*Lectures and Essays*is given at THIS LINK.

Karl Pearson completed and edited William Clifford's *Common Sense of the Exact Sciences*. We give an extract from Pearson's Introduction at THIS LINK.

**1. Lectures and Essays (1879).**

**1.1. Review by: A Ephraim.**

*Revue Philosophique de la France et de l'Étranger*

**9**(1880), 450- 463.

These remarkable metaphysical and moral studies are the work of an English mathematician, W K Clifford, whose premature death removed him from both science and philosophy. Some words of biography will suffice to acquaint us with our author. William Kingdom Clifford was born at Exeter on May 4, 1845. After beginning his studies in his hometown, he entered in 1860 to King's College, London; there, he showed a particular aptitude for mathematics without neglecting the other branches of human knowledge. In 1863, he came to the University of Cambridge. It seems that his independent intellect has always led him to follow personal research rather than the regular course of studies. Nevertheless he ranked second in the final Mathematics Examinations (second Wrangler in the Tripos) in 1867. Fellow of Trinity College in 1868, professor of applied mathematics at the University College London in 1871, he was elected a member of the Royal Society in June 1874. He was already known for outstanding papers published in the most famous English journals. Inquisitive and open to all the new ideas, he studied, expounded, and discussed with the same ardour, work on non-Euclidean geometry and the works of Spencer. The theory of evolution and natural selection fascinated him; he had accepted it with enthusiasm, but not blindly and never gave up the rights of his equally gifted intelligence to criticism and invention. In 1874, he felt the first attacks of the chest disease that would prevail. After he unsuccessfully sought health cures in Spain, Algeria, and Madeira, he died in March 1879. "Here was a man," we are told by his biographer M F Pollock, "who utterly dismissed from his thoughts, as being unprofitable or worse, all speculations on a future or unseen world; a man to whom life was holy and precious, a thing not to be despised, but used with joyfulness; a soul full of life and light, ever longing for activity, ever counting what was achieved as not worthy to be reckoned in comparison with what was left to do. And this is the witness of his ending, that as never man loved life more, so never man feared death less. He fully realized the great words of Spinoza, which were often in his mind and on his lips, Homo liber de nulla re minus quam de morte cogitât [A free man thinks of death least of all things]." It would be unfair to judge him solely on the works he left. One cannot ask of a man to give all his measure in thirty-three years. But we must congratulate his friends Messrs Leslie Stephen and F Pollock who have carefully collected his scattered writings in English journals; they assembled two volumes entitled 'Lectures and Essays', preceded by a moving introduction from which we have borrowed the short biographical information that we have given.

**2.**The Common Sense of the Exact Sciences (1946).

**2.1. Review by: Jane Oppenheimer.**

*The Quarterly Review of Biology*

**32**(1) (1957), 57.

Clifford's *Common Sense of the Exact Sciences* was edited, completed, and first published posthumously by Karl Pearson in 1885. Alfred A Knopf issued in 1946 a new edition edited by James R Newman; the present *Dover* edition is an unabridged and unaltered republication of the latter. It includes Pearson's preface to the first edition, Newman's introduction to the 1946 edition, and a preface to the latter prepared by Bertrand Russell. Enlightening and stimulating as these various commentaries prove, the primary significance of the volume must attach to Clifford's own chapters, which treat number, space, quantity, position, and motion with both originality and exceptional lucidity. The book was first conceived during a period when mathematics was in a dramatic stage of metamorphosis. It is of value to professional mathematicians, philosophers, and historians in its revivication of the author's role in that movement. It is of equal interest to other less overtly involved in mathematics for the consummate and uncommon clarity with which it presents concepts common to the thinking of every scientist. Both Knopf and *Dover* are to be thanked for making this inexpensive and eminently readable edition easily accessible to old and new students of science alike.

**2.2. Review by: T A A Broadbent.**

*The Mathematical Gazette* **31** (294) (1947), 119-120.

No doubt many of us at some time or other have come on this book of Clifford's and, whatever our mathematical level at the time, must have been astonished and delighted by the superb clarity and easy mastery of that long out-of-print volume. Mathematics has changed and grown since 1885, but so often on lines which Clifford foresaw that sixty years have not unduly dimmed the freshness and value of his writings. Like Riemann, whom he so much admired, Clifford was both versatile and original in thought; like Riemann, too, disease brought a brilliant life to an untimely end. His life has been recounted in a memoir by Sir Frederick Pollock, prefixed to Clifford's Lectures and Essays, and in it there is one passage, too well known and too lengthy to quote in full, from which a sentence or two may be extracted, describing an ideal which all teachers must admire, though most of us will do so despairingly. Pollock found trouble in grasping Ivory's theorem, but had his difficulties cleared away while talking with Clifford: "he appeared not to be working out a question, but simply telling what he saw... real and evident facts which only required to be seen ... the only strange thing was that anybody should fail to see it in the same way."

**2.3. Review by: N A Court.**

*The Scientific Monthly* **63** (3) (1946), 242.

With nearly all more or less educated people, even arithmetic is a "bookish" subject, let alone algebra or geometry. Before we have the time and the opportunity to learn about these matters from actual experience - by "common sense" - the school pounces upon us with its textbooks. Further learning becomes clothed in all the paraphernalia of the erudite, with all its forbidding symbolisms, its learned vocabulary, and all its - goodness-knows-by-whom - revealed truths and rules. It is therefore very refreshing to find someone who reminds us that in spite of all these learned trappings the basic rules of arithmetic and algebra are nothing more and nothing else but "common sense"; especially if this is done in as simple and as convincing a manner as in the book under review. The study of space begins with the assertion: "Geometry is a physical science." By now we have grown quite accustomed to this point of view. But in the eighties of the last century, when the "ideal world of geometry" was still excellent currency, this was a bold statement. Clifford develops the basic notions of geometry, using solids as his point of departure. He anticipated some of the ideas which later became popular owing to the writings of Henri Poincaré. The author does not limit the scope of his discussion to the mathematical equipment that is the common possession of most readers. He tries to add to this store of knowledge and to widen the mathematical horizon of those who are willing to make the effort of following him in his entertaining presentation.

**2.4. Review by: John Lighton Synge.**

*Amer. Math. Monthly* **54** (1) (1947), 54-55.

The original work as planned by Clifford was to have been entitled *The First Principles of the Mathematical Sciences Explained to the Non-Mathematical*. This would have been a clumsy title, but more descriptive of its nature than *The Common Sense of the Exact Sciences*, the title finally adopted in accordance with a preference expressed by Clifford shortly before his death in 1879. He left the manuscript unfinished. The labour of revision and completion was begun by R C Rowe and finished by Karl Pearson. The first edition appeared in 1885, and this was followed by a second and a third edition, but the book has now been a long time out of print, so that the present edition is very welcome. It is essentially a reproduction of the third edition, the notable additions being a Preface by Bertrand Russell and an Introduction by the Editor, James R Newman. Every teacher of mathematics, particularly elementary mathematics, should read this Preface. I would like to quote the whole of it, because it would make a better review of the book than I can write. However, the following quotation must suffice: "A taste for mathematics, like a taste for music, can be generated in some people, but not in others .... Pupils who have not an unusually strong natural bent towards mathematics are led to hate the subject by two shortcomings on the part of their teachers. The first is that mathematics is not exhibited as the basis of all our scientific knowledge, both theoretical and practical: the pupil is not convincingly shown that what we can understand of the world, and what we can do with machines, we can understand and do in virtue of mathematics. The second defect is that the difficulties are not approached gradually, as they should be, and are not minimized by being connected with easily apprehended central principles, so that the edifice of mathematics is made to look like a collection of detached hovels rather than a single temple embodying a unitary plan. It is especially in regard to this second defect that Clifford's book is valuable." ...

There are five chapters with the following titles: Number, Space, Quantity, Position, Motion. These titles give a rough idea of the scope of the book. There is a good deal of material open to criticism on various grounds, but there runs through the whole work a thread of something which, if not pure gold, looks very like it. Would that a similar thread ran through the textbooks of to-day! Writers of textbooks should ponder the fact that killing the interest of students is an easy task; its stimulation is a much more subtle thing, and they should not be ashamed to learn from a master of exposition in this field. If the textbook writer is an active research mathematician, as Clifford was, he would do well to investigate Clifford's secret of the interest-grasping simile and the complete absence of talking-down to his readers.

**2.5. Review by: Gairdner Moment.**

*The Quarterly Review of Biology* **22** (1) (1947), 59.

Undoubtedly one of the seminal books of the nineteenth century, it belongs alongside of Poincaré's 'Foundations' and Karl Pearson's 'Grammar of Science'. Although more limited in scope than either, it cuts every whit as deep. It should be added that Clifford's is an extremely sophisticated and mathematical type of common sense.