Such Silver Currents: The Story of William and Lucy Clifford 1845-1929 by M. Chisholm, Lutterworth Press (www.lutterworth.com), pp 208, £17.50, ISBN 0718830172.

William Kingdon Clifford died at the age of 33 in 1879. He left behind a mathematical legacy in geometry and algebra that lives on both under his own name (as in Clifford algebras, Clifford’s theorem for Riemann surfaces, Clifford-Klein space forms etc.) and also those of others (the Hopf fibration and the Dirac operator). Even that remarkable output formed but a part of his short life’s work for, after seven years in Cambridge spent evolving from an Anglo-Catholic into a radical humanist, he engaged in series after series of public lectures where he advanced his newfound philosophy with missionary zeal, preaching that “truth and right are to be got at by free enquiry and the love of our comrades for their own sakes and nobody else’s”. Thus he trod from the Dialectical Society to the Republican Society, the Royal Institution to the Sunday Lecture Society … and he also made room, or at least so one supposes, for the London Mathematical Society where for a period he was a member of Council. Clerk Maxwell, writing a reference for Clifford for a Chair at UCL, perhaps best summed up his works, saying that “.. they tend not to the elaboration of abstruse theorems by ingenious calculations, but to the elucidation of scientific ideas by the concentration on them of clear and steady thought”. And it seems he tried to live his life that way too.

The book under review traces out the significant parts of this mayfly existence, but does so in parallel with that of his wife, Lucy Clifford, who outlived him by 50 years. They married in 1875; he died only four years later, but she never remarried. Yet paradoxically her eternal widowhood became a way of life which led her to become very close to an extraordinary number of literary figures who clearly enjoyed her company immensely. William used to sign off his letters to her with an agnostic “be free” instead of “goodbye” and in a sense that is what she tried to be, while never shaking off her devoted memories of him. She earned her keep (for despite a subscription for her and her daughters after William’s death she needed to work) as a literary correspondent for The Standard and a gossip columnist for The Athenaeum (which later became the New Statesman). Both Cliffords had earlier moved in literary circles, in particular through the acquaintance of George Eliot, but now as a critic, a hostess and an author in her own right, Lucy formed friendships with Rudyard Kipling, Bernard Shaw, Henry James, Oliver Wendell Holmes and many others, all carefully described in the chapters of the book. She formed enemies too – clearly Virginia Woolf could not stand her, and regarded her merely as a gossip, and in old age as a relic from another century.

The author of Such Silver Currents has no such aversion to Lucy Clifford, and the production of the book is obviously a labour of love. Her sympathy with the main character makes her occasionally less than objective, but she has put in an enormous amount of work to produce this volume and paints a believable picture of the talented couple. In fact, the book grew out of a series of presentations of the world of the two Cliffords given in 1995/96 by Monty and Roy Chisholm beginning in the University of Kent and going onto the Isaac Newton Institute and elsewhere. These were lectures on the mathematical, literary and historical aspects of their lives, accompanied by an exhibition of photographs. Those who participated in the meetings, as I did, learned a great deal from them. I personally was unaware of the breadth of Clifford’s interests until I read the Collected Works.

The book deals with the mathematics in two ways. The first account is influenced by Roy Chisholm’s liking for Clifford analysis, an attempt to construct a higher-dimensional version of complex analysis, but the chapter also discusses in some detail Clifford’s geometrical thinking about the possible curved structure of space. The second is a more personal reflection by Roger Penrose which includes the role of Clifford parallels in twistor theory and his own diagrammatic notation for invariants which Clifford seems to have invented 75 years earlier. But intriguingly, Penrose’s favourite is the pure plane geometry of Clifford chains – the incidence properties of the circles that pass through triples of points of intersection of a configuration of lines. This result still has a modern charm and the interested reader can see an interactive version on the web (www.cut-the-knot.org/Curriculum/Geometry/ CliffordChain.shtml) where a nice proof of the theorem by Morley (which seems to owe more to Lagrangian interpolation than geometry) can be found.

Lucy Clifford’s work unfortunately has had a less enduring appeal. While her plays, novels and short stories were often at the time controversial in content they now hardly merit a footnote in the history of Victorian literature. It is Lucy’s life which dominates the book, but it is William’s work that survives. Does that say something about mathematics or about us mathematicians?

Nigel Hitchin University of Oxford