In this remarkable little book Godfrey Harold (better known as "G.H.") Hardy, perhaps the best mathematician in Britain in the opening decades of the 20th century, writes reflectively and intimately about the merits of his field of scholarly endeavour.

It's rare indeed to glimpse a great scientist in his declining years, and rarer still to absorb - through the observations of a man who contributed so much to it in his own unique way - a something of the dominant tweed-and-pipe-tobacco atmosphere of Cambridge University's Trinity College, as it was between the wars.

Mathematics, Hardy believes, is not viewed as clearly as it might be. While it forms a fundamental tool of all other Earth and physical sciences, in isolation it is poorly understood and is often seen as a series of aimless abstractions.

He balances the everyday maths of the engineer or chemist against the pure maths whose framework was established by the Greeks. To illustrate its "beauty and seriousness" he works through a couple of the better known proofs from Euclid and Pythagoras. But, beautiful or not, he ultimately concludes "the 'real' mathematics of the 'real' mathematicians such as Fermat is almost wholly 'useless'." Little wonder then that the book reveals a little of the satisfaction Hardy derived from an academic life in one of the world's great universities and at the cutting edge of his science.

Apology is a book that can be read on a couple of levels: as a scientific monograph or as a social testament drawn from a period and environment that was exceptionally rich and also produced such literary luminaries as Bertrand Russell and Ludwig Wittgenstein. Simultaneously, the same time and place became a forcing house for so much great work in experimental physics.

As small as it is, Apology, in its current edition, is actually two books in one: its lengthy foreword/biography by novelist Charles Percy (better known as C.P.) Snow, and Hardy's spare and ascetic bones.