In fact, so much of the book is told from Paul Wittgenstein’s point of view that one suspects it began life as a straightforward biography of him and then broadened as Waugh became fascinated by the Wittgenstein family and their money. Certainly Waugh devotes far more space to Paul than he does to Paul’s siblings, including his more famous younger brother, the philosopher Ludwig Wittgenstein, about whom he is content simply to repeat well-known anecdotes. Where Waugh’s real interest lies is in showing that Paul’s life and personality are as extraordinary and fascinating as Ludwig’s.

Paul Wittgenstein was a concert pianist who seemed, at the outbreak of the First World War, on the brink of a glitteringly successful career. During the war (in which, like Ludwig, he served in the Austrian army), however, Paul lost his right arm in the course of an heroic reconnaissance mission for which he was later decorated. After he was captured by the Russians, he used his time in captivity to learn how to play the piano using just his left hand, and, amazingly, was able, after the war, to resume his career as a concert pianist, playing works specially written for him by the most distinguished composers of the day, including, most notably, Ravel. Paul’s life story has never been told before in such detail, nor with such sympathy. And though he is shown to be at times arrogant, maddeningly obstinate and heavy handed, he emerges from this book as what Waugh clearly believes him to be: a hero.

The book begins with Paul’s debut performance in December 1913 and then, by way of providing the background to that occasion, tells the stories of Paul’s father and his siblings, dwelling in particular on the suicides of Paul’s older brothers, Hans and Rudolf. From a literary point of view, this first section is a tour de force. So many narrative threads are wound together that it is a wonder, and testimony to Waugh’s great gifts as a writer, that the whole thing does not become unravelled. From a historical point of view, Waugh’s approach is cautious; he does not attempt to draw general conclusions and is careful to sift documented fact from hearsay and gossip.

It is only in this first section, however, that the book attempts to give equal weight to the eight siblings of the Wittgenstein family. By the time we get to the First World War, the focus is firmly on Paul. Waugh has an excellent section on the third suicide in the family – that of Kurt, who shot himself, for reasons that remain a mystery, at the end of the war – but of the remaining members of the family, the three sisters, Hermine, Helene and Gretl, he says comparatively little. The story of Gretl’s unsatisfactory marriage to the American Jerome Stonborough, and of her relationships with her unremarkable sons, Thomas and John, is told in probably more detail than it merits, but, even then, it does not occupy much space, and, as for Hermine and Helene, they remain invisible throughout the book until the last section, when they become the cause of great strife among their siblings over the question of how much of the family wealth ought to be given to the Nazis.

What The House of Wittgenstein shows is that, however interesting it might be to follow the creation, spending and losing of a vast fortune, it cannot compare to the fascination exerted by exceptional individuals. This book will be read by those wanting a detailed and historically accurate account of the deal the Wittgensteins made with the Nazis, but it will, one suspects, attract far more readers because of its utterly absorbing account of the military, musical and personal heroics of Paul ­Wittgenstein.