a mathematician.

Now Flowers was a decent enough fellow (so far as ‘Alan St Aubyn’ could draw one), but even my unsophisticated mind refused to accept him as clever. If he could do these things, why not I?

What we do may be small, but it has a certain character of permanence; and to have produced anything of the slightest permanent interest, whether it be a copy of verses or a geometrical theorem, is to have done something utterly beyond the powers of the vast majority of men. And—

As I had plenty of opportunities to realize in the future, Hardy had no faith in intuitions or impressions, his own or anyone else’s. The only way to assess someone’s knowledge, in Hardy’s view, was to examine him.

high thinking of one kind is always likely to affect high thinking of another

It is quite true that most people can do nothing well. If so, it matters very little what career they choose, and there is really nothing more to say about it. It

There is something else, though, at which he was clearly superior to Einstein or Rutherford or any other great genius: and that is at turning any work of the intellect, major or minor or sheer play, into a work of art. It was that gift above all, I think, which made him, almost without realizing it, purvey such intellectual delight.

Henry James’s notebooks,