CHAPTER LII
MATHEMATICS
There is no single book in the English language, save the Britannica, in which the whole body of mathematical knowledge is examined and classified with special reference to the inter-relation of its various parts and to the results obtained in the neighboring domains of physics, chemistry, and engineering. Text-books necessarily have a somewhat narrow purpose, namely to teach the student how to solve problems in a single given field; wide views over the surrounding country can, therefore, seldom be afforded. The Britannica, however, does for English readers, what the Encyclopädie der Mathematischen Wissenchaften does for German, and more, in that in the Britannica the shadowy borderlands are illuminated and the roads cleared which connect the mathematical and the experimental sciences. In fact if anyone possessed every mathematical text-book that had ever been published, he would still find the articles full of suggestion to him, for in them the whole subject has been presented, in all its complex bearings, logically and as a whole.
History
It is nearly 4,000 years since a mathematician was last deified in the person of Amenophis, and as far as can be ascertained only one other of his calling ever received this honour, and he also was an Egyptian who had entered into his godship a full thousand years earlier (Vol. 9, p. 46). To the ancient Egyptians mathematics owes the first fragmentary ideas of arithmetic and mensuration, but little else, for despite their amazing mechanical achievements very little record of purely mathematical knowledge has come down from them. It was the Greeks, starting with Thales (600 B.C.), who really created the sciences of geometry and numbers. To them we owe the great abstract ideas which dominate the science. The Greek period lasted till the capture of Alexandria by the Mohammedans, A.D. 640, at which time the Arabian school took shape, and to it we owe the development of algebra (al-jebr-wa’l-muqubala, which means the transposition and removal [of terms of an equation]). With the Renaissance the centre of scientific research shifted to Western Europe and from then on the boundaries of mathematical knowledge were rapidly extended, till to-day the subject is the common ground on which all the physical sciences meet. The student is referred to the article Mathematics (Vol. 17, p. 878), by A. N. Whitehead, fellow and senior lecturer in mathematics, Trinity College, Cambridge, for a brilliant exposition of the foundations of the subject.
The professed mathematician will, of course, not need any set guide to his reading, but it may be well to point out one or two articles which he will find especially worthy of his attention.
Leading Articles
The article Probability, (Vol. 22, p. 376), by Professor Edgeworth, author of Mathematical Psychics, and numerous papers on the calculus of probabilities, gives, to the best of our belief, the only statement of the whole problem in the English language. That on Algebraic Forms (Vol. 1, p. 620), by Major Macmahon, former president of the London Mathematical Society, includes a number of results not previously published. The article Elasticity (Vol. 9, p. 141), by A. E. H. Love, professor of natural philosophy in the University of Oxford, embodies the experience of a distinguished mathematician who has made this subject the object of his special study for years. Sir George Darwin (son of Charles Darwin) in the article Tide (Vol. 26, p. 938) summed up the results of his life’s work. The new electrical theory of the properties of Matter (Vol. 17, p. 891) is discussed by Sir J. J. Thomson, professor of physics, Cambridge, who has done more than anyone else to develop it. There are many other valuable articles, e.g., Geometry, Axioms (Vol. 11, p. 730), and Geometry, Non-Euclidean (Vol. 11, p. 724), by A. N. Whitehead; Units, Dimensions of (Vol. 27, p. 736), by Professor J. A. Fleming; Energy and Energetics (Vol. 9, p. 398 and p. 390), by Sir Joseph Larmor; Groups, by Prof. Burnside, author of Theory of Groups of Finite Order. Articles which will be found highly useful to the engineer are Mensuration (Vol. 18, p. 134); Earth, Figure of (Vol. 8, p. 801); Geodesy (Vol. 11, p. 607); Strength of Materials (Vol. 25, p. 1007).
Leading Contributors
The mathematician will at once recognize the peculiar fitness of the contributors to deal with the subjects allotted to them, and this fitness is the more noticeable in the following list, arranged in alphabetical order, which names and briefly describes the distinguished mathematicians who have collaborated in the Britannica, and indicates the principal articles written by each.
H. F. Baker, Fellow and Lecturer of St. John’s College, Cambridge. Cayley Lecturer in Mathematics in the University. Author of Abel’s Theory and the Allied Theory, etc.: